Magnetic fields in star-forming regions: a multi

Transcrição

UNIVERSITAT DE BARCELONA
Institut de Ciències de l’Espai (CSIC–IEEC)
Magnetic fields in star-forming
regions: a multi-wavelength
approach
Memòria presentada per
Felipe de Oliveira Alves
per optar al grau de
Doctor en Ciències Fı́siques
Barcelona, 2011
Programa de Doctorat d’Astronomia i Meteorologia
Memòria presentada per Felipe de Oliveira Alves per optar al grau de Doctor en
Ciències Fı́siques
Director de la tesi
Dr. Josep Miquel Girart
Just like a star across my sky
Just like an angel off the page
You have appeared to my life
Feel like I’ll never be the same
Just like a song in my heart
Just like oil on my hands
Honour to love you
Like a Star
Corinne Bailey Rae
Dedico este trabalho aos meus pais Antônio e Cidinha
à minha irmã Marina
à minha esposa Anna Laura
e às duas estrelinhas que nasceram para iluminar minha vida:
meus sobrinhos Hézrom e Enzo...
Acknowledgments
This work could not have progressed without the support of all the people who were by my
side during its whole development. Hereby I would like to express my deep gratitude to them in
their native languages, when possible.
• Estic molt agraı̈t al meu supervisor de tesi, Dr. Josep Miquel Girart, que m’ha transmès gran
part del seu enorme coneixement amb molta paciència i respecte. Puc dir amb seguretat que
tot el que vaig aprendre en radioastronomia li dec principalment a ell. També li estic molt
agraı̈t per donar-me l’oportunitat d’estar en contacte amb distints grups de recerca de tot el
món, cosa que m’ha motivat i preparat per al futur com astrònom professional. Finalment
li agraeixo el fet d’introduir-me i apropar-me a la cultura catalana i de fer-me prendre una
gran estima per ella.
• Gostaria de agradecer ao Professor Gabriel Franco, não somente pelos ensinamentos transferidos, mas também pela grande amizade de longos anos. Seu apoio foi fundamental para
alcançar esta etapa. Muito obrigado também pelos vários momentos de descontração, que
tornaram mais agradáveis os momentos de seriedade.
• Volia agrair a tot el grup de formació estel.lar del Departament d’Astronomia i Meteorologia
de la Universitat de Barcelona (DAM-UB), de l’Institut de Ciències de l’Espai (IEEC-CSIC)
i de la Universitat Politècnica de Catalunya (UPC): Robert Estalella, José Marı́a Torrelles,
Rosario López, Àngels Riera, Aina Palau, Álvaro Sánchez-Monge, Pau Frau, Gemma Busquet, Josep Maria Masqué i Marco Padovani. També estic agraı̈t a la Inma Sepúlveda,
Maite Beltrán i l’Òscar Morata, que segueixen col.laborant activament amb el grup, tot i la
distància. Moltes gràcies per l’intercanvi d’idees que m’ha resultat sempre molt interessant
i, principalment, motivador. Gràcies per l’ajuda que mai m’ha estat denegada, per la bona
atmosfera de les reunions i gràcies, sobretot, per l’amistat. Espero mantenir la col.laboració
amb aquest grup que, sense cap dubte, és molt competent.
• I would like to thank Dr. Qizhou Zhang, from the Harvard-Smithsonian Center for Astrophysics, for his support on the reduction and analysis of submillimeter data. Our weekly
scientific meetings were of invaluable help. I also wish to thank all colleagues that I met
iii
iv
Chapter 0. Acknowledgments
during my visit in 2008. The impressive scientific atmosphere of the CfA was strongly
encouraging for the progress of this thesis.
• I would like to thank also Dr. Ramprasad Rao for his support on reduction and interpretation
of submillimeter polarization data. The two weeks in Hawaii were simply unforgettable
not only for the natural beauty of the Big Island, but also for the friendly ambient in the
Submillimeter Array. Mahalo!
• I would like to thank Dra. Shih-Ping Lai, from the Institute of Astronomy of the National
Tsing Hua University in Hsinchu (Taiwan), for her support on the molecular line data reduction and modeling of polarization maps. Thanks for the intensive help. Still, the funny
moments with Tien Hao, Chao-Ling and Tao-Chung in the laboratory will be never forgotten. Xiè xiè.
• I would like to specially thank Dr. Wouter Vlemmings, from the Argelander Institut für
Astronomie in Bonn (Germany), for his collaboration in the project of water masers. His
always available help and dedication were crucial for the successfulness of this work. Also,
his guidance on my search of future positions will be always remembered. In addition, I
wish to thank all colleagues from the AIfA and the Max-Planck of Bonn, who made my
visit a much better! Special hug to Arturo, my mexican brother.
• Me gustarı́a agradecer al Dr. José Acosta Pulido, del Instituto de Astrofı́sica de Canarias,
por su importante soporte en la reducción de los datos en infrarrojo. Gracias por su intensa dedicación al proyecto y envidiable paciencia. Aprovecho para saludar también a los
grandes amigos que hice durante esta estancia: Luis, Ariadna, Raúl, Maritza, Alejandro,
Jonay y, en especial, Adal, un gran amigo, compañero de piso y colega de profesión. En fin,
mi hermano Guanche!
• I’d like to thank the staff involved with the facilities that I used to obtain the scientific
results of this thesis. So, thanks to the “behind-scenes” people on the Observatório do Pico
dos Dias (LNA/MCT, Itajubá, Brazil), William Herschel Telescope (ING, Canary Islands,
Spain), Submillimeter Array (SMA, Hawaii, USA) and Very Large Array (VLA, Socorro,
USA).
• Agradeço aos meus pais que, mesmo longe, sempre me mandaram muita energia positiva
para concluir este processo. Seu amor incondicional foi certamente um dos pilares que me
deram força para seguir. Agradeço também à minha irmã Marina, ao Armando e aos meus
dois sobrinhos Hézrom e Enzo que compartilharam dessa energia. Amo vocês!
• Quero agradecer à minha querida esposa Anna Laura por seu apoio incondicional ao longo
destes 4 anos. Obrigado por todo amor, carinho e paciência que me foram dados de forma
inesgotável. Com certeza, esta etapa foi vivida com muito mais alegria estando ao seu lado.
Te amo muito!
v
• Me gustarı́a agradecer a los compañeros del ICE-IEEC y, en particular, del “cyber”, por la
amistad y apoyo. Gracias a Jacobo, Nataly, Jonatan, Enrique, Elsa, Daniela, Jorge Jiménez,
Jorge Carretero, Martin, Carlos, Diego, Ane, Ana, Anais, Santi, Antonio, Alina y Josep
por los momentos de diversión y por hacer la vida diaria en el “cyber” más alegre. Gracias
también a los investigadores y profesores por su constante atención cuando se les necesitaba.
Finalmente, gracias a la Isabel Moltó, Pilar Montes, Eva Notario, Josefa Lopez y Maria Paz
Moreno por su constante soporte administrativo.
• Agradezco a los amigos del DAM Andreu, Héctor, Pere, Nadia, Dani, Rosa, Carmen, Javi
M., Javi C., Laura, Albert, Jordi, Sinue, Aidan y Maria por la amistad y por hacer los dı́as
de reunión más divertidos.
• Agradezco también al Ministerio de Ciencia e Innovación y al Consejo Superior de Investigaciones Cientı́ficas por la financiación recibida durante el transcurso de esta tesis.
• Agradeço aos amigos brasileiros que moram em Barcelona (e também aos que estão longe)
e que sempre me deram muita força para seguir adiante com esta etapa. Muito obrigado!
• Finalmente, agradeço a Deus.
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Stages of formation of a protostar . . . . . . . . . . . . . . . . . . .
Example magnetized collapse model and observational data . . . . . .
General case of a polarized light . . . . . . . . . . . . . . . . . . . .
Paramagnetic dissipation - Davis & Greenstein mechanism . . . . . .
Scheme of generation of polarized radiation . . . . . . . . . . . . . .
Examples of optical polarization maps of molecular clouds . . . . . .
Examples of scattered near-infrared polarization vectors . . . . . . . .
Comparison of distance measurements via polarization and extinction
Observational relation between B and the volume density . . . . . . .
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3
4
5
8
9
11
12
13
16
2.1
2.2
2.3
2.4
Polarization map of the Pipe nebula as obtained from Hipparcos stars
Distribution of the observed position angles for the Hipparcos stars . .
Parallax-polarization diagram for the Pipe nebula . . . . . . . . . . .
Polarization of background stars in the same field of Hipparcos stars .
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26
27
29
31
3.1
3.2
Mean optical polarization map of the Pipe nebula . . . . . . . . . . . . . . . . .
Polarimetric properties of the Pipe nebula . . . . . . . . . . . . . . . . . . . . .
38
40
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
Observed line-of-sights for the optical polarimetry in the Pipe nebula . .
Distribution of polarimetric errors with respect to the magnitude . . . .
Distribution of P and θPA of the polarization vectors in the Pipe nebula .
Anti-correlation between mean polarization angle and dispersion . . . .
Polarization data at core scales toward the B59/stem regions . . . . . .
Polarization data at core scales toward the stem . . . . . . . . . . . . .
Polarization data at core scales toward the stem/bowl interface . . . . .
Polarization data at core scales toward the “diffuse” stem/bowl interface
Polarization data at core scales toward the bowl . . . . . . . . . . . . .
Dependence of the mean polarization with respect to AR . . . . . . . .
Color-magnitude diagram for stars in Field 43 . . . . . . . . . . . . . .
Extinction diagrams toward the observed Pipe fields . . . . . . . . . . .
Polarizing efficiency toward the Pipe nebula . . . . . . . . . . . . . . .
46
48
49
52
53
54
54
55
55
58
60
61
63
vii
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viii
LIST OF FIGURES
4.14 Polarization maps of Fields 06 and 26 . . . . . . . . . . . . . . . . . . . . . . .
65
4.15 Polarization maps of Fields 27 and 35 . . . . . . . . . . . . . . . . . . . . . . .
66
4.16 Correlation between polarization parameters and K magnitude for Fields 26 and 27 67
4.17 The distribution of polarization angles for Field 38 . . . . . . . . . . . . . . . .
69
4.18 Square root of the second order structure function for the individual fields . . . .
71
4.19 Structure function for Fields 3, 6 and 26 . . . . . . . . . . . . . . . . . . . . . .
71
4.20 Second–order structure function for distinctive regions in the Pipe nebula . . . .
72
4.21 Confidence intervals of the S F solutions . . . . . . . . . . . . . . . . . . . . . .
75
5.1
Example of a LIRIS image with the polarization setup . . . . . . . . . . . . . . .
82
5.2
DSS optical image of the near-IR science targets . . . . . . . . . . . . . . . . . .
83
5.3
Distribution of σP with J magnitudes . . . . . . . . . . . . . . . . . . . . . . . .
87
5.4
Distribution of near-IR polarization angles . . . . . . . . . . . . . . . . . . . . .
91
5.5
near-IR polarization map of NGC 1333 . . . . . . . . . . . . . . . . . . . . . .
92
5.6
Comparison between optical and near-IR polarization maps . . . . . . . . . . . .
94
5.7
Comparison between optical and near-IR polarization angles . . . . . . . . . . .
95
5.8
Spectral Energy Distribution of the optical and near-IR data . . . . . . . . . . . .
96
5.9
Polarizing efficiency of the observed zone . . . . . . . . . . . . . . . . . . . . .
97
5.10 CO molecular spectra toward the observed line-of-sight . . . . . . . . . . . . . .
99
6.1
VISTA image of NGC 2024 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2
SMA dust continuum map of FIR 5 with quasi-uniform weighting . . . . . . . . 109
6.3
Maps of Stokes Q and U emission . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.4
Dust continuum polarization toward FIR 5 and distribution of polarization angles
6.5
CO (3 → 2) emission associated with FIR 5 and FIR 6 dust cores . . . . . . . . . 114
6.6
6.7
112
Position-Velocity plot of the CO (3 → 2) emission . . . . . . . . . . . . . . . . . 115
Distribution of polarization toward NGC 2024 FIR 5 . . . . . . . . . . . . . . . 116
6.8
Plane-of-sky magnetic field geometry for NGC 2024 FIR 5 . . . . . . . . . . . . 117
6.9
VLA cm emission associated to the Hii region in NGC 2024 . . . . . . . . . . . 121
6.10 CO outflows interaction in FIR 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.11 CO spectrum of the outflows interacting zone . . . . . . . . . . . . . . . . . . . 124
7.1
Millimeter and submillimeter magnetic field configurations of IRAS 16293-2422
129
7.2
Contours of H2 O maser emission in IRAS 16293-2422 . . . . . . . . . . . . . . 131
7.3
H2 O maser Stokes I spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.4
Scheme of the distribution of dust and molecular material in IRAS 16293-2422 . 133
7.5
Stokes I, polarized fraction and polarization angle spectra of IRAS 16293-2422 . 134
7.6
Stokes V spectrum of IRAS 16293-2422 . . . . . . . . . . . . . . . . . . . . . . 135
7.7
Linear polarization map of IRAS 16293-2422 . . . . . . . . . . . . . . . . . . . 136
7.8
Dependence between θ and linear polarization . . . . . . . . . . . . . . . . . . . 137
LIST OF FIGURES
ix
7.9
χ2 fit on the H2 O maser spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8.1
Oberved relation between B and the n for the present data . . . . . . . . . . . . . 142
x
LIST OF FIGURES
List of Tables
2.1
2.2
2.3
B-band linear polarization of Hipparcos stars . . . . . . . . . . . . . . . . . . .
Polarization of background stars . . . . . . . . . . . . . . . . . . . . . . . . . .
Stars relevant to the estimate of the distance to the Pipe nebula. . . . . . . . . . .
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25
32
4.1
4.2
4.3
4.4
Observed zero polarization standard stars. . . . . . . . . . .
Observed high polarization standard stars. . . . . . . . . . .
Mean polarization and extinction data for the observed fields
Structure function parameters for the Pipe nebula . . . . . .
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47
47
50
74
5.1
5.2
5.3
5.4
5.5
5.6
Log of the observations . . . . . . . . . . . . . . . . .
Standard stars . . . . . . . . . . . . . . . . . . . . . .
Observational results for the unpolarized standard stars.
Observational results for the polarized standard star. . .
J−band polarization data . . . . . . . . . . . . . . . .
R-band polarization data . . . . . . . . . . . . . . . .
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84
88
88
89
90
93
6.1
6.2
6.3
6.4
Parameters of the continuum and line observations
FIR 5: main component . . . . . . . . . . . . . . .
Sub-millimeter dust condensations . . . . . . . . .
SMA polarization data from NGC 2024 FIR 5 . . .
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108
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110
113
7.1
Possible H2 O maser components in IRAS 16293-2422 . . . . . . . . . . . . . . 132
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Contents
Acknowledgments
iii
Resumen de la tesis:
Campos magnéticos en regiones de formación estelar: una aproximación multi-longitudinal
xvii
1 Introduction
1.1 What causes star formation? . . . . . . . . . . . . . . . . .
1.2 Linear polarimetry: mathematical formalism . . . . . . . . .
1.3 Mechanisms of grain alignment and dust polarization . . . .
1.4 Molecular line polarization . . . . . . . . . . . . . . . . . .
1.5 Multi-wavelength polarimetry . . . . . . . . . . . . . . . .
1.5.1 Optical and near-infrared polarimetry . . . . . . . .
1.5.2 Submillimeter and millimeter polarimetry . . . . . .
1.5.3 Mid-infrared polarimetry: the ambiguity problem . .
1.5.4 Centimeter polarimetry . . . . . . . . . . . . . . . .
1.6 The magnetic field-density dependence . . . . . . . . . . . .
1.7 The thesis science cases: objects at distinct dynamic regimes
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1
1
4
6
10
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15
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16
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19
20
22
22
27
30
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3 Optical polarimetry toward the Pipe nebula
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
35
36
2 An accurate determination of the distance to the Pipe nebula
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Observations and data reduction . . . . . . . . . . . . . .
2.3 The sightline toward the Pipe nebula . . . . . . . . . . . .
2.3.1 Magnetic field structure . . . . . . . . . . . . . .
2.3.2 Interstellar dust distribution . . . . . . . . . . . .
2.4 Distance . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
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xiv
CONTENTS
3.3
3.4
Polarization at the Pipe nebula . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
41
4 Polarimetric properties of the Pipe nebula at core scales
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Data acquisition and reductions . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Mean Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Polarization maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Deriving AV from 2MASS data . . . . . . . . . . . . . . . . . . . . . .
4.4 Polarizing efficiency toward the Pipe nebula . . . . . . . . . . . . . . . . . . . .
4.5 Fields showing interesting polarization distributions . . . . . . . . . . . . . . . .
4.5.1 Field 06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Field 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Field 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.4 Distribution of polarization and position angles as function of the 2MASS
KS magnitude for Fields 26 and 27 . . . . . . . . . . . . . . . . . . . . .
4.5.5 Comments on the Fields with high mean polarization degree . . . . . . .
4.6 The Structure Function of the polarization angles in the Pipe nebula . . . . . . .
4.6.1 Basic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.2 Qualitative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.3 Comparison with Houde et al. (2009) . . . . . . . . . . . . . . . . . . .
4.6.4 Comparison with Falceta-Gonçalves et al. (2008) . . . . . . . . . . . . .
4.6.5 Summary of the S F analysis . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 Near-infrared polarimetry on NGC 1333
5.1 Introduction . . . . . . . . . . . . . .
5.2 Observations . . . . . . . . . . . . .
5.2.1 Near-infrared observations . .
5.2.2 Optical observations . . . . .
5.3 Data Analysis . . . . . . . . . . . . .
5.3.1 Photometry . . . . . . . . . .
5.3.2 Polarimetric analysis . . . . .
5.3.3 Standard stars . . . . . . . . .
5.4 Polarization properties . . . . . . . .
5.4.1 Infrared data . . . . . . . . .
5.4.2 Comparison to optical data . .
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CONTENTS
5.5
5.6
5.7
5.8
Extinction and efficiency of alignment . . . . . . . . . . . . . .
Intrinsic polarization from YSO’s . . . . . . . . . . . . . . . .
The magnetic field in NGC 1333 . . . . . . . . . . . . . . . . .
5.7.1 The distribution of dust and molecular gas in NGC 1333
5.7.2 The field morphology as traced by the diffuse gas . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
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. 93
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6 The magnetic field in the NGC 2024 FIR 5 dense core
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Dust Continuum Emission . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Distribution of the polarized flux . . . . . . . . . . . . . . . . . . . . . .
6.3.3 CO (3 → 2) emission . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Polarization properties . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2 Magnetic field properties . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.3 Magnetic field around FIR 5A: gravitational pulling or Hii compression?
6.4.4 Multiple Outflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.5 Unipolar molecular outflow . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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7 Spectro-polarimetric observations of H2 O masers toward IRAS 16293-2422
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1 H2 O maser emission . . . . . . . . . . . . . . . . . . . . . . . .
7.3.2 Polarized emission . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Modeling the polarized emission of the water maser . . . . . . . . . . . .
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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8 Conclusions
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139
xvi
CONTENTS
Resumen de la tesis:
Campos magnéticos en regiones de
formación estelar: una aproximación
multi-longitudinal
1. Introducción
Las estrellas nacen en grandes complejos de nubes de gas molecular y polvo compuestas predominantemente por hidrógeno molecular. La evolución de una nube molecular depende de varios
factores fı́sicos, principalmente de su tamaño, forma, temperatura y densidad. Para que se formen
estrellas en la nube es necesario que su gravedad supere la presión térmica generada en su interior.
Sin embargo la evolución dinámica de las nubes moleculares no depende solo de sus condiciones
internas, otros agentes exteriores pueden jugar un papel fundamental, como la turbulencia interestelar o los campos magnéticos interestelares que las atraviesan. La presencia de material ionizado
en las nubes (aunque en una proporción muy pequeña) hace que éstas sean sensibles a la presión
magnética. Ésta, a su vez, puede tener un papel muy importante en la evolución dinámica de la
nube por ser un mecanismo de soporte contra el colapso gravitatorio. Los trabajos de Shu et al.
(1999, 2006) indican que los campos magnéticos son importantes no solamente en la evolucón de
las nubes moleculares, sino también en otros mecanismos asociados a la formación estelar, como el transporte de momento angular y impulsión de jets. No obstante, algunas teorı́as reclaman
que la turbulencia supersónica, generada por gradientes de presión, regula la tasa de formación
de estrellas más efectivamente que el campo magnético (Elmegreen & Scalo 2004; Mac Low &
Klessen 2004). Está claro que ambos están presentes en las nubes moleculares, y el debate actual
está en determinar cual de estos mecanismos es el dominante.
Un parámetro observacional comúnmente usado para estimar el grado de magnetización de
una nube es el cociente masa-flujo magnético, λ ≡ (M/Φ), es decir, la cantidad de masa dentro de
un tubo de flujo magnético. En la teorı́a clásica de formación estelar se supone que las nubes moleculares bajo la influencia de un campo magnético son regiones inicialmente subcrı́ticas (λ < 1),
xvii
xviii
Resumen de la tesis
lo que indica que el colapso gravitacional aún no ha empezado debido a la resistencia magnética.
El proceso de colapso gravitacional se produce vı́a difusión ambipolar. Esto permite una contracción de la nube cuasi-estáticamente, hasta que el cociente masa-flujo magnético alcance λ > 1
(estado supercrı́tico), o sea, la presión magnética deja de ofrecer soporte al colapso gravitacional.
En este caso, el campo magnético debe asumir una morfologı́a de “reloj de arena” como resultado
del arrastre de las lı́neas de campo por las partı́culas que caen hacia el centro de masa del sistema.
Este modelo, previsto por Tassis & Mouschovias (2004) y Mouschovias et al. (2006), ha sido confirmado por observaciones recientes de la emisión térmica polarizada de objetos jóvenes (Girart
et al. 2006; Rao et al. 2009; Girart et al. 2009).
El método más directo para poder estimar las propiedades de los campos magnéticos interestelares es medir la polarización de la radiación interestelar. Sin embargo, la emisión polarizada en
regiones de formación estelar suele ser una pequeña fracción del flujo total, por lo que se necesita
realizar observaciones con una alta sensibilidad. En las nubes moleculares se puede obtener información del campo magnético a partir de la polarización producida por granos de polvo y en la
emisión de transiciones rotacionales de moléculas.
Los granos de polvo interestelares pueden producir polarización si están alı́neados por algún
mecanismo (normalmente el campo magnético ambiente) que los convierte en un medio dicróico
a la radiación incidente. Este efecto es más efectivo en longitudes de ondas cortas (visible e
infrarrojo cercano), en donde la sección eficaz del grano es muy grande. Como resultado, la
radiación al atravesar un medio poblado por partı́culas de polvo (e.g. una nube molecular) quedará
parcialmente polarizada, ya que la componente del campo eléctrico incidente paralela al eje más
largo del grano habrá sido dispersada o absorbida al atravesarlo. El mecanismo responsable del
alineamiento de los granos de polvo es todavı́a tema de discusión (Lazarian 2003, 2007), pero está
generalmente aceptado que las partı́culas de polvo giran con el eje de rotación paralelo a las lı́neas
de campo magnético (Davis & Greenstein 1951; Draine 1996; Hoang & Lazarian 2008, 2009). De
la misma manera que los granos de polvo polarizan la radiación incidente, al emitir fotones estos
también estarán polarizados. La radiación polarizada del polvo se observa en longitudes de onda
más largas (infrarrojo lejano, submilimétrico y milimétrico). En el visible e infrarrojo cercano se
utilizan estrellas de fondo para medir la polarización, cuyos vectores trazan el campo magnético
proyectado en el plano del cielo. En cambio, los vectores de polarización que se derivan de las
observaciones de la emisión del polvo en el infrarrojo lejano y submilimétrico son perpendiculares
al campo magnético proyectado en el plano del cielo. A parte de poder derivar la morfologı́a del
campo magnético, la medida de la dispersión de los ángulos de polarización permite determinar su
intensidad. El grado de alineamiento de los granos de polvo interestelar viene dado por el cociente
P/AV , donde P es el grado de polarización lı́neal y AV la extinción visual. El limite observacional
de este parámetro está alrededor de 3%/mag (Serkowski et al. 1975), lo que sugiere que el gas
difuso en la Galaxia no es un muy eficiente como polarizador.
La medida de la polarización de la radiación estelar producida por una nube molecular puede
servir de herramienta para determinar distancias a nubes moleculares cercanas a nosotros. Con la
Resumen de la tesis
xix
observación de estrellas ubicadas dentro de un rango de distancias en la misma lı́nea de visión de
una nube, es posible deducir su posición a partir del salto en el grado de polarización observado
en estrellas ubicadas detrás del objeto. Esta técnica, aplicada a nubes cercanas al Sol como Lupus
(Alves & Franco 2006) y la Pipe nebula (Alves & Franco 2007), resultó ser más precisa que
técnicas estándares como la determinación de distancias por extinción interestelar (Lombardi et al.
2006).
Cuantitativamente, el estado de polarización de la radiación normalmente se describe a partir de cuatro parámetros denominados parámetros de Stokes: I, Q, U y V. Mientras que los
parámetros de Stokes Q y U están asociados con la polarización lı́neal, el parámetro de Stokes
V está asociado con la polarización circular de la luz. De los dos primeros, podemos derivar
la intensidad polarizada y ángulo de la polarización lı́neal de la luz como IP = (Q2 + U 2 )1/2 y
θ = 21 tan−1 (U/Q), respectivamente. El parámetro de Stokes I está asociado con la intensidad total
de la luz.
Esta tesis está centrada en el estudio de regiones de formación estelar utilizando polarimetrı́a
a distintas longitudes de onda. Se ha utilizado una instrumentación diversa cubriendo un amplio
rango de longitudes de onda con el objetivo de obtener una descripción de las propiedades del
campo magnético a distintas escalas fı́sicas. A continuación, describimos qué información se
obtiene y qué tipo de ciencia es extraı́da en cada banda:
• Un mapa de polarización en el visible nos traza directamente como están distribuidas las
lı́neas de campo magnético en las regiones difusas de las nubes moleculares. Diversas herramientas nos permiten calcular el campo magnético a partir de los mapas de polarización
y obtener parámetros fı́sicos relevantes (como energı́a y presión) para estudiar los procesos dinámicos más presentes en nubes moleculares (e. g., Chandrasekhar & Fermi 1953;
Falceta-Gonçalves et al. 2008; Houde et al. 2009). En los capı́tulos 2, 3 y 4 de esta tesis, enseñamos resultados excepcionales acerca de la nube molecular oscura nebulosa de la Pipa,
una nube masiva pero con muy baja tasa de formación estelar. Su evolución dinámica está
asociada a sus impresionantes propiedades polarimétricas. Estos datos fueron obtenidos en
banda estrecha (R-band, λ0 ∼ 6474 Å) con el Observatório do Pico dos Dias (LNA/MCT,
Minas Gerais, Brasil).
• En el rango del infrarrojo cercano, la polarización proviene tanto por absorción diferencial,
como en el caso del visible, como por dispersión, conforme se observa en discos circunestelares de objetos jóvenes. En el primer caso, la ventaja sobre el visible se debe a que se puede
observar el campo magnético en regiones con una mayor extinción visual. No obstante, en
las dos bandas la polarización tiende a saturarse en regiones de muy alta densidad. Este
fenómeno causado por la despolarización (Goodman et al. 1990; Arce et al. 1998). En el
caso de la polarización por dispersión, ésta permite estudiar las propiedades de los discos
de polvo alrededor de estrellas jóvenes (e. g., Bastien & Menard 1990; Menard & Bastien
1992; Pereyra et al. 2009) o, a escalas más grandes, determinar las fuentes ionizadoras de
xx
Resumen de la tesis
regiones Hii (e. g., Kandori et al. 2007). En el capı́tulo 5, discutimos los resultados de
polarimetrı́a en la banda J (λ0 ∼ 1.25 µm) para una nube muy activa: NGC 1333. En la región observada, hay contribución de estrellas de fondo y de objetos estelares jóvenes, lo que
ha producido un complejo patrón de polarización. Los datos en infrarrojo son unos de los
primeros obtenidos con la cámara LIRIS en modo de polarización. LIRIS está instalada en
el Telescopio William Herschel (Observatorio del Roque de los Muchachos, Islas Canarias).
• En el rango de longitudes de onda (sub)milimétricas la emisión polarizada del polvo se
puede observar con radio telescopios de una antena sobre regiones amplias de las nubes
moleculares, o con radio telescopios de sı́ntesis de apertura que permiten trazar el campo
magnético a muy alta resolución espacial. Las observaciones de este tipo permiten estudiar
en el papel que juega el campo magnético en las partes más densas de las nubes moleculares
(n(H2 ) > 104 cm−3 ). Los procesos fı́sicos que regulan la fragmentación de nubes moleculares en pequeños núcleos y las formación de estrellas jóvenes (objetos de clase 0, I y
II) están sujetos a varios factores como el proprio campo magnético, el momento angular y
turbulencia. Los núcleos magnetizados al alcanzar un estado supercrı́tico deforman la estructura del campo. El campo magnético es el principal responsable de extraer el exceso de
momento angular del sistema (“frenado magnético”) y de lanzar los “jets”. En el capı́tulo 6
se estudia la emisión térmica del polvo a 870 µm de la fuente de masa intermedia NGC 2024
FIR 5 a partir de observaciones polarimétricas con el Submillimeter Array (SMA, Hawai,
EEUU) . En esta fuente se han detectado nuevos objetos y se ha estudiado la emisión polarizada del polvo gracias la alta sensibilidad del SMA. Los datos nos enseñan un patrón de la
polarización consistente con un núcleo protoestelar magnetizado en colapso.
• Las observaciones de la polarización en el rango centimétrico también proporcionan información acerca de las propiedades del campo magnético. El efecto Zeeman se puede medir
en transiciones rotacionales que emiten como máser de algunas moléculas como el OH, metanol y H2 O. En el caso de los máseres de agua, la lı́nea más comúnmente usada es la de
22 GHz. El efecto Zeeman en los máseres se puede medir a partir de la polarización circular
(el parámetro de Stokes V), y de aquı́ se puede calcular la intensidad del campo magnético
a densidades muy altas (109 cm−3 ). Los resultados en el rango del centimétrico (λ0 ∼ 1.3
cm) obtenidos con el Very Large Array (VLA/NRAO, Nuevo México, EEUU) se discuten
en el capı́tulo 7. Observamos la protoestrella de baja masa IRAS 16293-2422 y obtuvimos
la primera determinación de la intensidad del campo a densidades muy altas para este tipo
de fuentes.
2. Determinación de distancia en la nebulosa de la Pipa
La determinación de distancias a nubes moleculares es crucial para la calibración de los
parámetros fı́sicos asociados a ellas. De los varios métodos existentes, la determinación más
Resumen de la tesis
xxi
clásica está basada en la obtención de los excesos de color en un determinado sistema fotométrico
(e. g.: Strömgren) para un grupo de estrellas de fondo (respecto a la nube). No obstante, la disponibilidad de un catálogo de estrellas con distancias determinadas con una buena exactitud, como
es el caso del catálogo de Hipparcos, ha inspirado nuevos métodos de determinación de distancias
(Knude & Hog 1998; Alves & Franco 2006). En este trabajo proponemos el uso combinado de
estrellas del catálogo Hipparcos (ESA 1997) con datos de polarización en la banda visible B. El
objeto seleccionado es la nebulosa de la Pipa, una nube oscura masiva (10000 M⊙ , Onishi et al.
1999) pero con muy baja tasa de formación estelar.
Las observaciones fueron realizadas de 2003 a 2005, utilizando el telescopio IAG de 60 cm
del Observatório do Pico dos Dias (LNA/MCT, Brasil). La polarimetrı́a lineal en la banda B fue
obtenida para 82 estrellas Hipparcos en un rango de distancias entre ∼ 20 y 200 pc. La unidad
polarimétrica que se adjunta a la cámara CCD contiene una placa de media-onda (o “rotator”), un
prisma de calcita de Savart y una rueda de filtros. El rotator gira a pasos de 22.◦ 5, y un ciclo en
la modulación de la polarización es cubierto para cada rotación de 90◦ . Como consecuencia, las
dos imágenes resultantes del prisma de Savart (haces ordinario y extraordinarios generados por la
birrefringencia de la calcita) alternan de intensidad debido a la diferencia de fase introducida. Las
intensidades combinadas de cada posición del rotator permiten disminuir las irregularidades en la
respuesta pixel-a-pixel de la CCD. Además, la medida simultánea de los dos haces permiten que
las observaciones puedan ser realizadas en condiciones no-fotométricas y, a la vez, la polarización
de fondo es prácticamente nula. Ocho imágenes CCD fueron tomadas para cada estrella, con el
rotator cubriendo dos ciclos de modulación (0◦ , 22.◦ 5, 45◦ y 67.◦ 5 para un ciclo).
Tras el preprocesamiento de las imágenes (corrección por bias y f lat f ield), realizamos fotometrı́a de abertura en el par de imágenes polarizadas de cada estrella en cada una de sus ocho
posiciones. El grado de polarización lineal de cada objeto fue obtenido a partir de la diferencia de
magnitudes para cada par de haces. Para la reducción fotométrica, utilizamos el programa IRAF
(del National Optical Astronomy Observatory - NOAO). La reducción polarimétrica fue realizada con un paquete de códigos IRAF especı́ficamente desarrollado para calcular la polarización
(PCCDPACK, Pereyra 2000). La calibración instrumental se hace con la observación de estrellas
estándares no-polarizadas, de donde se saca el grado de polarización instrumental. La dirección
de referencia del rotator, de la cual se determina la orientación real de los vectores de polarización
en el plano del cielo, se obtiene de la observación de estrellas estándares con grado y ángulo de
polarización bien definidos.
Consideramos que la polarización observada se debe a la extinción diferencial por partı́culas
de polvo en la lı́nea de visión alineadas perpendicularmente al campo magnético. Según el mapa
de extinción 2MASS de la Pipa creado por Lombardi et al. (2006), su distribución del polvo y
del gas tiene una orientación predominantemente filamentosa. Nuestros datos muestran que las
estrellas más polarizadas (P & 1%) tienen ángulo de polarización perpendicular al eje largo de la
nube, lo que indica que su colapso ha ocurrido a lo largo de las lı́neas de campo magnético. Este
escenario, propuesto por Shu et al. (1987), culminará en la formación de estrellas de baja masa en
xxii
Resumen de la tesis
el futuro, pero ya observada en nubes más activas como Chamaeleon I, Lupus y Taurus.
Aunque la orientación del campo perpendicular al eje mayor de la Pipa sea dominante (ángulo
de posición θ ≃ 160◦ ), algunas estrellas con menor grado de polarización poseen ángulos de
polarización ortogonales a la componente dominante (θ ≃ 60◦ ). Se deduce que la componente de
polvo que produce esta polarización no proviene de la Pipa, sino de una nube más cercana, a una
distancia de unos 70 pc. Esta componente difusa ya habı́a sido detectada anteriormente por Leroy
(1999).
El diagrama paralaje-polarización de nuestros datos enseña un claro aumento en el grado de
polarización para distancias superiores a 140 pc. El volumen ubicado enfrente de la Pipa está
prácticamente libre de polvo interestelar. Este resultado se reproduce para otras nubes oscuras
ubicadas relativamente lejos de la Pipa (Lupus, Alves & Franco 2006), lo que refuerza que el
sistema solar pueda estar dentro una cavidad conocida como “Local Bubble”. Algunos autores
proponen que esta burbuja pueda estar en interacción con una región adyacente conocida como
Loop 1 (Egger & Aschenbach 1995). La medidas de la extinción interestelar hacia esta lı́nea de
visión son consistentes con nuestros datos de baja polarización.
Podemos estimar la distancia analizando las estrellas con paralajes trigonométricos entre 6
y 8 mas (125 < dπ < 167 pc). A partir del objeto con grado de polarización más bajo, HIP
84930 (P = 0.044%), podemos determinar un lı́mite inferior de 140 pc para la distancia. Por
otro lado, promediando los valores de paralaje trigonométricos de los tres objetos con grado de
polarización más grande (P > 1%, HIP 84391, HIP 84696 y HIP 85318), obtenemos un valor
de distancia de 145 ±16 pc. En los campos en donde se han detectado estrellas Hipparcos poco
polarizadas también se detectan algunas estrellas que poseen ángulos de polarización alineados
con las estrellas Hipparcos más polarizadas (o sea, perpendicular al filamento de la Pipa). Aunque
estas estrellas de campo no tienen una determinación de distancia precisa, podemos deducir que
son estrellas de fondo cuya polarización se produce debido al material más denso de la Pipa.
Nuestra estimativa de distancia concuerda con valores obtenidos para nubes oscuras considerablemente más activas que la Pipa, como ρ Ophicuchi (139 ± 9 pc, Vaughan et al. 2006) y Lupus
(140 ± 10 pc, Franco 2002; Alves & Franco 2006). Esto indica que el medio interestelar en estas
direcciones puede estar de alguna manera asociado, formando una única estructura a gran escala.
3. El campo magnético de la nebulosa de la Pipa a gran escala
El estudio de la evolución dinámica de nubes moleculares es marcado por una discusión todavı́a inconcluyente sobre qué fuerzas son las dominantes en este proceso: turbulenta o magnética.
La formación de estrellas de baja masa como resultado de un colapso cuasiestático de materia a lo
largo de las lı́neas de campo magnético fue propuesto por varios autores (e. g., Mestel & Spitzer
1956; Mouschovias & Paleologou 1981; Lizano & Shu 1989), pero la falta de coherencia en la
determinación de algunos parámetros teóricos (como la escala temporal de este proceso), hizo que
los modelos de formación estelar generada por turbulencia supersónica fuesen citados como más
Resumen de la tesis
xxiii
realistas (Elmegreen & Scalo 2004; Mac Low & Klessen 2004). No obstante, los modelos recientes de evolución dinámica por difusión ambipolar demuestran que dichas inconsistencias no son
ciertas (Tassis & Mouschovias 2004; Mouschovias et al. 2006). Observaciones polarimétricas recientes muestran que las nubes moleculares tienen un campo magnético relativamente intenso (e.
g., Pereyra & Magalhães 2004; Girart et al. 2006). En este trabajo, seguimos estudiando la nebulosa de la Pipa. Esta nube masiva filamentosa, que posee una tasa de formación estelar muy baja
(solamente la región del núcleo B59 presenta formación estelar: Brooke et al. 2007), alberga unos
160 núcleos moleculares densos (Alves et al. 2007), de los cuales los menos masivos (. 2M⊙ )
no están gravitacionalmente ligados. Proponemos que este estado global inactivo esté relacionado
con el campo magnético de la nube.
Las observaciones fueron realizadas entre 2005 y 2007 con el telescopio IAG de 60 cm y con
el telescopio de 1.6 m del Observatório do Pico dos Dias (LNA/MCT, Brasil). La configuración
instrumental, ası́ como la descripción del modo polarimétrico de observación están descritos en el
capı́tulo 2 de éste resumen y también en Magalhães et al. (1996). Realizamos polarimetrı́a CCD
en la banda R en 46 campos localizados a lo largo de la Pipa, de los cuales 12 fueron observados
con el telescopio IAG de 60 cm. El tiempo de integración total para cada posición del rotator fue
de 10 minutos partidos en 5 exposiciones de 120 s. Los 34 campos restantes fueron observados
con el telescopio de 1.6 m. Con este telescopio una exposición de 120 s para cada posición del
rotator fue suficiente para obtener la señal deseada. En total, obtuvimos la polarización lineal de
unas 12 000 estrellas de campo, de las cuales 6 600 poseen P/σP ≥ 10. Esto corresponde a más
de 100 estrellas para la mayorı́a de los campos observados.
En este trabajo solamente se analizan los valores medios de grado y ángulo de polarización
para cada campo. El análisis detallado de cada uno es el tema central del próximo capı́tulo, pero
anticipamos que la mayor parte de los campos muestran una distribución estándar (es decir, gausiana) de los ángulos de polarización (θ), a excepción de algunas direcciones con un patrón un poco
más complejo. Los valores medios de polarización obtenidos varı́an entre 1 y 15%, mientras que
los θ son más bien uniformes (hθi ≃ 160◦ -190◦ ). En este estudio consideramos que la polarización
es debida a la absorción diferencial producida por granos de polvo alineados perpendicularmente
a las lı́neas de campo magnético (Davis & Greenstein 1951). El mapa de polarización obtenido
traza la topologı́a del campo magnético que se encuentra predominantemente perpendicular al eje
mayor de la nube.
La Pipa se puede dividir en tres regiones según sus propiedades de la polarización. Si analizamos el grado medio de polarización combinado con la dispersión de los ángulos de polarización
para cada campo, vemos que el extremo noroeste de la Pipa (donde está ubicado B59) posee la
polarización media más baja (alrededor de 1–2%) y la dispersión más grande. A lo largo de la
parte filamentosa (o stem, palabra en inglés para representar el tubo de la pipa), hemos observado
que la polarización aumenta ligeramente con respecto a B59, de la misma forma que la dispersión
también disminuye. Finalmente, en la parte amorfa y más masiva (el bowl, palabra en inglés para representar la concavidad de la pipa) se encuentran los campos más polarizados, con valores
xxiv
Resumen de la tesis
jamás observados en otras nubes (hasta el 15%). Este pico está acompañado por un mı́nimo en
los valores de dispersión en θ (. 5◦ ). Además, el alineación vectorial entre los campos del bowl
es más evidente. El gradiente observado en los parámetros polarimétricos entre B59 y el bowl es
más acentuado para campos que contienen alguno de los núcleos densos e inactivos detectados por
Alves et al. (2007), que son los campos con mayor extinción visual (0.8 . AV . 4.5 magnitudes).
También se observa un ligero gradiente en estos parámetros (aunque no tan marcado) para campos
que no contienen núcleos densos.
La anticorrelación entre el grado medio de polarización hPi y la dispersión ∆θ de los ángulos
de polarización es evidente. Este gradiente podrı́a deberse a efectos de proyección del campo total
en el plano del cielo como resultado, por ejemplo, de un cambio de dirección. Sin embargo, esto
no explicarı́a la eficiencia de alineación de granos de polvo calculada para cada campo. En la Pipa
encontramos una dependencia creciente entre hPi y AV , lo que quiere decir que la eficiencia de alineación en B59 es más pequeña que en el bowl. Utilizamos la ecuación de Chandrasekhar-Fermi
para estimar la intensidad del campo magnético en el plano del cielo (Chandrasekhar & Fermi
1953). De los trabajos de Lada et al. (2008) y Muench et al. (2007) determinamos la densidad
volumétrica de la envolvente de cada núcleo (que corresponde a la zona observada en la polarimetrı́a óptica) como ∼ 3 × 103 cm−3 , y anchos de lı́nea medios del orden de 0.45 km s−1 para
toda la nube. Teniendo en cuenta estos parámetros como valores de entrada, estimamos el campo
magnético como 17, 30 y 65 µG para B59, stem y bowl, respectivamente. Con el mapa de extinción de Lombardi et al. (2006), asumimos una extinción media de 3 magnitudes para la zona
observada en la polarimetrı́a con la que estimamos un cociente masa-flujo supercrı́tico para B59,
pero subcrı́tico para el stem y el bowl
La distribución filamentosa del material de la Pipa es la morfologı́a esperada para nubes que
tienen su evolución regulada por un campo magnético muy intenso. Su colapso ocurre a lo largo de
las lı́neas de campo, en lugar de perpendicular a ellas, debido a la intensa resistencia magnética (Fiedler & Mouschovias 1993; Tassis & Mouschovias 2007). Estimamos la presión magnética ejercida por el gas difuso contra el colapso lateral (Pmag = B2 /8π) como 12 ×105 y 2.6 × 105 K cm−3
para el bowl y el stem, respectivamente. Em ambos casos, la presión magnética es más grande que
la presión debido al peso de la nube (Pcloud /k = 105 K cm−3 , Lada et al. 2008), lo que corrobora
observacionalmente los modelos de colapso por relajación dinámica por difusión ambipolar. Nuestros resultados sugieren que las tres regiones de la Pipa pueden estar experimentando distintos
estados evolutivos: B59, el más evolucionado, presenta formación estelar activa por tener menor
soporte magnético contra el colapso gravitacional; el stem se encontrarı́a en un estado transitorio,
subcrı́tico pero a punto de formar estrellas; finalmente, el bowl es la región más magnetizada y,
por lo tanto, menos evolucionada, aunque la presencia de núcleos de polvo muestran que ya ocurre
fragmentación.
Resumen de la tesis
xxv
4. El campo magnético en la nebulosa de la Pipa a escalas de núcleos
densos de polvo
La baja eficiencia de formación estelar de nuestra Galaxia, estimada alrededor de 1.0% (Goldsmith et al. 2008), nos motiva a entender mejor los procesos fı́sicos que ocurren en el medio interestelar. Los dos mecanismos propuestos como reguladores de estos procesos son los campos
magnéticos y la turbulencia supersónica. Uno de los problemas más discutidos de la astrofı́sica
moderna es cuál de los dos es dominante. Hemos visto en el capı́tulo anterior que la nebulosa
de la Pipa parece ser el laboratorio apropiado para este tipo de estudio. La baja tasa de formación estelar observada (∼ 0.06%, Forbrich et al. 2009, 2010) combinada a un campo magnético
predominantemente perpendicular a su estructura alargada (Alves et al. 2008) sugieren que esta
nube molecular puede estar en un estado evolutivo primordial. Además de los de objetos jóvenes
detectados en B59 (Brooke et al. 2007), hay evidencia de que en el stem de la Pipa también hay
unas pocas estrellas jóvenes (Forbrich et al. 2009). No obstante, el bowl de la Pipa no presenta
ninguna señal de formación estelar, y la hipótesis propuesta por Alves et al. (2008) de que las tres
regiones de Pipa (B59, stem y bowl) están en estados evolutivos distintos sigue válida.
En este trabajo, analizamos en detalle cada campo observado y discutido en el capı́tulo anterior.
Para ello, optamos por estudiar las estrellas con P/σP ≥ 5 para aumentar nuestra estadı́stica.
La configuración instrumental y la estrategia observacional son las mismas de las descritas en
los capı́tulos 2 y 3. Hemos cambiado la forma de exponer los resultados, ya que con P/σP ≥
5 tenemos alrededor de 9700 estrellas que casi en su totalidad están asociadas a alguna fuente
2MASS.
Sorprendentemente la distribución de P muestra bastantes estrellas con polarización más grande que 15%, y seis estrellas con P > 19%. Por otra banda, los ángulos de polarización (θ) se
concentran alrededor de 180◦ lo que corresponde a una orientación perpendicular a la estructura
filamentosa de la Pipa. Esto quiere decir que, según previsto en el capı́tulo 3, hay una homogeneidad en el alineación de los granos de polvo y, consecuentemente, del campo magnético a gran
escala.
Las propiedades polarimétricas obtenidas de los valores medios en P y ∆θ para cada campo
nos enseñan una sorprendente anticorrelación entre estos dos parámetros. Los campos observados
en la lı́nea de visión de B59 presentan una dispersión muy alta (∆θ ≥ 10◦ ) que va bajando a lo
largo del stem yque tiene un mı́nimo en el bowl. Las únicas excepciones son los campos 15, 26
y 27, que poseen una dispersión demasiado ancha en comparación con otros campos en el stem.
Esta disminución en ∆θ es acompañada por un claro aumento en el grado de polarización medio
(hPi) en el mismo sentido.
En general, la mayorı́a de los campos en B59 presentan una dispersión muy ancha en θ.
Además, esta es la región más opaca de la nube y algunos campos presentan muy pocas estrellas con P/σP ≥ 5. Los mapas de polarización en B59 sugieren estructuras muy complejas, y los
valores medios de ángulos de polarización, θhPi , varı́an de un campo a otro. En esta zona, hay tres
xxvi
Resumen de la tesis
objetos identificados como objetos estelares jóvenes: KK Oph y las fuentes 11 y 16 del catálogo
de Forbrich et al. (2009). Las estimativas de distancia para KK Oph (Hillenbrand et al. 1992) indican que este objeto puede pertenecer a la Pipa y, por lo tanto, haber sido formado a partir de su
material. Las otras dos fuentes coinciden en posición con los campos 09 y 11, cerca de la interface
B59-stem.
Los mapas de polarización en el stem presentan una transición entre las caracterı́sticas observadas para B59 y el bowl. Los campos 22, 20 y 16 poseen una distribución muy estrecha en θ
(lo que es tı́pico para los campos en el bowl). Por otro lado, la dispersión en θ para el campo
15 es ancha como las observadas en B59. En esta región se encuentran dos de los cuatro objetos
estelares jóvenes identificados en el stem. Cerca de la zona de transición stem-bowl, hay dos de
los campos mencionados como de dispersión demasiado ancha en comparación con los otros campos a su alrededor: el 26 y el 27. Mientras que el campo 26 tiene un mapa de polarización que
parece trazar una estructura curva, el mapa del campo 27 está compuesto por dos componentes
con diferentes ańgulos de polarización.
Finalmente, en la región del bowl, encontramos los campos con un grado de polarización más
alto y una dispersión en θ menor. Cinco de los campos observados poseen hPi ≥ 10%. En su gran
mayorı́a, los ángulos de polarización están centrados en 170◦ . Se destacan los campos 35, que con
la menor dispersión observada revela que la energı́a turbulenta es insignificante, y el campo 38,
donde el grado de polarización más alto fue observado en contraste con una distribución bimodal
en θ. Si analizamos globalmente θhPi en función de la Ascensión Recta, vemos que gran parte
de estos valores se encuentran dentro del intervalo de 180◦ ± 20◦ , lo que quiere decir que el
campo magnético local es perpendicular al eje principal de la Pipa. Sin embargo, si analizamos
en detalle cada campo, vemos que aquellos que poseen baja extinción infrarroja tienen un valor
aproximadamente constante de θhPi a lo largo del stem. Por otro lado, los campos con mayor
extinción infrarroja tienen variaciones sistemáticas en θhPi , con un punto de inflexión alrededor de
AR ≃ 17h 18.5′ (la parte central del stem).
Para estudiar las propiedades de los granos de polvo que se encuentran en la Pipa es conveniente calcular la extinción interestelar asociada con los campos observados. Utilizamos el
catálogo 2MASS para construir diagramas de color-magnitud (CMD) para cada estrella y después compararlos con colores intrı́nsecos calculados previamente para la región de la Pipa (Dutra
et al. 2002). Encontramos que los datos de polarización están trazando zonas menos absorbidas
(0.6 ≤ AV ≤ 4.6 magnitudes). Algunos campos como el 26 y el 27 parecen presentar una cierta
correlación entre θ y las magnitudes K s de sus estrellas. Ambos muestran una dirección preferente
para estrellas con K s & 12 mag (θ > 150◦ ), lo que parece indicar que el mismo tipo de estructura
interestelar está presente en ambas lı́neas de visión. Además, si analizamos la dependencia de P
con la magnitud K s , vemos que el campo 27 presenta una absorción interestelar más homogénea
que el campo 26.
Los valores más altos de eficiencia de alineación, P/AV , observados en el medio interestelar
difuso hasta hoy no exceden los 3%/mag (Serkowski et al. 1975). Aunque los grados de polariza-
Resumen de la tesis
xxvii
ción que obtuvimos para algunas regiones como el bowl son sorprendentemente altos, los valores
de eficiencia de alineación están dentro del lı́mite observacional, lo que supone que el material
interestelar que compone la Pipa no difiere del que se encuentra en el medio interestelar difuso
ordinario. No obstante, la despolarización observada en otras nubes moleculares hacia ambientes
más densos no es reproducida en nuestros diagramas. Al contrario, hay una dependencia creciente de la polarización con AV . Aún más interesante es la dependencia de P/AV con la Ascensión
Recta. Hay un aumento substancial en la eficiencia de polarización del bowl en comparación a
B59 y stem, lo que es consistente con la distribución altamente uniforme de la lı́neas de campo
magnético observadas para esta región.
Para poder medir la relación entre el campo magnético y la turbulencia en la Pipa, aplicamos
un análisis estadı́stico para caracterizar mapas de polarización (Falceta-Gonçalves et al. 2008; Hildebrand et al. 2009; Houde et al. 2009; Poidevin et al. 2010): la función de estructura de segundo
orden (FS) de los ángulos de polarización, h∆θ2 (l)i. Ésta está definida como el promedio de la
diferencia en θ entre dos puntos separados por una distancia l (ecuación 5 de Falceta-Gonçalves
et al. 2008). Es, básicamente, una función de autocorrelación en θ que lo asocia a las escalas de
longitud dentro de la nube. Aplicamos la FS para nuestros datos de polarización en cada campo
y en una escala global. En el primer caso, los campos en B59 presentan una dispersión muy alta para todas las escalas fı́sicas consideradas (5.6 mpc < l < 0.35 pc). El escenario opuesto es
observado para los campos del bowl, donde se observa una muy baja dispersión. Los campos del
stem presentan distribuciones intermediarias, mientras que los campos 03, 06 y 26, para l & 0.1
pc, muestran la máxima dispersión, tı́pica de patrones de polarización aleatoriamente orientados.
Globalmente, todos los campos del bowl presentan una muy baja dispersión (h∆θ2 (l)i < 0.09◦ ) a
pequeñas (l < 0.08 pc) y grandes (0.08 < l < 5 pc) escalas. Este valor de dispersión es ligeramente
más alto para el stem y B59 en las dos escalas consideradas. Eso quiere decir que la Pipe nebula
es una nube magnéticamente dominada en todas escalas fı́sicas. La única contribución para un
campo turbulento se ve en los campos 03, que hay una estadı́stica muy baja de vectores, y 06, donde parece haber una correlación entre las lı́neas de campo y la nube de gas según enseña el mapa
de extinción. Además, campos en la interface stem-bowl también poseen una gran dispersión para
l > 0.4 pc compatibles con turbulencia super-Alfvénica. Un ajuste matemático sobre la FS nos
reveló que la longitud de turbulencia en la Pipa es del orden de pocos miliparsecs, mientras que el
cociente de energı́a turbulenta por magnética no supera a los 0.8 en la interface stem-bowl, y tiene
un mı́nimo en el bowl (δB2t /B20 = 0.1, donde δBt es la componente turbulenta del campo magnético
y B0 la uniforme).
5. Polarimetrı́a infrarroja en NGC 1333
La polarimetrı́a en el rango del infrarrojo cercano nos proporciona mapas de polarización en
regiones más densas de una nube molecular. Con esta técnica es posible observarlos a profundidades de algunas decenas de magnitudes, mientras que en el visible este valor suele ser un orden
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Resumen de la tesis
de magnitud más pequeño. La polarización de la luz estelar ocurre de manera similar al visible,
donde granos de polvo no esféricos giran perpendicularmente a las lı́neas de campo magnético,
y absorben la radiación incidente de manera diferencial. No obstante, hay evidencias de que este
fenómeno puede ser menos eficiente en regiones muy densas debido a la despolarización (Goodman et al. 1992, 1995; Gerakines et al. 1995). También es posible estudiar la distribución del polvo
en objetos estelares jóvenes y regiones Hii, pero en este caso la radiación polarizada es producida
por dispersión en lugar de absorción diferencial.
En este trabajo, estudiamos el material interestelar difuso de NGC 1333, a una pequeña distancia angular (∼ 5′ ) de la protoestrella de baja masa NGC 1333 IRAS 4A. La morfologı́a del
campo magnético de esta fuente se ha convertido en un modelo para teorı́as de formación estelar
de baja masa debido a su forma de reloj de arena. Ésta es la geometrı́a esperada cuando la fuente
alcanza un estado supercrı́tico y la atracción gravitacional supera la tensión magnética. Con la
polarimetrı́a infrarroja, además de obtener las caracterı́sticas del material interestelar en esta región, pretendemos estudiar el campo magnético a extinciones visuales más profundas para poder
compararlo con el campo de IRAS 4A.
Las observaciones fueron realizadas durante las noches de 26 y 27 de diciembre de 2006 y
13 de diciembre de 2007 con el Telescopio William Herschel, en el Observatorio del Roque de
los Muchachos (La Palma, Islas Canarias, España). Utilizamos el módulo de polarización de
la cámara infrarroja LIRIS para observaciones en la banda J. Observaciones complementarias
fueron realizadas en la banda R con el telescopio de 1.6 m del Observatório do Pico dos Dias
(LNA/MCT, Brasil). La configuración instrumental de las observaciones en el visible es la misma
descrita en los capı́tulos 2 y 3. Estos datos tienen un aspecto comparativo que nos ayuda a verificar
lea calidad de los datos en infrarrojo. La observación de estrellas estándares polarizadas y nopolarizadas nos proporcionó parámetros de calibración instrumental. Los datos fueron reducidos
con el programa de tratamiento de datos IRAF, del NOAO, y con paquetes especı́ficos para el
cálculo de la polarización.
Con la polarimetrı́a infrarroja alcanzamos observar estrellas con magnitud J ≃ 18. Los grados
de polarización P J varı́an entre 1.6 y 4.9%, mientras que la distribución de ángulos de polarización
θ presenta una componente principal centrada en 165◦ . Una estrella solamente tiene un ángulo de
polarización divergente (θ ≃ 49◦ ). El error en la polarización está dominado por la estadı́stica de
fotones.
La distribución bimodal en θ también fue observada en trabajos anteriores (Tamura et al. 1988).
La componente dominante es generada puramente por absorpción dicróica y por lo tanto traza la
geometrı́a del campo magnético proyectada en el plano del cielo. La estrella con θ divergente
es una estrella T-Tauri clásica, lo que quiere decir que la polarización observada es generada por
dispersión simple en su disco circunestelar. En los datos visibles, otros objetos estelares jóvenes
detectados poseen ángulos de polarización orientados similarmente, ası́ como algunas estrellas
con muy bajo grado de polarización y podrı́an estar ubicadas enfrente a la nube.
Los datos en la banda R concuerdan a la perfección con el infrarrojo. La discrepancia media
Resumen de la tesis
xxix
en θ es del orden de 6.5◦ , lo que indica que el funcionamiento de LIRIS en modo de polarización
es cientı́ficamente fiable. Con estos dos conjuntos de datos, analizamos la Distribución Espectral
de Energı́a de la polarización lineal observada. Prácticamente, todas las estrellas se encuentran
bajo el lı́mite observacional medido por Whittet et al. (1992) para NGC 1333 (λmax ≃ 0.86 µm),
pero concentradas alrededor de λmax ≃ 0.55 µm, que es el valor tı́pico para el medio interestelar.
Calculamos la eficiencia de polarización (o de alineación de granos) de NGC 1333 con el
cociente P/AV . La extinción visual AV fue estimada a partir de los colores J − H, H − K y J − K
extraı́dos del catálogo 2MASS. Comparamos los colores observados con los colores intrı́nsecos de
distintos tipos espectrales (obtenidos de Tokunaga 2000) a través de la curva de extinción extraı́da
de Cardelli et al. (1989). Un ajuste por mı́nimos cuadrados nos proporcionó los tipos espectrales y
la extinción visual AV para cada estrella del campo. La eficiencia de alineación calculada presenta
una clara despolarización hacia extinciones visuales más altas que también fue observada en otras
nubes moleculares activas como Taurus y Ophiuchus (Arce et al. 1998; Whittet et al. 2001, 2008).
La dependencia entre P/AV y AV parece seguir la ley de potencia determinada observacionalmente
para varias objetos (P/AV ∝ (AV )−0.52 , Whittet et al. 2008).
La distribución de gas molecular y polvo en Perseus se destaca por perfiles espectrales noGausianos (Ridge et al. 2006a; Pineda et al. 2008). En la dirección de NGC 1333, mapas de
CO indican la existencia de componentes de gas a distintas velocidades, lo que puede sugerir una
estructura estratificada. La región estudiada en este trabajo se extiende por el halo de NGC 1333,
muy cerca de estructuras filamentosas densas en las cuales está ubicada IRAS 4A.
El campo magnético inferido de nuestros mapas de polarización trazan lı́neas de campo que
no concuerdan con el campo a pequeñas escalas obtenidos con mapas de más alta resolución
(Girart et al. 2006; Attard et al. 2009). Especı́ficamente, hay una diferencia de ∼ 90◦ entre la
dirección del campo magnético dentro de la envolvente densa en IRAS 4A y la derivada en este
trabajo. En lugar de explicar posibles procesos fı́sicos capaces de producir cambios drásticos en
la morfologı́a del campo a escalas fı́sicas tan diferentes, creemos que los dos conjuntos de datos
trazan distintas componentes de gas. Los espectros de 12 CO y 13 CO para la región observada
en infrarrojo nos indican que hay por los menos 3 componentes de velocidades distintas: una
emisión débil a 2 km s−1 , el pico en 13 CO a 7.6 km s−1 y el pico en 12 CO a 6.7 km s−1 . Este
último tiene la misma vLSR del gas denso en IRAS 4A. Por lo tanto, nuestros mapas en infrarrojo y
visible probablemente trazan el campo magnético promediado a lo largo de distintas componentes
de velocidad detectadas en la lı́nea de visión.
6. El campo magnético en el núcleo denso NGC 2024 FIR 5
La teorı́a de formacı́on estelar ha avanzado mucho en la última década con el desarrollo de nuevas tecnologı́as. Los receptores instalados en antenas e interferómetros son cada vez más sensibles
a la emisión térmica de polvo en nubes moleculares. El Submillimeter Array (SMA, Hawai) es un
interferómetro que está optimizado para observaciones en longitudes de onda submilimétricas,
xxx
Resumen de la tesis
donde el polvo es más brillante. Además de emisión en contı́nuo, también es posible detectar un
gran número de lı́neas moleculares con el amplio ancho de banda de sus receptores. En sus configuraciones más extendidas, la emisión del gas difuso es filtrado, y por eso podemos estudiar las
caracterı́sticas del gas denso encontrado a pequeñas escalas fı́sicas.
Utilizamos el SMA para observar la emisión polarizada del núcleo denso de masa intermedia
NGC 2024 FIR 5. Esta fuente se encuentra en la región más activa de la nube molecular gigante
NGC 2024. Esta zona está compuesta por una extensa región Hii limitada por gas denso molecular
en su parte posterior y por una filamento denso de polvo en su parte anterior. La fuente ionizadora
del gas caliente es IRS 2b (Bik et al. 2003; Kandori et al. 2007), una estrella OB masiva con una
luminosidad de 105.2 L⊙ . NGC 2024 FIR 5 forma parte de una cadena de núcleos protoestelares
ubicados en el material denso detrás de la región Hii. Nuestro interés en esta zona es estudiar la
configuración del campo magnético en esta fuente y su posible interacción con su entorno.
Las observaciones fueron realizadas el 24 de noviembre y el 19 de diciembre de 2007 en configuración compacta. Los datos en contı́nuo fueron obtenidos en la ventana atmosférica de 345
GHz con con un ancho de banda de 1.9 GHz. Además de los calibradores estándares (ganancia y
paso de banda), observamos calibradores de polarización para obtener la polarización instrumental. Los mapas limpios de los parámetros de Stokes I, Q y U fueron generados a partir de las
visibilidades calibradas. A partir de éstos mapas obtuvimos los mapas de grado (P) y ángulo (θ)
de polarización. También detectamos emisión molecular CO (3→2) intensa con una resolución
espectral de 0.7 km s−1 .
Las observaciones con el SMA han resuelto la componente principal de emisión asociada a FIR
5 en dos condensaciones de polvo (5A y 5B) separadas por ∼ 4.5′′ , y otros picos de intensidad
más débiles a su alrededor. El análisis de la emisión del polvo en 5A y 5B nos proporciona una
densidad columnar de ∼ 1023 cm−2 y masas de 1.09 y 0.38 M⊙ , respectivamente. La emisión
polarizada del polvo está asociada principalmente a la condensación 5A, donde alcanza valores de
54 mJy beam−1 (∼ 15%), pero también hay emisión débil asociada a 5B. Se observa evidencia de
despolarización hacia los picos de emisión en contı́nuo de 5A y 5B. En los mapas de la emisión de
CO (3→2) detectamos un flujo molecular muy intenso y colimado y que parece estar propulsado
por 5A, lo que sugiere que esta componente puede estar en un estado más evolucionado que 5B.
Para obtener la geometrı́a del campo magnético a partir de un mapa de emisión polarimétrica,
debemos girar los vectores polarización por 90◦ . De este modo, vemos que el campo en 5A
posee una estructura fı́sicamente más interesante que 5B, donde hay una distribución más uniforme pero una baja estadı́stica de vectores. El campo en 5A traza la morfologı́a reloj de arena
prevista en modelos teóricos para núcleos densos en estado supercrı́tico. A partir de la ecuación de Chandrasekhar-Fermi (Chandrasekhar & Fermi 1953), estimamos la intensidad del campo
magnético en 5A a partir de la dispersión de las lı́neas de campo (9.6◦ ), de su densidad (∼ 106
cm−3 ) y del ancho de lı́nea asociado a la turbulencia (0.87 km s−1 , obtenidos a partir de datos
de formaldehı́do de Mangum et al. 1999). El valor del campo fue estimado en 2.2 mG. Con este
parámetro, calculamos el cociente masa-flujo como λ = 1.6, que corrobora los indı́cios de que
Resumen de la tesis
xxxi
la fuente ya está en proceso de colapso. Estimamos también el cociente de energı́a turbulentamagnética como βturb ≈ 0.33, lo que quiere decir que la energı́a magnética domina sobre la turbulenta. Hicimos un cálculo inverso para determinar la cantidad de masa necesaria para producir
la curvatura magnética observada por colapso gravitacional. El valor encontrado, 2.3 M⊙ , está
sujeto a una grande incertidumbre, pero vemos que es consistente con valores tı́picos para fuentes
de masa intermedia y que es similar a la masa calculada del polvo para 5A+5B.
En este momento, es conveniente comparar la tensión magnética generada por las lı́neas de
campo con la presión radiativa, de ionización y térmica de la región Hii. A gran escala, hay evidencias de que el gas ionizado se esté expandiendo hacia el gas denso donde se encuentran las
fuentes submilimétricas. Datos de Matthews et al. (2002) y Crutcher et al. (1999) han revelado
que el campo magnético de la nube no haya resistido a esta expansión y se haya distorsionado. Verificamos si esta presión es suficiente para alterar la configuración magnética también a pequeñas
escalas y, en particular, en FIR 5. Observamos que este valor no supera la tensión magnética y,
por lo tanto, la curvatura observada se debe únicamente a la atracción gravitacional.
La emisión CO (3→2) detectada en FIR 5 es dominada por un flujo molecular intenso propulsado por 5A en una dirección norte-sur. Detectamos emisión CO también asociada a FIR 5: sw
a más altas velocidades y con la misma orientación. Curiosamente, en los dos casos, solo hemos
detectado emisión a velocidades corridas al rojo (vLSR > 11 km s−1 ), sin ninguna contraparte azul
(la única emisión corrida al azul que se detecta en nuestros mapas proviene de FIR 6). Creemos
que esto se debe a que el flujo molecular corrido al azul es inyectado directamente en la región
Hii, y que por eso se disocia por su interacción con los fotones UV.
7. Observaciones espectro-polarimétricas de máseres de agua en 162932422: obtención de campos magnéticos a densidades muy altas
Los máseres son herramientas muy útiles en el estudio de campos magnéticos en las zonas en
qué son generados. En el caso particular de máseres de agua, que normalmente son detectados
en regiones de formación estelar y en las envolventes de estrellas evolucionadas, esta técnica
nos proporciona las propiedades del campo a densidades del orden de 109 partı́culas por cm3 ,
cuando uno de sus niveles rotacionales encuentran las condiciones de excitación ideales. A estas
densidades, la transición (616 − 523 ) que se observa a 22 GHz emite radiación polarizada debido a
su interacción por efecto Zeeman con el campo magnético local.
Recientemente, varios estudios han comprobado la eficiencia de la espectro-polarimetrı́a de
máseres para investigar campos magnéticos a altas densidades (e. g., Sarma et al. 2001, 2002;
Vlemmings et al. 2002, 2006a). Esta técnica ofrece una solución al problema de la despolarización
√
en regiones muy densas. Según la relación empı́rica B ∝ n (Fiebig & Guesten 1989; Crutcher
1999), las valores tı́picos de intensidad de campo magnético esperados para fuentes excitadores
de máseres de H2 O son del orden de algunas decenas de mG.
Para probar por primera vez esta técnica en una fuente de baja masa, hemos elegido IRAS
xxxii
Resumen de la tesis
16293-2422, un prototipo de núcleo protoestelar binario clase 0 con una estructura magnética bien
establecida. Observaciones en el rango del submilimétrico de Rao et al. (2009) revelaron una
topologı́a de reloj de arena para el campo magnético a escalas de 900 UA’s. Este campo, estimado
en 4.5 mG, parece ser intenso lo suficiente para quitar el exceso de momento angular del núcleo y
alterar su dinámica rotacional.
Las observaciones fueron realizadas con el Very Large Array (VLA, New Mexico, USA) en su
configuración A el 25 y 27 de junio de 2007. El correlador espectral fue sintonizado para la banda
K y centrado en la frecuencia de reposo correspondiente a la transición máser (22235.08 MHz).
El ancho de banda (10.5 km s−1 ) y la velocidad central fueron determinados para poder cubrir el
rango de velocidades de las componentes más intensas ya observadas. La resolución espectral del
receptor de 128 canales fue de 0.08 km s−1 . Además de la calibración estándar por ganancia y paso
de banda, observamos fuentes polarizadas para calibrar los receptores de polarización circular R y
L. De las correlaciones entre estas visibilidades (RR, LL, RL, LR) obtenemos los parámetros de
Stokes para cada canal y de aquı́ los mapas de grado P y ángulo θ de polarización.
La emisión máser observada no está resuelta y aparece predominantemente a velocidades corridas al rojo respecto a la velocidad de la nube. El pico de intensidad es de ∼ 167 Jy beam−1 y
ocurre a vLSR ≃ 7.4 km s−1 . Si tenemos en cuenta los mapas de alta resolución de Chandler et al.
(2005), vemos que nuestra detección está a una distancia de solamente 38 UA’s de la fuente Aa
de su catálogo, una de las dos condensaciones resueltas dentro de la componente más brillante de
IRAS 16293-2422. El espectro de la emisión máser tiene un perfil claramente no-Gausiano, y se
distinguen por lo menos tres componentes independientes. Analizadas en conjunto, estás componentes trazan un gradiente de velocidad de ∼ 3.5 km s−1 y parecen estar distribuidas linealmente,
lo que sugiere que están asociadas a regiones de choque.
La emisión polarizada linealmente posee un perfil muy similar al de la emisión total, aunque
corresponda en su máximo a solamente ∼ 2.5% de su intensidad. El espectro del parámetro de
Stokes V (polarización circular) presenta un perfil P-Cygni inverso, que es la forma esperada
debido al Efecto Zeeman (∝ dI/dν). De este parámetro, pudimos determinar la intensidad de la
componente del campo magnético proyectada en la lı́nea de visión como ∼115 mG.
Para obtener una caracterización completa de la zona excitadora, hemos intentado ajustar los
parámetros observacionales con un código de transporte radiativo que busca determinar sus propiedades fı́sicas tales como temperatura de brillo (T b ∆Ω) y el ancho de lı́nea de emisión térmica
intrı́nseco (∆νth ) (Nedoluha & Watson 1992; Vlemmings et al. 2002). Este último está relacionado
con la distribución de velocidades de partı́culas del medio y nos proporciona la temperatura del
gas excitador. Además, el ángulo entre la orientación 3D de las lı́neas de campo magnético y la
lı́nea de visión también es un parámetro de salida del código y, con él, podemos determinar la
intensidad total del campo una vez que ya conocemos la intensidad en la lı́nea de visión.
Sin embargo, debido a las componentes no resueltas, el perfil de nuestro espectro de emisión
es muy ancho para un ajuste satisfactorio del código. El ancho de lı́nea intrı́nseco calculado es demasiado grande cuando comparado a observaciones interferométricas de lı́neas de base muy largas
Resumen de la tesis
xxxiii
(e. g., VLBA). No obstante, considerando las determinaciones previas del campo magnético en
IRAS 16293-2422 para componentes de polvo, la intensidad de 115 mG calculada para densidades
superiores a ∼ 108 cm−3 está dentro del valor esperado y representa una solución válida para la
despolarización.
8. Conclusiones
Esta tesis está fundamentada en un intenso trabajo observacional en casi su totalidad. Exploramos la técnica polarimétrica en cuatro longitudes de ona distintas: visible, infrarrojo cercano,
submilimétrico y centimétrico. En el visible y el infrarrojo, consideramos que la polarización se
produce por absorción dicróica de la luz de estrellas de fondo, aunque algunos objetos jóvenes
del catálogo infrarrojo poseen polarización intrı́nseca generada por dispersión. El patrón de polarización observado indica la distribución de las lı́neas de campo magnético proyectadas en el
plano del cielo. La polarización en el submilimétrico se genera por emisión térmica de polvo y
también está relacionada con la componente en el plano del cielo del campo magnético. La polarización en el centimétrico se produce por efecto Zeeman de la molécula de agua, y nos proporciona
informaciones del campo magnético proyectado en la lı́nea de visión.
Observamos cuatro regiones moleculares en distintos estados evolutivos, según nos indica la
morfologı́a del campo magnético obtenida de los datos de polarización. Primeramente, utilizamos la polarimetrı́a de estrellas Hipparcos para obtener una estimación precisa de distancia a la
nebulosa de la Pipa: 145 pc. Esta nube parece representar el prototipo de un objeto en un estado
evolutivo muy primordial, antes de que una formación estelar global haya ocurrido, como es evidenciado por la presencia de muchos núcleos densos inactivos. Nuestros resultados muestran que
el campo magnético global es dominante en su evolución dinámica, y que esta parece ser regulada
por difusión ambipolar. A escalas más pequeñas, aunque algunos núcleos indican una configuración magnética no tan uniforme, un análisis multi-escalar corrobora que la turbulencia en la Pipa
es sub-Alfvénica en casi toda su extensión. Por otra banda, los datos en infrarrojo cercano nos
permitieron observar más profundamente que en la Pipa, pero esta vez elegimos un objeto más
evolucionado, con formación estelar intensa: NGC 1333. La geometrı́a del campo magnético a
extinciones visuales de hasta 11 magnitudes posee una componente uniforme y, aunque nuestros
datos estén limitados por una baja estadı́stica, está geometrı́a también es observada en el visible.
Los datos en infrarrojo trazan el gas difuso alrededor de la protoestrella IRAS 4A, pero no parece
haber una correlación clara entre el campo magnético del gas difuso y del gas denso asociado al
núcleo. Sin embargo, los datos en infrarrojo parecen ser el promedio del campo magnético del
gas a distintas componentes de velocidad y, por lo tanto, no debe estar necesariamente asociado al
campo del gas denso. En el rango del submillimétrico, observamos la estructura magnética de la
fuente de masa intermedia NGC 2024 FIR 5. La emisión térmica en contı́nuo de polvo resuelve
la fuente en dos condensaciones. La más brillante (5A) se encuentra en un estado evolutivo más
avanzado, lo que es indicado por el intenso flujo molecular propulsado por ella. La emisión pola-
xxxiv
Resumen de la tesis
rizada asociada a esta condensación nos traza un objeto en estado supercrı́tico, donde el colapso
gravitacional ha superado la tensión magnética (morfologı́a reloj de arena). Finalmente, la emisión máser observada en el rango del centimétrico nos ha proporcionado la intensidad del campo
magnético a densidades muy altas. La fuente observada, IRAS 16293-2422, posee una fuerte y
estable emisión máser de agua. El espectro de polarización circular (parámetro de Stokes V) es
consistente con lo que se espera de una emisión Zeeman. Estimamos una intensidad de 115 mG
en una zona excitadora con n ≃ 109 partı́culas por cm3 , densidades hasta hoy no alcanzadas por
datos en emisión de polvo debido a despolarización.
En este trabajo, comprobamos la importancia del campo magnético a distintas escalas fı́sicas.
Observamos que hay una dependencia lineal creciente entre el campo magnético y las densidades
trazadas. Sin embargo, las intensidades estimadas parecen estar entre un régimen de colapso
dominado por el campo magnético, donde B ∝ n0.47 , y un régimen turbulento (B ∝ n0.66 ). No es
posible derivar un modelo de evolución dinámica basado solamente en las estructuras magnéticas
obtenidas porque observamos una muestra muy hetereogénea. Sin embargo, está claro que el
campo magnético tiene un papel importante en este proceso.
Chapter 1
Introduction
1.1 What causes star formation?
Newborn stars are found in molecular clouds. The low temperatures (∼ 10 - 50 K) and high
volume densities in molecular clouds provide the ideal conditions to the formation of molecules,
which can be used, along with the dust particles, as excellent probes of the physical and chemical
conditions of the molecular clouds. Within the molecular cloud, it is well known the existence
of smaller structures called clumps. This process is not straightforward and several agents are responsible either to accelerate or prevent the formation of clumps. Cloud collapse occurs when the
gravitational pull generated by their own large reservoir of mass surpasses the gas thermal pressure which, in turn, acts outwardly. However, other factors may also have to be taken into account
in regulating the cloud evolution. Turbulence propagating through the interstellar medium is responsible to create overdense regions, which may posses initial conditions for star formation, but
also disturb gravitationally bound clumps. Another physical entity which may affect the dynamics
of the molecular clouds and control star formation is the magnetic field. Molecular clouds are
composed mainly by neutral particles, although there is a tiny, yet dynamically significant, fractions of ionized particles. The collisions between ions and neutral particles makes the molecular
clouds to be ”sensitive” to the presence of the interstellar magnetic field that thread them. Thus,
the ionization fraction of a cloud is closely related to the role of the magnetic field in the collapsing
process. Finally, external agents like massive stars also disturb the cloud environment with their
powerful winds and strong radiation field, disrupting its structure or changing their chemical composition. It is clear that both turbulence and magnetic fields are present in real clouds. The issue
consists in finding which of those mechanisms is dominant in the whole star formation process (or
in particular stages of this process). This issue is still a vivid matter of debate.
An observational quantity commonly invoked to measure the role of the magnetic fields in
the evolution of molecular clouds is the mass-to-flux ratio (M/Φ), defined as the amount of mass
within a magnetic flux tube. Usually this quantity is given with respect to the critical mass-to-flux
ratio, defined as the critical mass in an object whose gravity is about to overcome the magnetic
1
2
Chapter 1. Introduction
pressure. For example, in the case of a disk of uniform density the critical values is Mcrit /Φ =
√
1/2π G (Nakano & Nakamura 1978). It is convenient to calculate the observed mass-to-flux
ratio in terms of the critical ratio as λ ≡ (M/Φ)obs /(M/Φ)crit . In the ”classical” star formation
theory (the ambipolar diffusion theory), clouds are initially magnetically subcritical (λ < 1), so the
magnetic fields provide support to avoid global collapse of the cloud. They evolve quasi-statically
to form clumps through the ambipolar diffusion process. The ambipolar diffusion consist in the
slow drift of the neutral to the center, which increases λ. At some point, the center of the cloud
reaches the supercritical state (λ > 1) and start to collapse in a quasi free-fall time.
Turbulence models are based on the formation of gravitationally bound cores by gas compression. The whole molecular cloud is assumed to be super-Alfvénic and supercritical so that weak
fields will not prevent self-gravitating collapse. An observational evidence of the degree of turbulence of a cloud is given by molecular spectroscopy. The state of a gas is sampled via distinct
species which trace distinct phases. As an example, N2 H+ (1-0) is synthesized and excited only in
high density environments, while CO isotopologues, for being very abundant and having a very
low dipole moment, represent better the diffuse gas in molecular clouds. In addition, molecular
spectroscopy also determines the evolutionary state of some objects by its chemical composition.
The linewidth of molecular spectral data reveals how strong are the gas motions in the LOS within
the cloud. These motions are usually sorted by subsonic (lower than the sound speed for a particular medium), as suggested by narrow lines, or supersonic (faster than the sound speed), which
results in broader lines. If a molecular cloud posses a very strong magnetic field, the ionized
material is linked tighter to the field lines and turbulence is weak. Therefore, magnetic field and
turbulence play opposite roles in the cloud dynamical evolution.
The process of formation of a low-mass star (in a relatively isolated environment) involves
several stages which are schematically represented in Fig. 1.1. The evolutionary steps are sorted
based on the observed Spectral Energy Distribution (SED) from optical to millimeter wavelengths.
The first step consists on the fragmentation of a molecular cloud into several clumps through
the processes previously mentioned. Those clumps harbor prestellar cores which, depending on
various physical conditions (e. g., mass, external pressure and the magnetic field), will start to
contract, forming a very embedded protostar at the center (also called a class 0 object). At this
stage, the gas motions in the core envelope are characterized by infall and rotation. Powerful mass
ejection is also observed in the form of bipolar molecular outflows, which are often parallel to the
molecular core rotation axis. Class 0 sources are usually observed by cold gas tracers detected
at longer wavelengths (submillimeter and millimeter bands). At an age of ∼ 105 years from the
beginning of the contraction, the SED peak displaces from submm to mid-infrared emission. In the
Class I stage, the protostar is still embedded and optically invisible, but the molecular envelope is
more tenuous and the outflow activity is not as powerful. As it evolves, the envelopes completely
dissipates and the protostars is just surrounded with a well defined flattened disk: we have a Class
II (or T-Tauri) star. The disk produces an “infrared excess” due to the absorption of stellar UV
photos and reemission in longer wavelengths. This effect “flattens” the shape of the SED at the
1.1. What causes star formation?
3
Figure 1.1: Evolutionary track of a protostellar core until the formation of a protoplanetary disk
(Credits: Luca Carbonaro).
mid- and far-infrared bands, however, it peaks at near-infrared bands. Finally, Class III (or Post TTauri) stars includes both pre-main-sequence stars and Zero Age Main Sequence Stars (“ZAMS”),
which refers to stars where the nuclear fusion of Hydrogen sets in. Their SED resembles a black
body emission peaking at ∼ 1 to 2 µm. The protostellar disk evolves to a protoplanetary disk and
little or no trace of circumstellar material is observed. Theoretical and observational work has
provided support to this evolutionary model (Shu et al. 1987; Lada & Kylafis 1991; Andre et al.
1993), although timescales and energies involved vary according to their mass range.
The works of Shu et al. (1999, 2006) indicate that magnetic fields likely play an important role
during many of these stages. Modeling of magnetized cloud collapse via ambipolar diffusion and
magnetohydrodynamic regimes reveals the crucial role of magnetic field in the dynamic evolution
of such objects (Tassis & Mouschovias 2005; Galli et al. 2006). Apart from supporting clouds
against collapse, magnetic fields are potentially crucial ingredients for the necessary transport of
angular momentum and for launching of jets. Although some theories claim that turbulent supersonic flows (alfvénic gas motions, section 1.5.1) drives star formation in the interstellar medium
(Elmegreen & Scalo 2004; Mac Low & Klessen 2004), some new results demonstrate that the theory of ambipolar diffusion driven collapse reproduces properly observed molecular cloud lifetimes
and star formation timescales (Tassis & Mouschovias 2004; Mouschovias et al. 2006).
During the last decade, several works have provided observational support to models of magnetized collapsing clouds. Such models predict that protostellar cores at early phases (Class 0
and I) possess a distribution of field lines which resembles a hourglass shape as a result of the
gravitational pulling toward the center (Fiedler & Mouschovias 1993; Galli & Shu 1993; Tassis &
Mouschovias 2004; Mouschovias et al. 2006). With the advent of new astronomical facilities, this
morphology was confirmed through observations of the dust continuum polarized emission from
dense molecular cores. The hourglass configuration was observed in low-mass (Girart et al. 2006;
Rao et al. 2009) and high-mass (Girart et al. 2009; Cortes et al. 2008; Beuther et al. 2010) protostellar cores, indicating that magnetically controlled collapse may be a global phenomenon. Simulation works reproduced reasonably the physical properties of turbulent and magnetized clouds
obtained observationally (Falceta-Gonçalves et al. 2008; Gonçalves et al. 2005, 2008). Figure 1.2
shows the comparison between observational and synthetic data related to the plane-of-sky (POS)
4
Figure 1.2: Left: Plane-of-sky component of the magnetic field in NGC 1333 IRAS 4A (Girart
et al. 2006). Right: Comparison between data (red vectors) and collapse model of a magnetized cloud considering ambipolar diffusion (blue vector) applied to IRAS 4A (Gonçalves et al.
2008).
magnetic field component of the low-mass protostellar core NGC 1333 IRAS 4A.
The most straightforward method to observe interstellar magnetic fields is though polarization
observations. In the next section, we briefly describe the mathematical formalism to account
for the polarization emission. Since most of the techniques used in this thesis are to observed
the polarization produced by interstellar grain, in the following section I review on the physics
involved in the alignment of grains with respect to the interstellar medium as well as the production
of polarized light. Then I describe what type of science we can extract by using polarimetric
observations at different wavelengths. Finally, the goals and motivation of this thesis is given.
1.2 Linear polarimetry: mathematical formalism
The polarized light from astrophysical objects was first observed by Hall (1949) and was attributed to the differential extinction of starlight when it crosses media containing elongated dust
grains preferably aligned. It is generally only a few percent of the total intensity. Observationally,
the polarized light detected by any instrument is defined as
)
Imax − Imin
,
P = 100
Imax + Imin
(
(1.1)
where Imax and Imin correspond to the maximum and minimum of intensity, respectively. For an
unpolarized flux, Imax = Imin and equation 1.1 vanishes. The most general state of light possesses
a partial and elliptical polarization degree. It is thus decomposed into two beams:
• Natural: unpolarized beam of intensity I(1 − PE ) and
1.2. Linear polarimetry: mathematical formalism
5
Figure 1.3: General case of a polarized beam (elliptical polarization): the scheme shows a
projection of the E -field vector on the xy plane (the x direction points to the North Celestial
Pole).
• Total and elliptically polarized, with Intensity IPE = (Q2 + U 2 + V 2 )1/2
where P is de polarization degree and I (radiation total intensity), Q, U and V are the Stokes
parameters which will be defined shortly.
The wave vector of a polarized beam draws an ellipse in the celestial sphere. The angle θ
between the semi-major axis of the ellipse and the North-South direction (measured in a counterclockwise sense from the NS direction) is called the position angle (P.A.) of the vibrational
plan. The ratio of the semi-minor to semi-major axis of the ellipse is defined as tan β (Fig. 1.3).
Therefore, the Stokes parameters are defined as (Serkowski 1974):
Q = IPE cos 2β cos 2θ = IP cos 2θ
(1.2)
U = IPE cos 2β sin 2θ = IP sin 2θ
(1.3)
V = IPE sin 2β = IPV
(1.4)
where P = PE cos 2β is the degree of linear polarization and PV = PE sin 2β is the degree of
elliptic polarization, which is positive if the vector rotates clockwise and negative if it rotates
counterclockwise. In terms of linear and circular polarization vector basis, the Stokes parameters
6
can be formulated as
I = ε2x + ε2y
Q =
ε2x
−
ε2y
(1.5)
(1.6)
U = 2ε x εy cos δ
(1.7)
V = 2ε x εy sin δ
(1.8)
I = ε2l + ε2r
(1.9)
and
Q = 2εl εr cos δ
(1.10)
U = −2εl εr sin δ
(1.11)
V = ε2l − ε2r
(1.12)
where ε x and εy are the vector projection on a linear basis ( x̂, ŷ); εl and εr are the projection on a
circular basis (r̂, l̂) and δ is the phase difference between each vector.
By a rearrangement of equations 1.2 and 1.3, we have
P = (Q2 + U 2 )1/2 /I
1
tan−1 (U/Q).
θ =
2
(1.13)
(1.14)
These are the essential quantities in the study of linear polarization: the degree of polarization
(1.13) and the P.A. (1.14). Unlike polarization vectors, the Stokes parameters are additive. It
means that the Stokes parameters which describes a mix of various beams of incoherent light is
the sum of parameters of each component.
1.3 Mechanisms of grain alignment and dust polarization
It is generally accepted that dust grains rotates with their long axis perpendicular to magnetic
field lines. The physical mechanism through which grains achieve this final dynamical state is still
a matter of debate (Lazarian 2003, 2007). Since this is not the main scope of this thesis, a brief
overview will be provided. The first step on grain alignment theory was done shortly after the
discovery of interstellar polarization. Almost simultaneously, the first models were proposed by
Davis & Greenstein (1951) and Gold (1952), the former based on paramagnetic relaxation and the
latter based on mechanical alignment.
Although the current view of grain alignment theory is elegantly developed with new physical
ingredients, Davis & Greenstein mechanism is still commonly invoked in the literature as the
dominant process. It proposes that spinning dust grains containing magnetic momentum reach
the most stable state of energy when they are rotating perpendicularly to the magnetic field lines
1.3. Mechanisms of grain alignment and dust polarization
7
into which they are immersed. Paramagnetic dissipation (or relaxation) happens due to the initial
misalignment between the internal field of the grain (Bg ) and the external field (B0 ). This generates
a mechanical torque which acts to align the grain magnetization and the external field (Fig. 1.4).
A brief quantitative view of this process is given next. A torque is the temporal derivative of
the angular momentum ~L of the spinning grain. Once its rotational energy is given by Erot = 12 Iω2
(where I is the grain moment of inertia and ω the angular speed), we have
dErot
˙
~ω
= I(~
ω. ω
~˙ ) = ~L.~
ω = N.~
dt
(1.15)
~ is the cumulative magnetic torque suffered by the grain. According to the formulation of
where N
Davis & Greenstein (1951), when the axis of larger angular momentum lies parallel to the external
field and to the grain angular speed, the torque no longer applies and the system achieves a stable
state where energy is invariant. Thus the left side of equation 1.15 vanishes and ~L is conserved.
However, the expected paramagnetic relaxation time scale is too large to be an efficient mechanism
of the grain alignment in the interstellar medium.
Nowadays the most successful models consider that anisotropic radiation fields are also capable to align dust grains and, in fact, suggest that this mechanism is more effective than the
paramagnetic relaxation (Hoang & Lazarian 2008, 2009). The alignment via radiative torques was
first studied by Dolginov (1972), who proposes ideal conditions for alignment even under weak
radiation fields. As an example, the radiation fields produced by Hii may generate a high degree
of grain alignment due to the anisotropy in the temperature. Later, Draine (1996) showed that this
mechanism could be much more efficient and present in the universe than previously thought. The
magnitude of those torques has been recently considered substantial for a great variety of grains
(Lazarian 2003).
There is an alternative mechanism to align the grains without invoking to the magnetic fields:
mechanical alignment through anisotropic particle flux, which was also proposed soon after the
discovery of polarized light from astrophysical objects (Gold 1952). This process is supposed to
occur in low dense media with a very residual interaction between photons and particles. However,
no observational support to this model has been presented so far.
Independently of the true mechanism that takes place in the interstellar medium, a final configuration where grains rotate perpendicularly to field lines and parallel to each other is expected. In
regions of the interstellar medium with a significant amount of dust grains (molecular clouds) this
mechanism generates a partially dichroic medium: Dust grains are believed to have some fraction
of atoms containing magnetic momentum in their composition. Therefore they are expected to
interact with electromagnetic waves which fill the interstellar medium. When the radiation fields
pass through dusty clouds, the grains may absorb or scatter the electric field component parallel to
its longest axis. This is so because free electrons in the grain respond more easily to the oscillating E-field component at this direction. As a consequence, the transversal, non-absorbed E−field
component survives to this interaction and leaving the region of aligned dust grains practically
unaltered (Fig. 1.5, left panel), so the outcoming radiation is polarized. The magnetic field is
8
ω
θl
Bg
B0
Figure 1.4: Scheme of a spinning dust grain with internal field Bg and immersed in a uniform
field B0
a vectorial physical entity, so one can conclude that the closer is the magnetic field field to the
plane-of-sky, the higher is the polarization degree. Conversely, if the field is in the line-of-sight
(LOS) direction, the net polarization flux is zero since there is no preferred direction on the grains
distribution on the POS. Therefore, it is worth to emphasize that linear polarization maps trace the
2-D component of the magnetic field as projected against the plane-of-sky. In order to obtain a
full 3-D picture of the magnetic field, it is necessary to observe the LOS field component, which
can be measured using different observational techniques.
When the polarization map of a portion of the sky is obtained, it traces the mean direction of
this transversal field component, which in turn is perpendicular to the mean direction of grains
longer axis. Since that the size of interstellar dust has the same order of magnitude as shorter
wavelengths, this effect is observed at visible and near-infrared bands and, therefore, is limited
to low extinction media (a few magnitudes). Due to this constraint, optical and near-infrared
polarization maps are usually associated with the diffuse gas (n(H2 ) ∼ 102 -103 cm3 ) present in
molecular clouds at large physical scales.
Similarly, the thermal continuum emission which arises from non-spherical, rotating dust
grains aligned with the magnetic field is also polarized (Hildebrand 1988). In this case, the polarization vectors are parallel to the mean orientation of the elongated grains (Fig. 1.5, right panel).
This effect is detected at longer wavelengths, specifically at far-infrared, submillimeter and millimeter bands.
It is important at this point to introduce a quantity called efficiency of grain alignment, defined
as the ratio of polarization to visual extinction (P/AV ). This quantity is related to the degree of
alignment that some ensemble of dust grains can achieve. For the case of differential extinction,
and assuming an ideal scenario where the polarizer medium is highly efficient, Mie computations
predict that P/AV should be not larger than 14% mag−1 for visible wavelengths (Whittet 2003).
Observations have proved that this ideal scenario is far from being reached. The maximum ef-
1.3. Mechanisms of grain alignment and dust polarization
9
Eperp
B
Epar
B
ω
ω
S
Dust grain
Dust grain
Eperp
Epar (thermal emission)
S
S
Figure 1.5: Left: polarized light produced by differential extinction (optical and near-infrared
wavelengths). Right: polarized light produced by thermal emission (radio wavelengths).
ficiency observed for the Galactic interstellar medium is ∼ 3% mag−1 (Serkowski et al. 1975),
indicating that the diffuse gas is not a good polarizer.
The dust polarization observations provide information of the projected magnetic field morphology in the plane-of-sky. However, there is no direct way of measure the magnetic field
strength. Instead, the assumptions of magnetic grain alignment theory combined with polarization maps are the most straightforward way to estimate the field strength. Chandrasekhar & Fermi
(1953) proposed one of the first methods to calculate field strengths by correlating the dispersion of position angles (P.A.) of polarization vectors with the degree of turbulence, in such a way
that ordered fields are represented by vectors with a very low dispersion in P.A. and vice-versa.
Quantitatively, it is expressed by
B∝
1
∆θPA
(1.16)
where ∆θPA is the angle dispersion. Ostriker et al. (2001) showed that this relation is accurate only
for strong field cases, where ∆θPA ≤ 25◦ . Nevertheless, it is still a good approximation to derive
the POS magnetic field intensity.
Recently, a more elegant formulation based on statistical arguments has proven to be more
accurate to derive the magnetic field properties in a molecular cloud. This approach determines an
autocorrelation function for the position angle by measuring the dependence of the angle dispersion with respect to the distance between each pair of vectors. Very recently, several authors have
used this method to study the dynamical state of molecular clouds by comparing the length scale
through which turbulence or magnetic field prevails (Falceta-Gonçalves et al. 2008; Hildebrand
et al. 2009; Houde et al. 2009). If a large sample of polarization data is available, it is possible
to compare distinct physical scales within the same cloud. A more detalied explanation of this
method is given in Chapter 4 of this thesis.
10
1.4 Molecular line polarization
Under the presence of a magnetic field, the rotational lines split in magnetic sub-levels, and
the emission can be polarized, in some cases circularly and in others linearly. The “amount” of
splitting of the sub-levels, δνZ (in frequency terms) and also called Zeeman splitting, is proportional to the magnetic field strength and to the molecular magnetic moment. Except for masers,
in molecular clouds the Zeeman splitting can be measured in molecules with a large magnetic
moment (CN, OH, CCH). The Zeeman lines detected in the interstellar medium have linewidth,
δV, usually wider than δνZ and, in this cases, only the line-of-sight component of the field can be
determined through the circular polarization. In practice, assuming that the receivers of a radiotelescope are sensitive to circularly polarized radiation (left and right), so the separation between
the spectral lines detected in each receiver is proportional to BLOS . This difference is precisely the
Stokes Parameter V when defined in a circular basis (equation 1.12). Therefore, Stokes V ∝ dI/dν
(the mathematical representation of the difference between the line signals of each receiver where
I is the line intensity and ν is the frequency) which, in turn, is proportional to BLOS . For some
cases of maser emission (like OH), the Zeeman components are resolved (δνZ > δV) and the LOS
field strength can be directly derived from the Zeeman splitting term δνZ . The theory of Zeeman
processes in molecular clouds is well explained in Crutcher et al. (1993).
Molecules with a small magnetic moment can still show polarized emission if the different
magnetic sub-levels are populated unequally. In this case the polarization is linear (Goldreich &
Kylafis 1981, 1982). Collisions do not distinguish between the different sub-levels, so they tend
to populate equally them. Only anisotropic radiation will make possible the rise of molecular
linear polarization. But there are others factors that affect the degree of polarization, such as the
magnetic field field geometry respect to the LOS and line optical depth.
1.5 Multi-wavelength polarimetry
For most of the scientific results described in the next sections, we assume that the dust grains
are aligned perpendicularly to the magnetic field lines (as stated before there is not proof that the
alternative alignment mechanism, mechanical alignment, is efficient in molecular clouds). Therefore, the polarization maps obtained in visible and near-infrared bands use background stars with
respect to the observed molecular cloud and the polarization is parallel to the POS component
of the ambient magnetic field, while the dust polarization maps at submillimeter and millimeter
wavelengths have to be rotated by 90◦ in order to trace the magnetic field.
1.5.1 Optical and near-infrared polarimetry
The Galactic magnetic field has been extensively investigated by several authors via optical
polarimetry (Mathewson & Ford 1970; Klare et al. 1972; Axon & Ellis 1976). Those studies
suggest that the Galactic field lies mainly in the Galactic plane, although some large structure is
1.5. Multi-wavelength polarimetry
11
Figure 1.6: POS component of the magnetic field as derived from optical polarimetry for the
Lupus 1 (left panel) and the Musca dark clouds (right panel). Both data sets were collected at
the Observatório do Pico dos Dias (LNA/MCT – Brazil). Lupus data are still unpublished while
the Musca data are from Pereyra & Magalhães (2004)
also seen out of the plane (Axon & Ellis 1976). Locally, the magnetic field may assume distinct
morphologies which depends on the dynamical properties of the interstellar medium. Figure 1.6
shows some examples of complex magnetic field configurations in the Lupus and Musca dark
clouds (Pereyra & Magalhães 2004). Polarization maps provide help to study the dynamical state
of molecular clouds as indicated by the magnetic field morphology, as well as the grain properties
of such objects. Nevertheless, the accuracy on the determination of the POS field geometry depends largely on the statistics of the collected data. Optical/near-infrared polarimetry is based on
the observation of background (or “field”) stars supposedly located behind the cloud whose field
geometry is to be established. Therefore, it is important that the observed cloud is not far from the
Galactic plane, where a large number of background stars can be sampled. In addition, as already
mentioned in section 1.3, this technique is less sensitive to high visual extinction regions, where
the field stars may be largely obscured.
Infrared polarization in star-forming regions can be connected to dust scattering rather than
differential absorption. In this case, polarized light arise from infrared reflection nebulae associated to disks and envelopes of young stars. Maps of polarization due to dust scattering have their
pattern usually correlated to the distribution of material around the sources. As examples, Simpson
et al. (2006) and Kandori et al. (2007) estimated the position of illuminating sources in plasmas
by analyzing centrosymmetric patterns obtained in their polarimetric maps for the hot components
of the gas. Those patterns are centered in candidate sources previously suggested as illuminating
stars or, in some cases, new candidates may be revealed via high resolution data (Fig. 1.7, left
panel). Also, some assumptions associated to the magnetic field morphology, grain properties and
the evolutionary stage of infrared sources can also be derived from the degree of core polarization
12
Figure 1.7: Left: near-IR polarization field of NGC 2024 (Kandori et al. 2007). The centrosymmetric pattern is centered in the ionizing source IRS 2b. Right: Image of RY Tau and its knots
(Pereyra et al. 2009). The black arrow is the H -band polarization vector, with is parallel to the
jet (perpendicular to the disk).
(Beckford et al. 2008).
Down to much smaller physical scales, Young Stellar Objects (YSO’s) also produce optical
and near-IR polarized light via scattering in their circumstellar disks. This phenomenon, studied
by several authors (Angel 1969; Brown & McLean 1977; Mundt & Fried 1983; Bastien & Menard
1990), is associated with the photometric properties of such disks. Specifically, it is possible
to derive the optical depth of circumstellar disks via polarimetry. There is a general trend that
polarization vectors generated in optically thin disks are produced by single scattering and are
oriented perpendicular to the disk plane. On the other hand, optically thick disks have a net
polarization direction parallel to the disk plane, since multiple scattering is expected in this case.
Several authors reported observational support to this trend. In particular, Pereyra et al. (2009)
carried out a H-band survey on YSO’s with distinct kinematics and disk properties, and obtained
exactly the bimodal distribution previously predicted (Fig. 1.7, right panel).
The polarization observations at visible/near-infrared wavelengths are limited by the visual
extinction. Only the diffuse gas of molecular clouds and core envelopes are sampled. Visual
extinctions (AV ) larger than a few tens of magnitude are usually opaque to the optical/near-IR
background starlight. Optical polarization studies toward molecular clouds have found that the
polarization fraction increases with AV for small values of AV , but at some point the polarization
degree ”’saturates” and remains constant as AV increases. This effect, usually called “depolarization”, seems to be a global phenomenon detected in a wide range of wavelengths (Goodman et al.
1992, 1995; Gerakines et al. 1995; Schleuning 1998; Matthews et al. 2001). The physical conditions which produce such effect are still a matter of debate but several factors should be consider.
Dust grains may lose their ability of keeping aligned to the magnetic field at increasing volume
densities, because of the increasing number of collisions or changes in the dust grain properties.
13
Figure 1.8: Left: diagram of Polarization Degree (P) × Trigonometric Parallax (π) for the Pipe
nebula (Alves & Franco 2007). Right: diagram of Visual Extinction (AV ) × Parallax for the Pipe
nebula (Lombardi et al. 2006).
Alternatively, twisted magnetic fields within the densest part of the cloud would produce the net
polarization flux to decrease.
Applications of optical linear polarimetry: a distance estimator for nearby clouds
Alternatively, optical polarimetry can be used to estimate distances to molecular cloud in a
similar way that interstellar extinction is used. As examples, this technique was adopted to determine distances to the Lupus clouds (Alves & Franco 2006) and the Pipe nebula (Alves & Franco
2007, Chapter 2 of this thesis). Basically, it consists of observations of background stars with well
known distances (e. g., Hipparcos stars: ESA (1997)) spread over the cloud angular size. If a
large distance range is covered, a sharp increase in the polarization degree of those stars located
in the cloud position and beyond is observed. This method is very useful to measure distance of
nearby objects because the expected contamination of foreground stars is only residual. Figure 1.8
shows a comparison between this technique and the similar one based on interstellar extinction
measurements in order to derive a distance value to the Pipe nebula. Both methods are consistent
within the measured uncertainties, the polarimetric distance being 145 ± 16 pc (Alves & Franco
2007) and the extinction distance being 130 ± 15 pc (Lombardi et al. 2006). Therefore, these
results make optical polarimetry a trustworthy method to determine distance of nearby molecular
clouds.
1.5.2 Submillimeter and millimeter polarimetry
Despite the observational techniques at submm/mm wavelengths are quite different from the
optical/near-IR, the data processing is similar. Yet, the polarization vectors trace the the projection
in the plane-of-sky of the grain orientation. A rotation of 90◦ is thus applied to this ensemble
of vectors in order to obtain the POS field projection. The dust thermal continuum emission at
14
submm/mm wavelength is proportional to the total column density of the molecular cloud, and
therefore to the visual extinctions. The dust emission in molecular cloud peaks at the far-IR. However, this spectral window is not accessible from the ground so polarimetric observations are sparse
(and done with airborne telescopes). The recently launched Planck satellite will provide far-IR polarization maps at large scale. Most of polarimetric observations are done in the submm regime,
where the dust is still very bright and it is accessible by ground based telescopes mounted at very
high altitudes (e.g. Mauna Kea). Because a high sensitivity is need for measuring the polarization,
the submm polarimetry usually trace region with high extinction (the densest parts of molecular
clouds). Polarimetric observations done with single-dish telescopes (JCMT, CSO, APEX) allow to
sample wide region of molecular clouds. On the other hand, the polarimetric observations carried
out with aperture-synthesis telescopes (SMA) allows to resolve out the extended component of the
molecular cloud and trace the dense cores and the circumstellar (disks) environments.
A part from the dust polarization at these wavelengths is possible to detect lineal and circular
polarized emission from molecular rotational transitions. However, for non-masing emission, the
linear polarization has been detected only in few cases for the CO rotational lines, and the circular
polarization for CN.
Applications of submm/mm polarimetry: studying the dynamics of protostellar cores
The science to be achieved in this case is related to the role of the magnetic field in the collapsing process. Submillimeter emission from protostellar cores trace the dust component usually
associated with their denser portions. If a fraction of this emission is linearly polarized, it suggests
that dust grains in the core are aligned with respect to the core magnetic field. Therefore, the final
map outlines the field configuration in the core, what carries several information on the dynamic
regime of the source. Among them, the evolutionary state of a protostellar core is obtained from
the magnetic field topologies observed. Several physical parameters like magnetic pressure and
magnetic-to-turbulent energy ratio can be derived from a single set (Girart et al. 2006). Moreover, when molecular data are combined with polarization data, hints on the kinematics of the
collapse process can be inferred. For example, effects of magnetic braking, which implies in
a non-conservation of the system angular momentum, can be detected when velocity gradients
traced by molecular line data are not consistent with centrifugally supported rotating disks. This
process is predicted by models (Basu & Mouschovias 1994; Mellon & Li 2008) and was already
confirmed obsevationally (Girart et al. 2009). Another example of how molecular line data and
polarization data can be combined is given by Frau et al. (2010), who found that cores in the Pipe
nebula with less ordered magnetic fields are more evolved chemically than magnetized cores.
For the case of molecular line polarization, it has being detected mainly toward in molecular
outflows powered by protostars or diffuse molecular gas around protostellar dense cores. These
observations provide a connection between the dense core magnetic field and the ambient field, and
may help to understand the dynamics of outflows. As an example, Girart et al. (1999) observed that
the outflow ejected by NGC 1333 IRAS 4A interacts with the magnetic field through Goldreich-
15
Kylafis detections in the CO (2 → 1) lines. Line emission in high-mass protostars were also
reported (Cortes et al. 2008; Beuther et al. 2010).
Finally, CN Zeeman data are good tracers for relatively dense gas (105 < n < 106 cm−3 )
and therefore important for cloud characterizations. Falgarone et al. (2008) observed several starforming regions and their magnetic field detections are mostly associated with dense cores in a
supercritical stage, what is consistent with ambipolar diffusion models. Others Zeeman species
are discusses in section 1.5.4.
1.5.3 Mid-infrared polarimetry: the ambiguity problem
Mid-infrared polarimetry is poorly reported in the literature compared to other wavelengths.
This is because, only recently mid-IR telescopes have included polarimetry in their observing
modes. At mid-infrared (MIR) wavelengths, the observed polarization is due to absorption by, or
emission from, aligned aspherical dust grains (see e.g. Aitken (1989)). Polarization arising from
scattering, which dominates at shorter wavelengths, can largely be neglected in the MIR because
of the negligible scattering cross-section of dust grains at MIR wavelengths.
The MIR is halfway between optical and radio bands, thus it possesses contribution of both
mechanisms, which implies an extra inconvenient to the data reduction. Observational projects
must take into account the disentangling of the two components in order to avoid ambiguity on the
orientation of polarization vectors. Observers must somehow circumvent this problem during the
data acquisition. An example of disentangling technique was suggested by Aitken et al. (2004),
who proposes that by imaging at a minimum of two wavebands (say, N and Q), one is able to
distinguish between polarization generated by dichroic absorption and thermal emission. Since no
MIR observations were performed for this thesis, and that this technique is not fully explored by
the astronomical community, no further discussions will be provided.
1.5.4 Centimeter polarimetry
The Zeeman effect is more easely measured at centimeter wavelengths through thermal emission of HI and OH and also from maser emission of SiO, H2 O and methanol lines (Troland &
Heiles 1982; Fiebig & Guesten 1989; Crutcher et al. 1993, 1996). Hyperfine transitions of each
species trace distinct densities. For example, OH Zeeman observations sample the diffuse components of the molecular cloud (n(H2 ) ∼ 102 -103 cm−3 ), so it is equivalent as using optical polarimetry of background stars. The difference is that OH observations have usually a very low angular
resolution (feq arcmin for single-dish radio telescopes), while the optical polarimetry is a pencil
beam technique. At the other extreme in the volume density regime, for example, the water masers
are excited at much more dense gas (n(H2 ) ∼ 109 -1010 cm−3 ).
At cm wavelengths there are other mechanism that produce polarized emission in the interstellar medium, such as, Faraday Rotation or synchrotron radiation. But this effects are out of the
scope of this thesis.
16
Figure 1.9: Compilation of several magnetic field strengths measurements using distinct Zeeman tracers (H i, OH and H2 O). Figure extracted from Fiebig & Guesten (1989).
1.6 The magnetic field-density dependence
The relationship between the magnetic field strength and the volume density of a collapsing
spherical cloud is given generally by the following power law: |B| ∼ ρκ . In this process, if the
magnetic field is weak enough to allow free-fall collapse, the conservation of magnetic flux and
cloud mass in the collapsing process leads to κ ∼ 2/3. Nevertheless, the gas motions of an
isothermal spherical cloud threaded by a strong magnetic field take place along field lines and form
a flattened structure. Under some assumptions on the hydrostatic equilibrium between gravity
and thermal pressures, the power law decreases slightly to 0.5 (a complete discussion on such
assumptions is found in Crutcher 1999). This value is confirmed by ambipolar diffusion models of
Fiedler & Mouschovias (1993), who predicted that κ ≃ 0.47. Figure 1.9 shows the observational
evidence of such dependence for field strengths ranging from µG in the diffuse media (n ≤ 100
particles per cm−3 ) to a few mG in core envelopes (n ≃ 107 particles per cm−3 ). Therefore, for
water masers pumping regions, a total B field strength of a few tens of mG is expected.
1.7 The thesis science cases: objects at distinct dynamic regimes
The science case of this thesis is focused in the study of the role of the interstellar magnetic
field in the star formation process at different physical scales. This study is connected with the gas
dynamics at distinct density components. For this purpose, an extensive observational work using
distinct astronomical facilities was performed. A multi-scale picture is achieved when distinct
magnetic field tracers are used. With this technique, the research described in this thesis aims
to study the evolution of astrophysical objects based on their magnetic field morphology. Starforming theories predict that both quantities are closely related, so the thesis goal is to search
1.7. The thesis science cases: objects at distinct dynamic regimes
17
for observational evidences for those models. In a more general aspect, this investigation aims
to provide an heterogeneous polarization database for molecular clouds at distinct evolutionary
stages.
This work is based mostly on observational results obtained in four distinct bands:
• Visible data (R-band, λ0 ∼ 6474 Å) collected with the Observatório do Pico dos Dias (OPDLNA/MCT, Minas Gerais, Brazil),
• Near-infrared data (J-band, λ0 ∼ 1.25 µm) collected with the William Herschel Telescope
(ING/ORM, Canary Islands, Spain),
• Submillimeter data (λ0 ∼ 0.87 mm) collected with the Submillimeter array (SMA, Hawai’i,
USA)
• Centimeter data (λ0 ∼ 1.3 cm) collected with the Very Large Array (VLA/NRAO, New
Mexico, USA).
The strategy adopted was multi-wavelength polarimetry in order to obtain the desired multiscale picture of the magnetic field. For the visible and near-infrared wavelengths, two molecular
clouds at very distinct evolutionary states are studied. At radio wavelengths, the magnetic field
structure and magnitude of two protostellar cores of distinct masses are analyzed.
In chapter 2, the results of optical polarization observations with the OPD toward Hipparcos
stars are reported. The idea is use polarimetry as an alternative tool to determine distances to
nearby molecular clouds.
In chapters 3 and 4, the global and local polarimetric properties of the Pipe nebula are described. The details of an extensive optical polarimetric survey performed with the OPD along
its whole structure are shown. This object is particularly interesting due to its low efficiency in
forming new stars, despite of its large mass (104 M ⊙ , Onishi et al. 1999). With this investigation,
we try to understand this unexpected quiescent state by probing its magnetic field morphology and
its effects on the cloud dynamical evolution.
In chapter 5, we report the results of polarization investigations toward NGC 1333, a very
active cloud where several low-mass protostars and YSO’s are found. The goal is to compare the B
field in the diffuse gas around IRAS 4A with respect to the B field properties derived from submm
observations. In order to achieve this goal, we used optical and near-IR polarimetric techniques
with the OPD and WHT.
In chapter 6, results of SMA dust continuum polarization data and CO line data toward the
intermediate-mass core NGC 2024 FIR 5 are described. This research aims to study the the magnetic field at core scales, taking advantage of the high sensibility of the SMA for polarization
investigations. Specifically, we intend to determine if the collapse regime of the core is regulated
by its magnetic field.
18
In chapter 7, VLA polarization observations of H2 O masers are used to study the magnetic
field of the low-mass protostar IRAS 16293-2422. Our goal is to determine the field strength at
very high densities, where usually dust observations are limited by the high visual extinction.
Finally, the conclusions of these investigations are stated in chapter 7. A compilation of the
achieved results are reported, as well as general conclusion is provided.
Chapter 2
An accurate determination of the
distance to the Pipe nebula1
2.1 Introduction
The knowledge of accurate distances to molecular clouds is crucial for calibrating the physical
parameters associated with them. Elegant methods for analysing star counts have been worked out
by many astronomers and are frequently used to estimate distance, extinction power, and radial
extension of interstellar clouds. However, these techniques are unable to give accurate distances
since they rely on assumptions that may be inadequate for the region under investigation.
Another classical approach has been to use the photometry of dense grids of stars in a photometric system able to measure accurate colour excesses and provide rather precise photometric
distances. Strömgren photometry has been successfully applied for this purpose, but stars with
spectral types later than G2 – G5 have not been accurately calibrated in this photometric system.
The availability of high-quality Hipparcos trigonometric parallaxes has inspired alternative
methods. For instance, Knude & Hog (1998) combined the (B−V) provided by the Hipparcos and
Tycho catalogues with spectral classification from the literature to estimate colour excesses, and to
further construct colour excess vs. distance diagrams for several local interstellar clouds. In spite
of this method being very useful as a first attempt at estimating the distance to local interstellar
clouds, the use of spectral types retrieved from survey catalogues may jeopardise the accuracy of
the obtained result.
The literature provides many examples where Hipparcos parallaxes are combined with other
measurements in order to yield distance estimates to objects of interest. For instance, in a previous
work we successfully combined Hipparcos parallaxes with linear polarimetry using CCD imaging
to investigate the distribution of the interstellar medium in the vicinity of the dark cloud Lupus 1
(Alves & Franco 2006).
1
Published in Alves, F. O. & Franco, G. A. P. 2007, Astronomy and Astrophysics, 470, 597
19
20
Chapter 2. An accurate determination of the distance to the Pipe nebula
In this paper we present the results of B-band linear polarimetry using CCD imaging obtained
for stars selected from the Hipparcos catalogue (ESA 1997) with lines of sight toward the Pipe
nebula, a dark cloud that seems to be associated with the large Ophiuchus molecular complex.
Although apparently a potential site for stellar formation, the Pipe nebula has not attracted
attention until recently. The detailed map of 12 COobtained by Onishi et al. (1999) for the whole
Pipe nebula point to a mass of ∼104 M⊙ and indicates that the nebula consists of many filamentary
structures. In spite of the many identified C18 Ocores whose masses are typically ∼30 M⊙, star formation seems to be active only on Barnard 59 (B 59), located at the northwestern extremity of the
nebula. However, there is evidence that B 59 is producing young stars with high efficiency (Brooke
et al. 2007). Based upon stars from the 2MASS catalogue, Lombardi et al. (2006) produced a highresolution extinction map of the Pipe nebula. The near infrared extinction map correlates well with
the molecular one and corroborates the estimated mass.
Previous distance estimates suggest that the Pipe nebula is a local cloud; however, the estimated values are rather uncertain. Onishi et al. (1999) suggest a distance of ∼160 pc, supposing
that this cloud is connected with the Ophiuchus dark cloud complex (they assumed the value estimated by Chini 1981). Lombardi et al. (2006) obtained 130+13
−20 pc from a method similar to the
one applied by Knude & Hog (1998), in agreement with the value suggested by de Geus et al.
(1989) and Bertout et al. (1999) for the distance to the Ophiuchus complex (note that de Geus
et al. formally estimate a distance range of 60–205 pc for the Ophiuchus dark clouds, with their
centre defined as 125±25 pc).
The good quality of our polarimetric data allows us to probe the interstellar medium in the
direction of the Pipe nebula and to obtain an accurate distance to this cloud.
2.2 Observations and data reduction
The polarimetric data were collected with the IAG 60 cm telescope at the Observatório do
Pico dos Dias (LNA/MCT, Brazil) in missions conducted from 2003 to 2005. These data were
obtained with the use of a specially adapted CCD camera to allow polarimetric measurements
— for a suitable description of the polarimeter see Magalhães et al. (1996). The B-band linear
polarimetry using CCD imaging was obtained for 82 Hipparcos stars with trigonometric parallaxes
πH ≥ 5 mas, which corresponds to a distance coverage up to 200 pc and ratios of the observational
error to the trigonometric parallax given by σπH /πH ≤ 1/5. The selected stars have lines of sight
toward a large region around the Pipe nebula, limited by Galactic coordinates: −5◦ < l < +4◦ ,
+1◦ < b < +9◦ , covering an area slightly larger than the one surveyed in molecular lines by Onishi
et al. (1999).
When in linear polarization mode, the polarimeter incorporates a rotatable, achromatic halfwave retarder followed by a calcite Savart plate. The half-wave retarder can be rotated in steps of
22.◦ 5, and one polarization modulation cycle is covered for every 90◦ rotation of this waveplate.
This arrangement provides two images of each object on the CCD with perpendicular polarizations
2.2. Observations and data reduction
21
(the ordinary, fo , and the extraordinary, fe , beams). Rotating the half-wave plate by 45◦ yields in
a rotation of the polarization direction of 90◦ . Thus, at the CCD area where fo was first detected,
now fe is imaged and vice versa. Combining all four intensities reduces flatfield irregularities.
In addition, the simultaneous imaging of the two beams allows observing under non-photometric
conditions and, at the same time, the sky polarization is practically canceled. Eight CCD images
were taken for each star with the polarizer rotated through 2 modulation cycles of 0◦ , 22.◦ 5, 45◦ ,
and 67.◦ 5 in rotation angle. For each star, an optimum integration time was chosen to obtain a high
signal-to-noise ratio, but they stay below the CCD saturation level.
The CCD images were corrected for readout bias, zero level bias, and relative detector pixel
response. After these normal steps of CCD reductions, we performed photometry on the pair of
polarized stellar images in each of the eight frames of a given star using the IRAF DAOPHOT
package. In many cases, we gathered as much as ∼106 counts per stellar beam after performing
aperture-photometry. From the obtained file containing count data, we calculate the polarization
by using a set of specially developed IRAF tasks (PCCDPACK package; Pereyra 2000). This set
includes a special purpose FORTRAN routine that reads the data files and calculates the normalized linear polarization from a least-square solution that yields the per cent linear polarization (P),
the polarization position angle (θ, measured from north to east), and the per cent Stokes parameters
Q and U, as well as the theoretical (i.e., the photon noise) and measured (σP ) errors. The last are
obtained from the residuals of the observations at each wave-plate position angle (ψi ) with respect
to the expected cos 4ψi curve and are consistent with the photon noise erros (Magalhaes et al.
1984). For a good review of the basic concepts and error analysis for polarimetric data obtained
with dual-beam instruments, the reader is referred to Patat & Romaniello (2006).
Zero-polarization standard stars were observed every run to check for any possible instrumental polarization and for systematic errors of our polarimetry. The measured polarizations proved
to be small and in good agreement with the values listed by Turnshek et al. (1990). The reference
direction of the polarizer was determined by observing polarized standard stars (Turnshek et al.
1990), complemented with polarized stars from the catalogue compiled by Heiles (2000). The
present project shared some of the observing nights with the one used to collect the data described
in our previous work (Alves & Franco 2006), to which we refer the reader for a detailed description
of the standard stars used and their standard errors.
Table 2.1 displays the obtained results for the observed stars, together with their identification
in the Hipparcos (HIP) catalogue (Column 1), the Michigan two-dimensional classification (Houk
1982; Houk & Smith-Moore 1988), when available (Column 2), equatorial coordinates for the
equinox 2000.0 (Columns 4 and 5), Galactic coordinates (Columns 6 and 7), visual magnitude
(Column 7), trigonometric parallax and standard error (Columns 8 and 9), polarization and measured error (Columns 10 and 11), and the orientation angle of the polarization vector (Column 12),
respectively. The polarization measured errors, σP , are smaller than 0.08% for all observed stars.
They are even substantially smaller than this in many cases because of the large gathered counts
of ∼106 and the small systematic errors of our polarimeter. This accuracy is corroborated by the
22
small errors found for the zero polarization standard stars (Alves & Franco 2006, Table 1).
As mentioned earlier, an optimum integration time was chosen to obtain a good signal-tonoise ratio for the selected target. Because the targets were usually bright, most of the obtained
CCD frames only allowed accurate polarization measurements for the Hipparcos program stars,
however, in few cases we were able to get the degree of polarization for other stars appearing in the
frames. Since this information will be useful in our later discussion, these results are introduced in
Table 2.2, which gives the star’s identification, when available (Column 1), equatorial coordinates
for equinox 2000.0 (Columns 2 and 3), Galactic coordinates (Columns 4 and 5), polarization and
measured error (Columns 6 and 7), and the orientation angle of the polarization vector (Column
8), respectively.
2.3 The sightline toward the Pipe nebula
2.3.1 Magnetic field structure
Based upon data from the 2MASS catalogue, Lombardi et al. (2006) constructed a highresolution extinction map of the Pipe nebula. The area covered by the map basically coincides
with the one investigated here. In Fig.2.1 we overlay the obtained polarization vectors in this extinction map. Since most of the observed stars show a low degree of polarization and these value
are not essential at this stage of our analysis, we have plotted polarized vectors proportional to the
square root of the polarization degree: with this convention one gets a better view of the orientation pattern. We interpret the polarization of background stars as due to dichroic absorption by a
medium of magnetically aligned grains. The polarization position angles therefore map the global
structure of the magnetic field within the medium.
At first glance we note, as indicated by the few highly polarized stars in Fig. 2.1, that the largest
filament from (l, b) ≈ (0◦ , 4◦ ) to (l, b) ≈ (357◦ , 7◦ ), corresponding to the “stem” of the “pipe”, is
roughly perperdicular to the large-scale magnetic field shown by the polarized stars (P & 1%)
in the region. This orientation suggests that the cloud collapse was steered preferentially along
the field lines and that magnetic pressure continues to support the cloud in the direction of the
elongation. In the stellar formation scenario proposed by Shu et al. (1987), this situation should
culminate in the formation of low-mass stars, similar to what is observed at other star formation
sites, such as the Chamaeleon I, Lupus, and Taurus-Auriga dark clouds (McGregor et al. 1994;
Strom et al. 1988; Tamura & Sato 1989, and references therein).
A more accurate analysis of Fig. 2.1 shows, however, some stars having polarization almost orthogonal to the one presented by stars with a higher degree of polarization. This fact led us to suppose the existence of two absorbing components subject to almost orthogonal magnetic fields. This
supposition may be tested by analysing the distribution of the obtained position angles. However,
the uncertainty in this quantity correlates with the signal-to-noise of the polarization measurement,
which is P/σ p (see for instance, Naghizadeh-Khouei & Clarke 1993), and since the majority of
2.3. The sightline toward the Pipe nebula
23
Table 2.1: B-band linear polarization of Hipparcos stars. For an explanation of each column,
see note below.
HIP
Spectral
Type
α2000
(h m s)
83194
83239
83541
83578
83659
84076
84131
84144
84147
84175
84181
84284
84314
84322
84355
84356
84391
84407
84416
84445
84494
84497
84533
84605
84609
84611
84636
84665
84684
84695
84761
84806
84851
84888
84907
84930
84931
84936
84987
84995
84999
F2 V
G1/2 V
K1 V
G3 V
B9.5 V
F3 IV/V
G0 V
G8 III
A0 V
B9 V(n)
G2 V
G0 V
F2/3 V
K2 V
F7 V
F8/G0 V
G8 III/IV
G8 IV
G0
B9/9.5 V
K1 III
G1 V
F0 V
B9.5 V
G0 V
G2/3 V
G3 V
G3 V
K0 V
F2 V
F6 V
F5 V
G8 III/IV
F7/8 IV + F/G
K0/1 V + (G)
A1 IV/V
A2 V
G1 V
G2 V
F0 V
G0 V
17 00 09.08
17 00 40.42
17 04 27.79
17 04 52.76
17 05 56.67
17 11 20.94
17 11 56.68
17 12 10.97
17 12 13.62
17 12 25.07
17 12 31.27
17 13 45.99
17 14 14.25
17 14 17.77
17 14 45.32
17 14 45.74
17 15 13.23
17 15 22.21
17 15 28.03
17 15 51.36
17 16 27.67
17 16 29.87
17 16 54.32
17 17 39.53
17 17 41.94
17 17 43.17
17 18 07.07
17 18 30.88
17 18 43.91
17 18 50.47
17 19 30.88
17 20 00.41
17 20 30.72
17 20 54.67
17 21 07.58
17 21 24.68
17 21 25.98
17 21 31.61
17 22 13.52
17 22 22.22
17 22 24.53
δ2000
(◦ ′ ′′)
-27 58 05.7
-27 47 32.4
-28 34 55.3
-27 22 59.2
-28 52 21.5
-25 01 53.4
-29 28 27.8
-27 02 31.7
-25 15 18.1
-27 45 43.2
-25 13 37.3
-24 03 07.9
-26 59 03.3
-28 42 24.4
-28 55 17.2
-25 55 26.0
-26 31 50.2
-27 58 13.1
-24 59 33.4
-30 12 38.2
-25 18 19.5
-27 33 54.9
-30 21 05.0
-26 37 44.3
-28 56 17.9
-30 46 13.7
-24 04 22.2
-29 33 19.8
-29 29 23.5
-25 10 37.0
-22 59 30.9
-30 25 44.9
-26 32 59.1
-27 20 39.7
-24 41 00.7
-26 26 05.7
-26 30 04.3
-22 55 33.1
-31 39 28.3
-31 17 50.5
-30 12 14.2
l
(◦ )
b
(◦ )
355.16
355.37
355.24
356.27
355.20
359.05
355.49
357.51
358.98
356.95
359.04
0.18
357.82
356.41
356.30
358.76
358.32
357.16
359.62
355.38
359.50
357.63
355.39
358.55
356.65
355.15
0.73
356.25
356.33
359.91
1.82
355.71
358.98
358.38
0.61
359.19
359.14
2.14
354.97
355.29
356.19
8.80
8.82
7.67
8.31
7.24
8.52
5.83
7.20
8.23
6.74
8.19
8.63
6.86
5.86
5.65
7.38
6.94
6.09
7.78
4.71
7.42
6.12
4.44
6.44
5.11
4.06
7.81
4.61
4.61
7.05
8.15
3.85
5.96
5.44
6.90
5.86
5.82
7.80
2.76
2.94
3.55
V
πH
σπ
(mag) (mas) (mas)
8.45
8.18
6.59
8.90
7.55
8.30
9.29
6.75
6.52
6.12
8.29
9.01
6.64
9.34
9.28
9.12
7.63
8.54
9.95
6.20
7.14
8.22
7.27
6.81
8.69
8.96
6.59
8.74
9.67
9.62
9.34
8.80
7.09
7.94
8.61
8.02
7.53
8.70
9.03
8.28
8.02
7.37
21.37
55.31
13.19
6.02
9.90
11.12
7.04
8.81
5.97
11.60
11.83
11.78
29.35
7.64
7.55
7.17
10.18
14.59
8.81
6.14
17.05
15.15
7.45
15.19
13.68
21.20
10.96
17.40
7.11
9.39
9.75
7.47
10.21
20.58
6.12
6.70
17.63
10.88
7.07
14.81
1.14
1.16
0.89
1.37
0.92
1.45
1.57
0.95
0.94
0.81
1.33
1.49
0.80
1.49
1.41
1.27
1.02
1.11
1.75
0.98
0.88
1.08
1.10
1.17
1.28
1.41
0.92
1.35
1.80
1.42
1.68
1.29
0.91
1.58
1.18
1.01
0.87
1.64
1.39
1.25
1.48
P
(%)
σP
(%)
θ
(◦ )
0.005
0.047
0.148
0.119
0.428
0.154
0.045
0.062
0.118
0.113
0.042
0.139
0.076
0.063
0.124
0.011
2.585
0.038
0.067
0.038
0.354
0.042
0.045
0.103
0.044
0.076
0.130
0.024
0.035
1.246
0.082
0.003
0.064
0.069
0.023
0.054
0.082
0.057
0.033
0.077
0.040
0.018
0.025
0.056
0.016
0.031
0.058
0.043
0.040
0.030
0.008
0.075
0.032
0.034
0.036
0.026
0.020
0.049
0.029
0.020
0.015
0.028
0.020
0.027
0.042
0.034
0.021
0.047
0.017
0.026
0.063
0.043
0.011
0.038
0.039
0.045
0.031
0.033
0.060
0.014
0.049
0.029
177.2
157.0
110.3
74.0
2.8
130.8
4.1
69.6
64.4
76.0
40.4
37.0
166.3
29.0
34.9
161.3
173.1
24.2
163.8
146.5
55.2
37.1
8.7
45.3
77.6
131.0
153.7
125.1
117.0
169.8
89.2
53.4
117.2
151.5
36.9
136.7
71.9
20.5
25.0
153.3
8.8
24
Table 2.1: continued.
HIP
85071
85081
85100
85132
85154
85176
85215
85246
85257
85278
85285
85299
85315
85318
85320
85391
85395
85521
85524
85538
85548
85561
85681
85703
85783
85797
85877
85882
85909
85920
85954
86086
86226
86278
86327
86376
86385
86633
86719
86858
86866
Spectral
Type
α2000
(h m s)
A2/3 IV
G8/K0 V
F0 V
K0 IV/V
K0 III
F5/6 V
G0
G
F8 V
A2/3 IV
G3/5 V
G3/6 V
F5 V
B9/9.5 V
G8 IV/V
B9.5/A0 V
G3 V
F3 IV/V
F0 V
G1/2 V
G2 V
K5 V
F5 V
F2 IV
B9 II/III
G2/3 V
F3 V
G5 V
G2/3 V
G3 V
F0 IV
F5 V
G0 V
F3 V
K5
F5 V
F8 V
F0 V
F8
F5 V
G8 IV/V
17 23 09.70
17 23 17.67
17 23 32.66
17 23 53.99
17 24 03.51
17 24 23.86
17 24 45.77
17 25 10.78
17 25 17.80
17 25 29.64
17 25 36.62
17 25 51.17
17 26 01.34
17 26 05.87
17 26 06.87
17 26 55.30
17 27 00.86
17 28 38.76
17 28 40.84
17 28 49.94
17 29 00.20
17 29 06.74
17 30 33.65
17 30 49.61
17 31 44.38
17 31 52.07
17 33 00.37
17 33 04.02
17 33 20.66
17 33 29.09
17 34 02.39
17 35 34.06
17 37 16.09
17 37 46.85
17 38 19.92
17 39 00.71
17 39 05.97
17 42 05.29
17 43 08.13
17 44 48.70
17 44 54.53
(◦
δ2000
′ ′′)
-25 05 51.1
-27 58 01.0
-31 42 01.2
-29 49 15.8
-23 50 39.5
-22 48 03.1
-27 46 42.7
-24 30 20.1
-26 08 45.8
-29 40 14.2
-21 37 54.1
-28 39 19.0
-23 10 17.4
-27 35 58.3
-28 32 35.9
-25 56 36.2
-25 16 17.5
-25 30 38.1
-31 23 03.0
-26 43 46.5
-24 20 11.1
-23 50 09.4
-27 12 11.8
-23 50 29.7
-26 16 10.8
-31 30 53.8
-24 19 22.5
-25 02 51.3
-27 28 10.7
-24 04 17.3
-23 01 52.6
-24 37 41.3
-24 35 36.1
-23 23 21.4
-27 12 18.2
-28 24 44.6
-26 56 14.6
-26 50 44.1
-26 10 37.1
-26 35 19.8
-24 41 02.4
l
(◦ )
b
(◦ )
0.53
358.16
355.10
356.69
1.69
2.61
358.50
1.28
359.92
357.01
3.75
357.90
2.51
358.81
358.03
0.30
0.87
0.87
355.97
359.87
1.90
2.34
359.69
2.55
0.62
356.23
2.41
1.81
359.80
2.69
3.63
2.47
2.71
3.79
0.62
359.68
0.94
1.37
2.06
1.91
3.55
6.28
4.65
2.51
3.50
6.81
7.32
4.49
6.23
5.30
3.30
7.73
3.80
6.81
4.34
3.81
5.11
5.46
5.02
1.77
4.32
5.60
5.85
3.73
5.52
4.02
1.13
4.84
4.43
3.07
4.88
5.33
4.18
3.87
4.42
2.28
1.51
2.28
1.76
1.91
1.38
2.35
V
πH
σπ
(mag) (mas) (mas)
7.28
9.42
7.76
7.59
6.67
8.65
9.73
9.80
9.11
6.82
8.37
9.03
8.19
7.49
7.78
6.42
9.49
7.06
7.60
8.63
8.39
9.61
8.55
7.39
6.05
9.55
8.48
9.66
9.48
8.55
7.36
7.70
8.72
8.28
10.35
7.68
7.70
8.10
10.01
8.80
8.84
6.33
14.78
12.34
12.56
6.19
14.95
10.08
18.23
8.10
5.25
20.78
14.24
9.28
6.43
8.71
7.71
7.99
9.06
11.12
13.19
17.25
55.03
11.20
10.46
7.47
9.34
9.70
13.47
8.62
13.91
13.38
18.51
14.37
8.98
18.49
12.29
19.38
5.67
10.16
10.21
8.77
0.88
1.79
1.08
1.13
0.90
2.26
1.94
1.79
1.49
1.05
1.21
1.52
1.11
1.17
1.14
0.85
1.35
1.81
0.99
1.34
2.00
1.68
1.82
0.96
1.10
1.63
1.37
1.50
1.60
1.28
2.00
1.06
1.26
1.78
2.22
1.07
1.18
1.08
1.80
1.55
1.44
P
(%)
σP
(%)
θ
(◦ )
0.251
0.044
0.033
0.025
0.339
0.101
0.042
0.066
0.036
0.633
0.083
0.042
0.090
1.226
0.026
0.049
0.049
0.028
0.110
0.043
0.049
0.010
0.091
0.083
0.020
0.037
0.065
0.042
0.022
0.053
0.033
0.053
0.073
0.083
0.029
0.025
0.065
0.444
0.109
0.087
0.273
0.021
0.029
0.021
0.021
0.038
0.043
0.024
0.027
0.038
0.057
0.039
0.045
0.054
0.027
0.029
0.067
0.050
0.040
0.044
0.017
0.024
0.041
0.031
0.037
0.039
0.038
0.032
0.029
0.025
0.018
0.042
0.070
0.016
0.033
0.050
0.029
0.042
0.029
0.051
0.010
0.024
74.2
39.9
64.7
108.3
81.4
111.5
46.6
13.0
80.4
170.6
127.4
167.8
57.6
159.6
169.6
102.0
178.2
125.0
80.5
107.9
167.2
126.8
32.7
107.3
123.1
54.2
169.1
138.3
141.1
78.3
179.4
168.7
54.5
140.1
114.8
42.8
69.5
147.1
178.4
125.7
147.2
Note: Columns 1 to 9 give the HIP number, spectral type, the right ascension and declination for the equinox 2000.0, Galactic longitude
and latitude, visual magnitude, trigonometric parallax, and standard error, respectively. Columns 10 and 11 give the obtained linear
polarization and measured error, respectively, and column 12 the position angle (measured from north to east) of the polarization
vector.
25
Table 2.2: Measured polarization for some stars contained in the same CCD frames as of the
Hipparcos stars. For an explanation of each column, see note below.
star
identification
α2000
(h m s)
(◦
δ2000
′ ′′)
l
(◦ )
b
(◦ )
P
(%)
σP
(%)
θ
(◦ )
Field of HIP 83194
-27 54 38.4 355.16 8.90 0.439 0.116
19.5
-27 54 26.4 355.18 8.87 0.717 0.156
26.9
HD 153351
-27 57 11.5 355.17 8.81 0.289 0.062 157.9
GSC 06818−02124
-27 59 47.8 355.17 8.74 0.710 0.057
12.6
Field of HIP 84144
CD−26 11983 17 11 47.58 -27 05 39.0 357.41 7.24 1.105 0.051
29.2
CD−26 11991 17 12 12.25 -26 58 48.9 357.56 7.23 2.090 0.117
18.3
Field of HIP 84611
HD 156198 17 17 29.04 -30 42 58.8 355.17 4.13 0.593 0.012
6.4
Field of HIP 84888
HD 156882 17 21 05.61 -27 25 04.5 358.34 5.36 0.091 0.048
90.7
Field of HIP 85797
HD 158598 17 31 34.96 -31 29 33.6 356.22 1.20 0.959 0.038 156.7
Field of HIP 86226
HD 159746 17 37 19.89 -24 33 54.0
2.74 3.88 0.793 0.053 136.3
Field of HIP 86327
17 38 06.62 -27 15 55.3
0.55 2.29 3.021 0.027 170.3
HD 316049 17 38 28.71 -27 13 00.7
0.63 2.24 3.736 0.108 169.0
Note: Star identification, when available, right ascension and declination for the equinox 2000.0, Galactic longitude and
latitude are given in columns 1 to 5, respectively. The other columns give the measured linear polarization, measured
error, and position angle (measured from north to east) of the polarization vector, respectively.
16 59 48.97
16 59 58.30
17 00 07.66
17 00 23.26
the observed stars show a low degree of polarization, the signal-to-noise is usually small for our
objects. To avoid polluting the distribution of the polarization angles by large uncertainties, only
stars having P/σP ≥ 2.0 were considered. The obtained distribution is given in Fig. 2.2 (left-hand
panel) and seems to support the existence of two, almost orthogonal, components. The shaded area
in this histogram represents stars having P/σP ≥ 4.0. Note that the bin [0◦ , 30◦ ] was shifted by
180◦ and appears at the end of the histogram. Stars belonging to the first component (∼60◦ ) show
a low degree of polarization, suggesting an origin in a low column-density medium (hereafter ‘diffuse component’), while many stars in the second component (∼160◦ ) are more heavily polarized
(hereafter ‘dense component’). We note that no stars introduced in Table 2.2 were included in the
histogram in Fig. 2.2; however, all star showing a relatively high degree of polarization, in that
table, have a position angle in the interval defined by the dense component.
One should be aware that a larger and more accurate sample is required in order to establish
the existence and characteristics of these two components; however, previous works have already
pointed out the complex nature of the magnetic field toward this direction in the solar neighbourhood. The skyplots presented by Axon & Ellis (1976, Figs. 1a and b) show this complexity
around the area investigated here and support the existence of two dominant components. More
26
0.1%
1%
o
8
7o
Galactic Latitude
6o
5o
4o
3o
2o
4o
3o
2o
1o
0o
359o
Galactic Longitude
358o
357o
356o
Figure 2.1: Dust extinction map of the Pipe nebula molecular complex obtained by Lombardi
et al. (2006), contour levels in steps of 0.m 5 and lowest contour AK = 0m
. 5. The positions of
the observed Hipparcos stars are marked by the filled circles, and the lines give the obtained
polarization vectors. The length of these vectors are proportional to the square root of the
degree of polarization, according to the scale indicated in the upper left-hand corner. Thick
lines refer to measurements having P/σP ≥ 4.
recently, Leroy (1999) analysed polarization data for stars with Hipparcos parallaxes in the solar
vicinity. The results indicate the existence, in some directions, of patches of polarizing material
closer than 70 pc. That seems to be the case of the diffuse component presented by our stellar
sample. Figure 2.2 (right-hand panel) shows the distribution of polarization angles as a function
of the Hipparcos parallaxes. If one take into account those stars belonging to the group with higher
signal-to-noise, (P/σP ≥ 4), the diffuse component seems to appear at a distance of about 70 pc
(πH = 14.37 mas – HIP 86226). The dense component seems to set in farther than that.
It is remarkable, from Fig. 2.1, that the two stars having lines-of-sight on each side of the northwestern extremity of the Pipe nebula (close to the location of B 59) show position angles that are
almost aligned with the direction of the stem and supposedly associated to the diffuse component.
Our measured polarization for HIP 84144 (left-hand side of the nebula) has a low signal-to-noise
27
5
8
10
π (mas)
number of stars
10
6
4
2
15
20
0
60
120
180
polarization angle (o)
60
120
180
Figure 2.2: left: Distribution of the observed position angles. The figure shows the histogram
obtained for 40 stars having P/σP ≥ 2. The shaded area represents stars with P/σP ≥ 4. The
distribution clearly suggests the existence of two components. right: Distribution of position
angles as a function of the Hipparcos parallaxes, where stars with P/σP ≥ 4 are represented
by filled circles. The ±1σθ were estimated using the method proposed by Naghizadeh-Khouei
& Clarke (1993). The shaded area indicates the suggested distance interval (145±16 pc) to
the Pipe nebula (see text).
and consequently a very suspicious value for the position angle; however, HIP 84175 (right-hand
side of the nebula) has a high signal-to-noise and its position angle can be trusted. This is among
the three stars having P/σP ≥ 4, position angle θ ∼ 75◦ , and a distance compatible with the
one expected for the Pipe nebula (see Fig. 2.2 (right-hand panel) and the discussion introduced in
Sect. 2.4), the other two stars are clearly identifiable to the left of HIP 84144 in Fig. 2.1.
In a forthcoming observational program we are planning to acquire deep CCD imaging polarimetry for lines of sight through dense cores in the Pipe nebula. The purpose of the intended
data is to investigate the geometry and influence of the magnetic field over this nebula in detail. It
is particularly interesting to examine the geometry of the magnetic field in the vicinity of B 59.
2.3.2 Interstellar dust distribution
Figure 2.3 shows a plot of the linear polarization against stellar parallax. The obtained distribution clearly shows a small degree of polarization at large parallaxes, for πH > 8 mas, followed
by a remarkably steep rise in polarization that occurs close to πH ≈ 7 mas, indicating that the Pipe
nebula is located at a distance of ∼140 pc. This value is consistent with the distance suggested
by Lombardi et al. (2006). Before trying to better estimate the distance to the Pipe nebula, it is
instructive to compare our parallax-polarization diagram with the parallax-extinction diagram ob-
28
tained by Lombardi et al. (2006, Fig. 11). As pointed out by those authors, their diagram shows
large scatters in the parallax and estimated interstellar absorption making the interpretation not
straightforward. It is worthwhile noting that the large scatters in parallax are mainly caused by
their being less restrictive in the selection criteria then we were; i.e. they accepted all stars with
ratio of the observational error to the trigonometric parallax given by σπH /πH < 1, while we used
σπH /πH ≤ 1/5 . On the other hand, uncertainties in spectral classification cause scattering in the
estimated extinction values. Because of that, the distance where the reddening sets in cannot be
clearly defined in their diagram as it can be in ours.
The parallax-polarization diagram shown in Fig. 2.3 suggests that the volume located in front
of the Pipe nebula is almost free of interstellar dust. The similarity of this diagram to the one
obtained for a region ∼23◦ apart in the Lupus dark cloud complex is remarkable (Alves & Franco
2006, see Fig. 4a). Both diagrams indicate that the clouds composing the Ophiuchus and Lupus
complexes may somehow be physically associated. It immediately raises the question of how
these clouds are related to the structure of the Galactic environment in the solar neighbourhood.
Current evidence suggests that the solar system is embedded in an irregularly-shaped low-density
volume (“local cavity”) of the local interstellar medium, partially filled with hot (∼106 K) coronal gas (“Local Bubble”, or LB for short) detectable in soft X-rays (e.g. Snowden et al. 1998;
Sfeir et al. 1999; Vergely et al. 2001; Lallement et al. 2003, and references therein). Although
there is some agreement that the hot component has likely been produced by a series of several
supernovae explosions within the past few million years (e.g. Maı́z-Apellániz 2001; Berghöfer &
Breitschwerdt 2002; Fuchs et al. 2006, and references therein), the global characteristics of all the
interstellar medium in the solar neighbourhood is a debated issue.
Two scenarios have been suggested for explaining at least some of the main observational facts.
One scenario claims the interaction of two physically separate phenomena. The LB is interacting
with its neighbouring superbubble shell (Loop I) generated by stellar winds or supernovae from the
nearby Scopius-Centaurus OB association, in turn resulting in a circular ring of neutral hydrogen
at the location of the interaction of these two shells. Inside this ring there is a sheet of neutral
hydrogen, forming a “wall” that separates the two bubbles (Egger & Aschenbach 1995). The other
scenario argues that the LB is part of an asymmetrically-shaped superbubble created by stellar
wind and supernovae explosions associated with the Sco-Cen association. The LB was sculpted
by the free expansion of this superbubble into the low-density interarm region surrounding the
solar system (Frisch 1981, 1995).
In the interacting bubbles’ model, the wall has an estimated neutral hydrogen column density,
N(H i), of ∼1020 cm−2 (Egger & Aschenbach 1995; Sfeir et al. 1999), which corresponds to E(b −
y) ≈ 0.m 013 (adopting the gas-to-dust ratio N(H)/E(b−y) = 7.5×1021 atoms cm−2 mag−1 suggested
by Knude 1978), and to a maximum expected degree of polarization of ≈0.16% (Serkowski et al.
1975). It is worth noting that the linear polarization is by definition a positive quantity, suffering a
positive bias that is not negligible at low polarization levels. By applying the method introduced by
Simmons & Stewart (1985), one may estimate the unbiased degree of polarization and confidence
29
distance (pc)
20
50
100 200
∞
2.5
P (%)
2.0
1.5
1.0
0.5
0.0
60
40
π (mas)
20
0
Figure 2.3: The obtained parallax-polarization diagram. Error bars (±1σπ , ±1σP ) are indicated
for stars with degree of polarization higher than 0.25%.
intervals. Most of the stars introduced in Table 2.1 showing low degree of polarization may in fact
be totally unpolarized, confirming the low-column density nature of the observed volume. Our
sample shows, however, 6 stars within 100 pc from the Sun which seem to present some degree
of polarization, supposedly caused by the diffuse component mentioned earlier in Sect.2.3.1. One
of these stars is HIP 83578 (d = 76+9
−7 pc) with a corrected degree of polarization P = 0.118%
[P = [0.076, 0.160]% – confidence interval at 99% (Simmons & Stewart 1985)], which suggests
the existence of absorbing material at distances smaller than ∼70 pc with a density consistent with
the expected one for the interface wall between the Local and Loop I bubbles. Although similar
results are obtained for the remaining 5 stars, they do not prove the existence of an interface
separating our local cavity from the Loop I bubble. Indead, the obtained polarization may be
produced by the interstellar matter outflowing from the Loop I bubble, in the sense proposed by
Frisch (1995).
Moreover, in a previous polarimetric investigation Tinbergen (1982) identified a dust cloud at a
distance between 0 and 20 pc from the Sun, with an inferred gas column density of ∼1019 atoms cm−2
and a very patchy distribution, since only about 30% of the stars in the surveyed region (350◦ <
l < 20◦ , −40◦ < b < −5◦ ) showed polarization above 2σ. High-resolution interstellar line studies
also show a complex multicomponent structure of the interstellar medium in this Galactic direction
(e.g., Crawford 1991; Genova et al. 1997).
30
2.4 Distance
Our stellar sample contains 19 stars with trigonometric parallaxes within the range 6 ≤ πH ≤ 8,
corresponding to the distance interval 125 ≤ dπ ≤ 167 pc. Among them, 10 show a low degree
of polarization, i.e. measured polarization smaller than 0.1%, indicating that they are supposedly
foreground objects and may be used to impose a minimum value for the distance to the Pipe
nebula. The farthest of them, HIP 84930, has a corrected degree of polarization P = 0.044%
(P = [0.000, 0.128]%) and measured parallax of πH = 6.12 ± 1.01 mas, which locates this star
at 163+33
−23 pc. Based on the data of this star alone, the lower limit for the value of the distance to
the Pipe nebula would be 140 pc, which corresponds to the upper limit suggested by Lombardi
et al. (2006). At only ∼4′ from HIP 84930 we find HIP 84931, another object with a low degree of
polarization and a measured parallax of πH = 6.70 ± 0.87 mas (149+23
−17 pc).
Figure 2.4 shows images from the Digitized Sky Survey centred, respectively, on HIP 83194
(left-hand panel) and HIP 84144 (right-hand panel), two frames from which we were able to
measure polarization for some of the field stars (see Table 2.2). Owing to the measured low degree
of polarization (P = [0.000, 0.041]% for HIP 83194 and P = [0.000, 0.156]% for HIP 84144,
confidence interval at 99%), both stars seem to be foreground objects at πH = 7.37 ± 1.14 mas
+22
(136+25
−19 pc) and π H = 7.04 ± 0.95 mas (142−17 pc), respectively, while the field stars prove the
existence of polarizing material beyond the location of HIP 83194 and HIP 84144 — none of the
field stars have accurate distance determination. HIP 83194 lies outside the limits of Fig. 2.1;
and HIP 84144, as mentioned in Sect 2.3.1, is the star on the left-hand side of the northwestern
extremity of the Pipe nebula having a polarization position angle supposedly aligned with the
Pipe nebula’s stem. The field stars show polarization with position angles consistent with the one
presented by stars affected by the dense component, and interestingly, the two stars in the field of
HIP 84144 show polarization roughly perpendicular to the large axis of the Pipe nebula.
The upper limit for the distance to the Pipe nebula is imposed by the star with the highest
degree of polarization in our sample, i.e. HIP 84391. Its measured parallax of πH = 7.17 ±
1.02 mas (140+23
−18 pc) limits the distance to ∼160 pc. Two other stars show a degree of polarization
higher than 1%, HIP 84695 at πH = 7.11 ± 1.42 mas (141+35
−24 pc), and HIP 85318 at π H = 6.43 ±
+34
1.17 mas (156−25 pc). A weighted average of these three parallaxes yields < π > = 6.91± 0.68 mas
(145+16
−14 pc), which can be accepted as the best estimate of the distance to the Pipe nebula. This
value is about 10% larger than the one recently suggested by Lombardi et al. (2006).
Three stars deserve a comment. They are the objects having P/σ p ≥ 4 and position angle
θ ∼ 75◦ , which were mentioned in Sect. 2.3.1. Their estimated distance locate them somewhere
between the front and the back sides of the Pipe nebula, and they show a degree of polarization
that is intermediate between the unpolarized foreground stars and the rather polarized background
ones. We designated them ‘midground’ objects in Table 2.3, which summarises the important
parameters of the stars relevant to the estimate of the distance to the Pipe nebula. An interesting
question that needs further investigation concerns the origin of the polarization shown by these
2.4. Distance
31
1%
HIP 83194
1%
HIP 84144
-27o 55’
Declination (2000)
Declination (2000)
00
00
-28o 05’
-27o 05’
17h 00m 30s
15s
00s
Right Ascension (2000)
16h 59m 45s
17h 12m 30s
15s
00s
11m 45s
Figure 2.4: Measured polarization for stars in the vicinity of HIP 83194 (left-hand panel) and
HIP 84144 (right-hand panel). The Hipparcos stars are centred on each panel. The length of
the vectors correlates linearly with the degree of polarization, according to the scale indicated
in the left-hand corner.
stars: is it produced by a foreground low column density medium or is the magnetic field in the
vicinities of the Pipe nebula characterised by two orthogonal components?
The last column of Table 2.3 gives the dust extinction, AK , estimated from the extinction map
obtained by Lombardi et al. (2006), and shows that all stars, but HIP 83194 located outside the
area mapped by them, have line-of-sight toward directions affected by dust extinction. In fact,
HIP 84391, the star showing the highest degree of polarization in our sample, seems to be in the
direction of the second lowest dust extinction among them, which is proof that the unpolarized
stars listed in this table are really foreground objects.
It is interesting to compare the obtained distance to the Pipe nebula with estimates for sites
of star formation in its neighbourings. Unlike the Pipe nebula that has attracted attention only
recently, many objects in its surroundings have been the subject of numerous investigations. One
of the most studied objects is the ρ Ophiuchi cloud complex, one of the nearest star-forming
regions, located about 14◦ to the northwest of the Pipe nebula, on the edge of the Upper Scorpius
subgroup in the Sco-Cen OB association. Quoted distances to the Ophiuchus dark clouds comprise
125 ± 25 pc (de Geus et al. 1989), 128 ± 12 pc (Bertout et al. 1999), and 165 ± 20 pc (Chini 1981).
Recently Vaughan et al. (2006) analysed the X-ray halo around GRB 050724, which has a line
of sight through the Ophiuchus molecular complex, concluding that the observed narrow halo
must have been caused by a concentration of dust at a distance of 139 ± 9 pc from the Sun. The
latter seems to be the best estimated value so far for the distance to the Ophiuchus dark cloud
complex and is in excellent agreement with the distance we obtained for the Pipe nebula. It is
worthwhile noting that the distance we obtained for the Pipe nebula is also in perfect agreement
32
Table 2.3: Stars relevant to the estimate of the distance to the Pipe nebula.
HIP
l
(◦ )
83194
84144
84930
84931
355.2
357.6
359.2
359.1
84175
85071
85154
357.0
0.5
1.7
84391
84695
85318
358.3
359.9
358.8
b
Pmin /Pmax a
(◦ )
(%)
foreground objects
+8.8 0.000/0.041
+7.2 0.000/0.156
+5.9 0.000/0.128
+5.8 0.000/0.163
midground objects
+6.7 0.089/0.135
+6.3 0.191/0.307
+6.8 0.235/0.438
background objects
+6.9 2.360/2.762
+7.0 1.045/1.426
+4.3 1.110/1.319
dmin /dmax b
(pc)
AK c
(mag)
117/161
125/164
140/196
132/172
—
0.12
0.16
0.16
147/194
138/184
141/189
0.08
0.15
0.23
122/163
117/176
131/190
0.10
0.19
0.24
a
lower/upper value for the degree of polarization at 99% confidence level (Simmons & Stewart 1985)
estimated 1σπ minimum/maximum trigonometric distance
c
estimated from the dust extinction map constructed by Lombardi et al. (2006)
b
with the distance of 145 ± 2 pc suggested for the Upper Scorpius subgroup (de Bruijne et al. 1997;
de Zeeuw et al. 1999).
Moreover, the distance obtained for the Pipe nebula is also very similar to the one suggested
for the Lupus 1 dark cloud (Franco 2002; Alves & Franco 2006), indicating that the interstellar
medium toward these directions may somehow be associated, forming a large interstellar structure.
It must be noted that our polarization data do not support the scenario proposed by Welsh &
Lallement (2005), which depicts the distribution of the interstellar gas toward the Ophiuchus and
Lupus dark clouds. According to their picture, dense gas exists at a distance of ∼50 pc from the
Sun toward these directions, which is not confirmed by our polarization data, unless the gas is
disassociated from dust.
2.5 Conclusions
By analysing the obtained B-band CCD imaging linear polarimetry for 82 Hipparcos stars
with the line of sight toward the area containing the Pipe nebula, we have reached the following
conclusions:
• There is evidence that the polarization angles have an almost orthogonal two-component
distribution. One of these components, if it exists, could be caused by a low column-density
medium (∼1020 atoms cm−2 ) closer than ∼70 pc, which may be either related to the interface
2.5. Conclusions
33
wall between the Local and Loop I bubbles or to some other kind of interstellar structure.
The other component seems to be caused by a higher column-density medium.
• We found that the “stem” of the “pipe” is aligned perpendicularly to the general direction of
the local magnetic field provided by the dense component. This fact may be an indication
that the stem is the result of a magnetically controlled collapse. To test this hypothesis
further, we are planning new observations to prove the densest parts of the Pipe nebula’s
“stem”.
• The distribution of linear polarization against trigonometric parallaxes suggests that the Pipe
nebula is located at a distance of 145 ± 16 pc from the Sun. The volume in front of this
cloud is almost empty of absorbing material. However, few stars up to about 100 pc show
clear signs of polarization, which may be caused either by an extended low column density
medium or by small diffuse clouds.
As a final remark, we notice that the Pipe nebula seems to provide a particularly suitable
laboratory in which to study the physical processes experienced by the interstellar clouds during
the phase of contraction to form low-mass stars. Such potential has been proven by the recent
identification of more than 150 dense cores in this cloud (Alves et al. 2007). Additionally, in
the scenario proposed by Preibisch & Zinnecker (1999, 2007), the Pipe nebula may be the place
where the next generation of nearby stars will be formed in a sequence just after the association
in ρ Ophiuchi. In fact, this process has already started in the northwestern part of the cloud, as
shown by the evidence in B 59, where there are at least 5 Hα known emission-line stars and at
least 20 other candidate low-mass young stars (Brooke et al. 2007), which suggest that this core is
producing young stars with high efficiency.
Chapter 3
Optical polarimetry toward the Pipe
nebula: Revealing the importance of the
magnetic field1
3.1 Introduction
Understanding the role that magnetic fields play in the evolution of interstellar molecular
clouds is one of the outstanding challenges of modern astrophysics. One problem related to star
formation concerns the competition between magnetic and turbulent forces. The prevailing scenario of how stars form is quasi-static evolution of a strongly magnetized core into a protostar
following influence between gravitational and magnetic forces. By ambipolar diffusion, i.e., the
drift of neutral matter with respect to plasma and magnetic field, gravity finds a way to overcome
magnetic pressure and eventually win the battle (e.g., Mestel & Spitzer 1956; Nakano 1979;
Mouschovias & Paleologou 1981; Lizano & Shu 1989). However, doubts about the validity of this
theory were expressed because of the apparent inconsistency between the expected and inferred
lifetimes of molecular clouds. This inconsistency inspired some researchers to propose a new
theory in which star formation is driven by turbulent supersonic flows in the interstellar medium.
Magnetic fields may be present in this theory, but they are too weak to be energetically important
(e.g. Elmegreen & Scalo 2004; Mac Low & Klessen 2004). It must be noted, however, that some
results (Tassis & Mouschovias 2004; Mouschovias et al. 2006) demonstrate that the ambipolar–
diffusion–controlled star formation theory is not in contradiction with molecular cloud lifetimes
and star formation timescales.
Previous optical polarimetric observations toward well-known forming molecular clouds have
enabled the large-scale magnetic field associated with these regions to be studied (e.g. Goodman
et al. 1990). In this work, we introduce the general results of a polarimetric survey conducted for
1
Published in Alves, F. O., Franco, G. A. P. & Girart, J. M. 2008, Astronomy and Astrophysics, 486, L13
35
36
Chapter 3. Optical polarimetry toward the Pipe nebula
the Pipe nebula, a nearby (130–160 pc, Lombardi et al. 2006; Alves & Franco 2007) and massive (104 M⊙ ) dark cloud complex that appears to provide a suitable laboratory for investigating
magneto-turbulent phenomena. The Pipe nebula exhibits little evidence of star formation activity
despite having an appropriate mass. Until now, the only confirmed star-forming region in this
nebula was B59 (Brooke et al. 2007), an irregularly-shaped dark cloud located at the northwestern end of the large filamentary structure that extends from (l, b) ≈ (0◦ , 4◦ ) to (l, b) ≈ (357◦ , 7◦ ).
This apparently low efficiency in forming stars may be an indication of youth. Alves et al. (2007)
identified, in this cloud, 159 cores of effective diameters between 0.1 and 0.4 pc, and estimated
masses ranging from 0.5 to 28 M⊙ , supposedly in a very early stage of development. A further
investigation of these cores (Lada et al. 2008) discovered that most of them appeared to be pressure confined and in equilibrium with the surrounding environment, and that the most massive
(& 2 M⊙ ) cores were gravitationally bound. They suggested that the measured dispersion in internal core pressure of about a factor of 2–3 could be caused by either local variations in the external
pressure, or the presence of internal static magnetic fields with strengths of less than 16 µG, or a
combination of both. The results derived from our optical polarimetric observations indicate that
the magnetic field probably plays a far more important role in the Pipe nebula.
3.2 Observations
The polarimetric data were acquired using the 1.6 m and the IAG 60 cm telescopes of Observatório do Pico dos Dias (LNA/MCT, Brazil) during observing runs completed between 2005 to
2007. These data were acquired by using a CCD camera specially adapted to allow polarimetric
measurements; for a full description of the polarimeter see Magalhães et al. (1996). R-band linear
polarimetry, by means of deep CCD imaging, was obtained for 46 fields, each with a field of view
of about 12′ × 12′ , distributed over more than 7◦ (17 pc in projection) covering the main body of
the Pipe nebula. The reference direction of the polarizer was determined by observing polarized
standard stars. For all observing seasons, the instrumental position angles were perfectly correlated with standard values. The survey contains polarimetric data of about 12 000 stars, almost
6 600 of which have P/σP ≥ 10. The results presented in this Letter are based on the analysis
of the latter group of stars. Details of observations, data reduction, and the analysis of the smallscale polarization properties within each observed area, will be described in a forthcoming paper
(Franco et al. 2010).
3.3 Polarization at the Pipe nebula
To analyze the polarization pattern in the Pipe nebula, we estimated the mean polarization
and position angle for each observed field. To improve the precision of the mean values, we
selected those objects with P/σP ≥ 10 and observed polarization angle θobs within the interval
(θav −2σ std ) ≤ θobs ≤ (θav +2σ std ) where, θav and σ std are the mean polarization angle and standard
3.3. Polarization at the Pipe nebula
37
deviation of each field sample, respectively. We then estimated the mean Stokes parameters for
each field, from the individual values for each star weighted by the estimated observational error.
Most fields show a distribution of polarization position angles that resembles a normal distribution,
although a more complex distribution is evident in some directions. A detailed analysis of these
distributions is beyond the scope of the present Letter and will be presented in the aforementioned
paper.
Figure 3.1 shows the mean polarization vectors overlaid on the 2MASS infrared extinction
map of the Pipe nebula derived by Lombardi et al. (2006). For most fields, the values of the
mean polarization and position angle were obtained from samples of more than 100 stars. The
high signal-to-noise ratio of our data set ensures good statistics in our analyses and implies that
the degree of polarization measured for most fields and, in particular, the significant range of
mean polarization values derived along the Pipe (from 1 to 15%) are truly remarkable. It is also
remarkable that the polarization position angle does not change significantly along the 17 pc extent
of the Pipe nebula covered by our observations (hθi ≃ 160◦ -10◦ for 37 of the 46 fields, where the
mean position angles are given in equatorial coordinates, measured from north to east). Although
the physical processes involved in grain alignment is a debated issue (see Lazarian 2003, for a
comprehensive review on this subject), it is widely believed that starlight polarization is caused by
the alignment of elongated dust grains by the magnetic field, as suggested by the pioneering work
of Davis & Greenstein (1951). Based on this assumption, the polarization map showed in Fig. 3.1
provides an outline of the magnetic field component parallel to the plane of the sky. The almost
perpendicular alignment between the magnetic field and the main axis of the Pipe’s stem is clearly
evident.
It is instructive to analyze the behavior of polarization properties along the Pipe nebula: the
left panels of Figure 3.2 present the distribution of the mean polarization and the polarization
angle dispersion as a function of the right ascension of the observed areas, which runs almost
parallel to the main axis of the Pipe’s stem. Since the polarization properties of each field are
inhomogeneous, a global analysis allows one to distinguish three regions throughout the cloud
with rather different features between them. These regions, separated by dashed-lines in Fig. 3.1
and 3.2, can be identified as: the B59 region, at the northwestern end of the cloud; the main
filamentary structure (the stem of the Pipe); and the irregular–shaped gas at the other extreme end
(the “bowl”). We note that fields without cores (open dots in Fig. 3.2) show a smaller variation in
polarization properties than fields with cores (filled dots).
The lowest mean polarizations are observed in the vicinity of B59, the only place in the Pipe
with evidence of star formation. Seven out of eight observed fields in this region show mean polarization degrees of around 1–2%. This region has a large polarization angle dispersion. Indeed, two
fields have a dispersion in polarization angles ∆θ & 25◦ – these are indicated in the botton right
panel of Fig. 3.2 by the arrowed dots – and show the lowest mean degree of polarization among the
observed fields. We point out that the field showing the highest dispersion in polarization angles
(∆θ ≃ 51◦ ) has a line of sight passing close to the densest core of B59, the most opaque region of
38
10%
8
o
7o
Galactic Latitude
6o
5o
4o
3o
2o
4o
3o
2o
1o
0o
359o
Galactic Longitude
358o
357o
356o
Figure 3.1: Mean polarization vectors, for each of the observed 46 fields, overplotted on the
dust extinction map of the Pipe nebula obtained by Lombardi et al. (2006). The lengths of
these vectors are proportional to the scale indicated in the top left-hand corner. Only stars
showing P/σP ≥ 10 were used in the calculus of the mean polarization and position angle.
The dashed-lines indicate the celestial meridians defined by 17h 14m 30s. 0 and 17h 27m 40s. 0 (see
text and Fig. 3.2).
3.3. Polarization at the Pipe nebula
39
the Pipe (Román-Zúñiga et al. 2007), and that our sample has only 12 stars for which P/σP ≥ 10.
Toward the stem region the mean polarization rises a few percent and the polarization angle
dispersion decreases slightly with respect to B59. Most fields containing dense cores show a mean
polarization degree (≃3–5%) that is higher than fields without cores (≃2–3%)). However, this
difference is unclear from the position angle dispersion values, which show a large range of values
for both types of field (∆θ ≃3◦ –12◦ ).
The bowl has a significantly different mean polarization and dispersion in position angles: for
this region, we measure the highest degree of polarization and the lowest dispersion in position
angles. Most observed fields in the bowl shows a mean polarization higher than about 8% (up
to 15%) and a dispersion in polarization angles of less than 5◦ . This part of the cloud has the
most precise alignment between the mean polarization vectors of neighboring fields. The high
polarization degree in the bowl is unusual, since the polarization degree of this type of dark interstellar clouds is typically 1 order of magnitude lower than we measure and rarely reaches such
high values (e.g., Vrba et al. 1993; Whittet et al. 1994, 2001, for optical polarimetric data on ρ
Oph, Chamaeleon I, and Taurus dark clouds, respectively). Such a result implies a high efficiency
of grain alignment for the interstellar dust in those fields, and that the magnetic field in the bowl
is aligned close to the plane of the sky (otherwise the efficiency would be even higher).
Figure 3.2 (top right panel) also indicates the distribution of ∆θ as a function of the mean polarization: it is a clear observational fact for the observed fields that the higher the mean polarization,
the lower the dispersion in polarization angles. The anti-correlation between the dispersion in
polarization angles and polarization degree has a similar dependence for fields with and without
cores. This anti-correlation could be due just to projection effects: the magnetic field direction
changes along the Pipe nebula. However, this scenario would imply a polarization efficiency and
a magnetic field strength (see below) that would be unusually high over the entire nebula. The star
formation activity in B59 probably precludes this scenario.
What can the aforementioned polarization properties tell us about the magnetic field in the
Pipe nebula? Our dispersion in polarization angles can be used to estimate the magnetic field
strength for the observed fields from the modified Chandrasekhar-Fermi formula (Chandrasekhar
& Fermi 1953; Ostriker et al. 2001). The volume density and line width of the molecular line
emission associated with the dust that produces the observed optical polarization and extinction
can be estimated from the molecular data available in the literature. Thus, extrapolating the median
volume density of cores given by Lada et al. (2008) to the optical polarization zone (which is
typically at a distance of about 5′ – 0.2 pc in projection – from the center of the cores), we obtain
a volume density of n(H2 ) ≃ 3 × 103 cm−3 . We also adopt the line width found for C18 O toward
the cores in B59 and the stem, 0.4 km s−1 , and the bowl, 0.5 km s−1 (the values used here are
the ones given by Muench et al. 2007). Assuming these values, we find that the magnetic field
strength in the B59 region, stem, and bowl, in the plane of the sky, are about 17, 30, and 65 µG,
respectively (the uncertainty in the values are probably less than a factor of 2). Adopting a mean
visual extinction of 3 mag for the molecular cloud traced by the optical polarimetry, we find that
40
B59
stem
bowl
Figure 3.2: left panels: Distribution of the mean polarization and of the polarization angle
dispersion, ∆θ, as a function of the right ascension of the observed areas, respectively. The
polarization angle dispersion is corrected by its mean error (i.e., ∆θ2 = σ2std − hσθ i2 ). The verti-
cal dashed–lines delimits the transition between regions with different polarimetric properties.
Filled and open dots represent values for fields with and without associated dense cores, respectively. As shown by the botton right panel, the regions traced by the optical polarimetry
have extinction of AV . 2.2 mag for fields without cores, while the ones associated with cores
show 0.8 . AV . 4.5 mag. Top right panel: Correlation between dispersion in polarization
angle and mean polarization. Botton right panel: Mean polarization versus visual absorption
derived from the 2MASS data for the observed stars with P/σP ≥ 10. The solid line represents
optimum alignment efficience (P(%) = 3 × AV ).
3.4. Conclusions
41
the mass–to–flux ratio is about 1.4 (slightly super-critical) for B59, in contrast to 0.8 and 0.4
(sub-critical) for the stem and the bowl, respectively.
The almost perpendicular alignment between the magnetic field and the main axis of the Pipe
nebula’s stem indicates clearly that this part of the cloud contracted in the direction of the field
lines. This agrees with predictions of the ambipolar-diffusion driven model, for which the first
evolutionary stage of a typical cloud is dynamical relaxation along field lines, almost without lateral contraction, until a quasi-equilibrium state is reached (e.g., Fiedler & Mouschovias 1993;
Tassis & Mouschovias 2007). Indeed, the magnetic pressure (Pmag = B2 /8π) of the diffuse part
of the cloud (where is most of the mass) is the dominant source of pressure in the direction perpendicular to the field lines (12 × 105 and 2.6 × 105 K cm−3 for the bowl and stem, respectively),
being higher than the pressure due to the weight of the cloud (Pcloud /k = 105 K cm−3 , according
to Lada et al. 2008). This can explain the clear elongated structure perpendicular to the magnetic
field of the whole nebula.
The derived mean polarization degree and dispersion in polarization angles are consistent with
a scenario in which the B59 region, the stem, and the bowl are experiencing different stages of their
evolution. The weak magnetic field derived for the B59’s neighboring appears to be the reason
for it being the only known active star-forming site in the cloud. Following the evolutionary
sequence, the stem with a mass–to–flux ratio close to unity would be the part of the cloud in a
transient evolutionary state, which is experiencing ambipolar diffusion but has not yet given birth
to stars. Finally, the high polarization degree of the bowl combined with the low dispersion in the
mean polarization vectors implies that the magnetic field in this part of the cloud has a major role
in regulating the collapse of the cloud material compared to the other parts. This would imply that
the bowl is in a primordial evolutionary state (in the sub-critical regime), not yet flattened neither
elongated. However, the presence of multiple and clearly evident cores implies that fragmentation
is already occurring inside the bowl. A similar case, in a more evolved state, appears to be the
Taurus molecular cloud complex (Nakamura & Li 2008).
3.4 Conclusions
We have described the global polarimetric properties of the Pipe nebula as an increasing polarization degree along the filamentary structure from B59 towards the bowl, while the dispersion
in polarization angles decreases along this way. Our results appears to indicate that there exist
three regions in the Pipe nebula of distinct evolutionary stages: since the mean orientation angle
of the mean polarization vectors is perpendicular to the longer axis of the cloud, this implies that
the cloud collapse is taking place along the magnetic field lines. We can subdivide the Pipe nebula
into the following components:
• B59, the only active star-forming site in the cloud. For the observed fields, we measure a
large dispersion in polarization angle and low polarization degree.
42
• The stem, which collapsed by means of ambipolar diffusion but has not yet given birth to
stars. It appears to represent a transient evolutionary state between B59 and the bowl.
• The bowl, which contains the fields of the highest values of mean polarization and the
lowest values of dispersion in polarization angle. These values imply that the dust grains in
the bowl are highly aligned by a rather strong magnetic field. For this reason, the bowl may
represent the start of the contraction phase during a very early evolutionary stage.
Chapter 4
Detailed interstellar polarimetric
properties of the Pipe nebula at core
scales2
This work consists in a detailed analysis core-by-core of the polarization data reported in Alves
et al. (2008). My main contribution to this work was the participation on most of the observing
sessions and the data reduction. The derivation of the visual extinctions of the observed fields was
performed by Dr. Gabriel Franco, while the application of the Second Order Structure Function
(Houde et al. 2009) to the polarization data was done by Dr. Josep Miquel Girart.
4.1 Introduction
The relatively low Galactic star formation efficiency (SFE, defined as the fraction of a molecular gas mass that is converted into stars) is one fundamental constraint on the global properties
of star formation. In our Galaxy the SFE is observationally estimated to be of the order of a few
percent when whole giant molecular complexes are considered. For instance, the detailed study
of the Taurus molecular cloud complex conducted by Goldsmith et al. (2008) provided a SFE
between 0.3 and 1.2%. Magnetic fields and supersonic turbulence are two mechanisms that are
commonly invoked for regulation of such small SFE. Magnetic fields may regulate cloud fragmentation by several physical processes (e.g., moderating the infalling motions on the density
peaks, controlling angular momentum evolution through magnetic breaking, launching jets from
the near-protostellar environment, etc). On the other hand, it is known that turbulence may play
a dual role, both creating overdensities to initiate gravitational contraction or collapse, and countering the effects of gravity in these overdense regions. The respective rules of magnetic fields
and interstellar turbulence in regulating the core/star formation process are, however, highly con2
Published in Franco, G. A. P., Alves, F. O. & Girart, J. M. 2010, The Astrophysical Journal, 723, 146
43
44
Chapter 4. Polarimetric properties of the Pipe nebula at core scales
troversial. For instance, some authors opine that magnetic fields are absolutely dominant in the
star formation process (e.g., Tassis & Mouschovias 2005; Galli et al. 2006), while others support
that super-Alfvénic turbulence provides a good description of molecular cloud dynamics, and that
the average magnetic field strength in those clouds may be much smaller than required to support
them against the gravitational collapse (see Padoan et al. 2004, and references therein).
The Pipe nebula, a massive filamentary cloud complex (104 M⊙, Lombardi et al. 2006) located
at the solar vicinity (145 pc, Alves & Franco 2007) which presents an apparently quiescent nature,
seems to be an interesting place to look for some answers on the physical processes involved in
the collapse of dense cloud cores and how they evolve until stars are formed.
Optical images of the Pipe nebula (see for instance the wonderful high quality image obtained
by Stéphane Guisard for the GigaGalaxy project1 ) or the dust extinction map obtained by Lombardi et al. (2006), show that this complex comprises many dark cores and sinuous dark lanes.
Although Alves et al. (2007) have identified 159 dense cores with estimated masses ranging from
0.5 to 28 M⊙ all over the entire Pipe nebula, the only known star forming active site in this nebula
seems to be restricted to its northwestern extreme (in galactic coordinates), the densest part of
the complex associated with the dark cloud Barnard 59 (B 59), which corresponds to only a small
fraction of the entire cloud mass. Actually, an embedded cluster of young stellar objects within
B 59 has been revealed by infrared images obtained with the Spitzer Space Telescope (Brooke
et al. 2007). The apparently low efficiency in forming stars observed for this cloud complex (only
∼0.06% according to Forbrich et al. 2009, 2010), suggests that the Pipe nebula is an example of
a molecular cloud in a very early stage of star formation. Indeed, in our previous paper (Alves
et al. 2008, hereafter Paper I) it has been suggested that the Pipe nebula may present three distinct
evolutionary stages, being the B 59 region the most evolved of them while the opposite extreme of
the cloud (the bowl) would be in the earlier stage. This suggestion seems to be reinforced by the
recent Spitzer census of star formation activity performed by Forbrich et al. (2009), who detected
only six candidate young stellar objects (YSOs) outside the B 59 region, four of them located in
the “stem” of the Pipe, none having been detected in the bowl. Moreover, the youthfulness of the
YSOs in B 59 is corroborated by the results obtained by Covey et al. (2010), who estimated a median age of about 2.6 Myrs to the candidate YSOs found in B 59. Interestingly, they suggest that
this population may be older than the well studied ones in Chamaeleon, Taurus, and ρ Ophiuchus,
respectively.
In Paper I we described the global polarimetric properties of the Pipe nebula as obtained from
mean values of polarization degree and dispersion in polarization angles calculated for stars having
P/σP ≥ 10. In the present paper we introduce the details of our data sample collected for 46
CCD fields, which are exactly the same as the one used in the previous work, and analyse the
polarimetric properties of the Pipe nebula at core scales. In order to increase the statistical sample
for each investigated field, we were less strict in our selection criteria accepting stars with P/σP ≥
5.
1
http://www.gigagalaxyzoom.org
4.2. Observations
45
4.2 Observations
4.2.1 Data acquisition and reductions
The polarimetric data were collected with the 1.6 m and the IAG 60 cm telescopes at Observatório do Pico dos Dias (LNA/MCT, Brazil) in missions conducted from 2005 to 2007. These
data were obtained with the use of a specially adapted CCD camera to allow polarimetric measurements — for a suitable description of the polarimeter see Magalhães et al. (1996). R-band linear
polarimetry was obtained for 46 fields (with field of view of about 12′ × 12′ each) distributed
over more than 7◦ (17 pc in projection) covering the main body of the Pipe nebula. The observing
lines-of-sight were visually selected from inspection of the IRAS 100 µm emission image of the
Pipe nebula prior to the publication by Lombardi et al. (2006) of the dust extinction map of this
cloud complex. In our selection we chose directions toward high dust emission as well as some
directions pointing to positions presenting lower emission but close to the main body of the complex as defined by the 100 µm image. After that, Alves et al. (2007) published their list of dense
cores and some of our selected fields turned out either to completely include one of these cores or
part of its outskirts. In Fig. 4.1 the observed lines-of-sight are overplotted on the dust extinction
map of the Pipe nebula obtained by Lombardi et al. (2006). The small squares roughly indicates
the areas covered by the observed frames.
When in linear polarization mode, the polarimeter incorporates a rotatable, achromatic halfwave retarder followed by a calcite Savart plate. The half-wave retarder can be rotated in steps of
22.◦ 5, and one polarization modulation cycle is covered for every 90◦ rotation of this waveplate.
This arrangement provides two images of each object on the CCD with perpendicular polarizations
(the ordinary, fo , and the extraordinary, fe , beams). Rotating the half-wave plate by 45◦ yields in
a rotation of the polarization direction of 90◦ . Thus, at the CCD area where fo was first detected,
now fe is imaged and vice versa. Combining all four intensities reduces flatfield irregularities.
In addition, the simultaneous imaging of the two beams allows observing under non-photometric
conditions and, at the same time, the sky polarization is practically canceled. Eight CCD images
were taken for each field with the polarizer rotated through 2 modulation cycles of 0◦ , 22.◦ 5, 45◦ ,
and 67.◦ 5 in rotation angle.
Among the 46 sky positions, twelve were observed at the IAG 60 cm telescope. At this telescope the integration time was set to 120 seconds and 5 frames were collected and co-added for
each position of the half-wave plate (totalizing 600 seconds per wave plate position). The remaining 34 fields were observed at the 1.6 m telescope, where the integration time for most of the
observed positions was also set to 120 seconds, being that only one frame was acquired for each
position of the half-wave plate. In order to have almost the same field of view, the latter telescope
was provided with a focal reducer.
The CCD images were corrected for read-out bias, zero level bias and relative detector pixel
response. After these normal steps of CCD reductions, we identified the corresponding pairs of
46
8o
1
2
o
7
3
5
15
Galactic Latitude
6o
17
13
12
9
10
4
6
7
8
11
14
16
18
23
20
25
5o
22
29
30
27
31
32
34 33
35
38
39
41 40
21
26
28
4o
19
24
37
36
42
43
44
45
3o
46
2o
4o
3o
2o
1o
0o
359o
Galactic Longitude
358o
357o
356o
Figure 4.1: Identification of the observed 46 lines-of-sight overplotted on the dust extinction
map of the Pipe nebula obtained by Lombardi et al. (2006). The small squares roughly indicates the observed CCD field of view, which in our case corresponds to about 12′ × 12′ . The
large retangles demarcate the areas detailed separately in Figs. 4.5 to 4.9 (colored version of
this and of the other figures are available in the online version of this paper).
stars and performed photometry on them in each of the eight frames of a given field using the
IRAF DAOPHOT package. From the obtained file containing magnitude data, we calculate the
polarization by use of a set of specially developed IRAF tasks (PCCDPACK package; Pereyra
2000). This set includes a special purpose FORTRAN routine that reads the data files and calculates the normalized linear polarization from a least-square solution, which yields the degree of
linear polarization (P), the polarization position angle (θ , measured from north to east) and the
Stokes parameters Q and U, as well as the theoretical (i.e. the photon noise) and measured errors.
The latter are obtained from the residuals of the observations at each waveplate position angle (ψi )
with respect to the expected cos 4ψi curve.
Zero polarization standard stars were observed every run to check for any possible instrumental
polarization, which proved to be small as can be verified by inspection of Table 4.1. The reference
direction of the polarizer was determined by observing polarized standard stars (Turnshek et al.
1990), complemented with polarized stars from the catalogue compiled by Heiles (2000). For all
observing seasons, the instrumental position angles showed a perfect correlation with the standard
values (see Table 4.2), and the expected uncertainty of the zero point for the reference direction
4.2. Observations
47
Table 4.1: Observed zero polarization standard stars.
HD
V
12021
98161
154892
176425
BD+28 4211
8.85
6.27
8.00
6.23
10.51
Turnshek et al.
PV (%)
Schmidt et al.
PV (%)
this work
PR (%)
—
0.017 (0.006)
0.050 (0.030)
0.020 (0.009)
—
0.078 (0.018)
—
—
—
0.054 (0.027)
0.106 (0.037)
0.028 (0.041)
0.027 (0.041)
0.031 (0.017)
0.066 (0.025)
Table 4.2: Observed high polarization standard stars.
HD
110984
111579
126593
155197
161306
168625
170938
172252
V
8.95
9.50
8.50
9.20
8.30
8.40
7.90
9.50
Turnshek et al.
PV (%)
θ (◦ )
5.70 (0.01)
6.46 (0.01)
5.02 (0.01)
4.38 (0.03)
—
—
—
—
91.6
103.1
75.2
103.2
Heiles
P (%)
5.19 (0.11)
6.21 (0.17)
4.27 (0.10)
3.99 (0.08)
3.69 (0.09)
4.42 (0.20)
3.69 (0.20)
4.65 (0.20)
θ (◦ )
90.6
103.0
77.0
103.9
67.5
14.0
119.0
148.0
this work
PR (%)
θ (◦ )
5.21 (0.19)
6.11 (0.09)
4.65 (0.11)
3.98 (0.07)
3.59 (0.23)
4.23 (0.07)
3.62 (0.11)
4.38 (0.14)
91.4
103.1
74.9
105.2
67.9
14.9
118.8
147.7
must be smaller than 1–2◦ .
4.2.2 Results
Our final sample contains 11 948 stars, being that 9 777 of them have P/σP ≥ 5, where σP
means the largest between the theoretical and measured errors, that is, about 3 200 stars more than
the ones used in the analysis conducted in Paper I which limited the sample to stars presenting
P/σP ≥ 10. A search in the archival Two-Micron All-Sky Survey (2MASS), available on-line
http://irsa.ipac.caltec.edu, identified 11 588 objects that could be associated to our observed stars, and the JHK s photometry was retrieved for them. For the remaining we usually failed
to associate a 2MASS object either because none was found inside the searched box (up to about
8 times the typical rms error of our astrometric solution) or, in case of the most crowded fields,
because the same 2MASS object could be assigned to more then one of ours.
Figure 4.2 gives the distribution of the estimated polarimetric errors, σP , as a function of the
J2MASS magnitude, for the observed stars. This figure shows that most of our stellar sample has
magnitude within the interval 10m ≤ J2MASS ≤ 15m and polarimetric error given by σP ≤ 0.5 %.
The obtained distribution suggests that the uncertainties are dominated by photon shot noise, as
expected for a sample collected with fixed exposure time.
The distribution of obtained degree of polarization for stars with P/σP ≥ 5 (Fig. 4.3 – right
panel) shows a surprising result: several stars present degree of polarization larger than 15%.
48
1.0
σP (%)
0.8
0.6
0.4
0.2
0.0
6
8
10
12
J2MASS (mag)
14
16
Figure 4.2: Distribution of the polarimetric errors as a function of the J magnitude as retrieved
from the 2MASS catalogue. The distribution shows characteristics of estimated errors dominated by photon shot noise.
Indeed, 6 objects present degree of polarization slightly larger than 19%. As far as we know,
these are the largest polarization produced by dichroic extinction ever observed — in the stellar
polarization catalogue compiled by Heiles (2000) one find only four stars, out of more than 9 000,
with degree of polarization higher than 10%, being that the highest of them equals to 12.47%.
The distribution of obtained polarization angles for stars with P/σP ≥ 5 (Fig. 4.3 – left panel)
shows a large concentration of values around θ ≈ 180◦ (in equatorial coordinates), that is, 76% of
this subsample has polarization angles between 160◦ and 10◦ , clearly indicating a high large scale
homogeneity in dust grain alignment (and supposedly in the geometry of the magnetic field) all
over the whole region. Since the main axis of the Pipe’s stem is almost in line with the west-east
direction, it clearly indicates that the observed polarization vectors are mainly perpendicularly
aligned to the longer axis of the cloud (see Paper I).
It is interesting to compare the distributions for stars having P/σP ≥ 5 with the ones having
P/σP ≥ 10, also shown in Fig. 4.3, and used in our previous work. Visually one can attest that
the distribution of polarization angles for both samples are quite similar. Indeed, the mean value
of both distributions differ by only 2◦ and the standard deviation of the sample having P/σP ≥ 5
is about 2.◦ 5 wider than the one for P/σP ≥ 10. On the other hand, as expected for a sample
with uncertainties dominated by photon shot noise, most of the stars included by the less tight
signal-to-noise condition are the ones presenting smaller degree of polarization.
The high values of polarization obtained in our survey is the result of differential extinction
produced by interstellar dust grains on the incoming/background stellar radiation. It is assumed
that a large fraction of those grains are aligned. The nature of such alignment is still a matter
of debate (see Lazarian 2003, for a comprehensive review on this subject), however, it is widely
4.3. Data Analysis
49
Figure 4.3: The obtained distributions for the 9 777 stars with P/σP ≥ 5 and for the 6 582
stars with P/σP ≥ 10, darker (salmon) and lighter (yellow) histograms respectively. Left panel:
distribution of the observed polarization angles; Right panel: distribution of the estimated
degree of polarization.
believed that the dominant process responsible for the alignment involves interaction between
the spin of the dust particles and the ambient magnetic field, as originally proposed by Davis &
Greenstein (1951).
4.3 Data Analysis
4.3.1 Mean Polarization
Apart from the difference in the adopted signal-to-noise, the results described in Paper I and the
ones presented in this work were obtained in the way described below and introduced in Table 4.3
which gives, for each observed field, coordinates (right ascension and declination), associated dark
core, when available, from the list compiled by Alves et al. (2007), the number of stars for which
we estimated polarization, and the number of stars with P/σP ≥ 5, in columns 2 and 3, 4, 5, and 6
respectively.
Mean polarization and polarization degree were estimated for each of the observed area adopting a procedure similar to the one used by Pereyra & Magalhães (2007), that is, to improve the
precision of the mean values, we selected only those objects with observed polarization angle θobs
within the interval (θmean − 2σ std ≤ θobs ≤ θmean + 2σ std ) where, θmean and σ std are the mean
polarization angle and standard deviation of each field sample (columns 7 and 8, respectively, in
Table 4.3). The mean Stokes parameters, hQi and hUi, for each field, were estimated from the
individual values for each star (qi , ui ), weighted by the error (σi ) according to
50
Table 4.3: Mean R-band linear polarization and extinction data for the 46 observed fields in
the Pipe nebula (see text for explanation on the columns).
Field alpha (J2000) delta Corea Observed Stars with
(h m s) (◦ ′ ′′)
stars
P/σ ≥ 5
01 17 10 28 −27 22 49 06
273
174
02 17 11 52 −27 03 49 —
165
64
03 17 11 21 −27 24 46 12
62
23
04 17 10 55 −27 44 26 —
400
211
05 17 12 30 −27 20 42 14
137
50
06 17 12 01 −27 37 06 08
271
91
07 17 13 53 −27 12 33 —
206
114
08 17 13 34 −27 45 46 —
807
486
09 17 14 52 −27 20 55 21
189
132
10 17 15 25 −27 18 09 —
191
174
11 17 15 15 −27 33 38 20
135
130
12 17 16 20 −27 09 32 25
198
189
13 17 17 12 −27 03 06 27
199
196
14 17 16 05 −27 31 38 23
282
280
15 17 18 27 −26 47 50 31
272
254
16 17 18 48 −27 11 36 —
382
319
17 17 19 36 −26 55 23 33
214
210
18 17 20 49 −26 53 08 34/40
327
201
19 17 22 43 −26 39 25 —
368
323
20 17 24 03 −26 20 35 —
451
400
21 17 21 48 −27 18 15 —
260
218
22 17 22 38 −27 04 14 41/42
102
97
23 17 27 13 −25 07 27 —
513
412
24 17 26 25 −25 58 09 —
748
520
25 17 28 07 −25 29 52 —
511
461
26 17 25 40 −26 43 09 48
247
126
27 17 25 28 −27 03 29 —
197
185
28 17 30 18 −25 09 50 —
254
240
29 17 29 14 −25 55 44 ∼70
98
95
30 17 28 12 −26 21 10 56
94
93
31 17 27 12 −26 42 59 51
284
271
32 17 27 24 −26 56 50 47
143
139
33 17 32 09 −25 24 18 91
329
313
34 17 32 54 −25 12 25 —
255
244
35 17 33 01 −25 46 00 ∼89
133
130
36 17 30 11 −26 48 42 —
144
142
37 17 31 18 −26 29 36 66
111
111
38 17 32 27 −26 15 49 74
127
127
39 17 38 56 −24 08 57 151
249
245
40 17 35 47 −25 33 01 109
80
77
41 17 36 27 −25 23 27 —
62
62
42 17 33 54 −26 14 11 —
181
177
43 17 33 24 −26 41 13 —
424
422
44 17 37 55 −25 12 40 132
119
114
45 17 39 50 −24 59 16 140
412
401
46 17 37 56 −26 15 32 —
363
353
a
b
c
θmean b
(◦)
9.7
12.9
28.9
15.9
0.9
128.7
167.3
7.6
6.3
4.2
170.8
176.5
0.9
176.0
7.7
2.2
171.6
164.2
167.7
32.2
179.1
158.1
7.1
175.1
174.2
142.3
143.2
172.9
160.2
160.6
155.1
164.1
169.9
168.9
171.7
160.4
169.8
172.6
6.5
165.2
170.8
174.6
167.3
0.7
177.9
169.8
σstd b
(◦)
10.65
15.04
24.93
13.08
16.82
40.79
12.75
8.80
10.76
7.72
6.76
4.87
5.76
4.40
10.90
4.92
5.91
9.59
7.06
9.86
8.73
5.35
9.44
7.61
5.58
32.79
11.43
5.86
5.90
2.54
5.12
4.58
4.04
3.17
2.37
3.76
3.40
3.36
6.07
4.07
4.30
3.05
3.03
3.76
5.51
4.13
Starsc
168
63
21
202
47
87
108
464
54
164
127
179
190
267
243
301
201
198
306
383
209
92
391
506
437
120
183
231
91
90
258
135
301
236
125
138
105
125
233
73
57
170
406
108
389
335
hPi
(%)
2.45
1.82
1.78
1.63
2.00
0.62
1.27
1.76
3.44
3.43
3.17
4.46
4.03
4.34
2.18
2.39
2.58
4.63
2.31
2.05
1.96
4.39
2.37
2.59
3.27
1.99
3.39
5.61
5.43
6.64
4.99
6.20
8.10
7.98
10.83
9.79
13.92
15.51
3.87
11.04
10.54
9.49
8.06
8.49
6.29
6.74
δP
(%)
0.82
0.85
0.96
0.79
1.07
1.36
0.61
0.63
0.98
1.23
1.14
1.01
0.69
0.93
0.78
0.50
0.76
1.68
0.79
0.73
0.38
1.33
0.74
0.76
0.74
1.49
1.30
1.16
1.52
2.17
1.59
1.54
1.30
1.38
1.80
1.62
2.29
2.85
1.04
1.84
2.16
1.68
2.07
1.51
1.57
1.59
θhPi
(◦)
3.1
9.8
48.8
14.8
179.7
149.8
169.3
9.2
3.5
4.4
171.3
176.8
1.3
176.1
5.3
2.6
171.8
163.0
167.2
32.5
0.8
157.0
7.1
174.2
173.9
152.9
142.2
173.3
160.8
160.6
156.1
164.5
169.3
169.9
171.3
160.1
170.6
173.4
7.8
167.0
170.0
174.3
167.2
0.2
177.5
169.6
∆θ AV
δAV
(◦) (mag) (mag)
9.65 2.54
1.25
13.72 0.63
0.35
23.75 3.88
2.00
12.38 1.59
0.74
15.67 2.53
1.09
40.21 2.33
1.19
11.74 2.06
0.97
7.40 1.58
0.78
10.04 3.03
1.49
7.29 3.33
1.67
6.21 2.32
1.17
4.32 2.72
1.22
5.62 2.03
0.94
4.11 2.82
1.42
10.63 2.32
1.16
3.52 1.98
0.98
5.58 2.07
0.91
8.60 3.64
1.81
6.35 1.86
0.94
9.23 1.49
0.68
8.05 2.33
1.16
4.82 3.03
1.50
8.79 2.03
0.99
6.52 2.12
1.05
4.91 2.17
1.08
32.52 2.21
1.26
11.19 2.21
1.10
5.35 3.18
1.59
5.46 3.59
1.76
2.42 2.79
1.39
4.61 3.47
1.73
3.92 3.81
1.88
3.22 4.38
2.16
2.54 3.91
1.87
1.95 4.48
2.23
3.65 3.24
1.51
3.11 4.53
2.15
3.26 4.48
2.11
5.83 2.29
1.10
3.88 3.55
1.66
4.19 2.81
1.36
2.91 3.21
1.53
2.84 3.10
1.53
3.59 3.65
1.79
5.24 4.04
1.95
3.82 3.55
1.65
Identification from Alves et al. (2007).
Obtained by a Gaussian fitting to the distribution of observed polarization angles (measured from the North Celestial Pole to
East).
Number of stars passing the selection criteria which were used to estimate the mean values, hPi and θhPi , (see text).
4.3. Data Analysis
51
P
(qi /σ2 )
hQi = P −2i
σi
P
(ui /σ2 )
hUi = P −2i
σi
The estimated mean polarization value hPi and its associated error δP are then given by
hPi =
δP =
p
hQi2 + hUi2 ,
δQ |hQi| + δU |hUi|
hPi
where δQ and δU are the estimated standard deviation for the mean Stokes parameters hQi and
hUi, respectively. The mean polarization position angle θhPi is given by
!
−1 hUi
θhPi = 0.5 tan
hQi
The number of stars passing the 2σ std filter, the obtained mean polarization, its estimated
uncertainty, and the polarization angle for the mean polarization vector are given in columns 9,
10, 11, and 12 of Table 4.3, respectively. Column 13 shows the dispersion of polarization angles
corrected in quadrature by the mean error of the polarization position angle, that is, ∆θ = (σ2std −
P
hσθ i2 )1/2 , where the mean error, hσθ i, was estimated from hσθ i = σθi /N, where σθi is the
estimated uncertainty of the star’s polarization angle2 .
The global polarimetric properties of the Pipe nebula were already presented in Paper I, and
show some interesting results. For instance, the obtained mean polarizations for the region of B 59
and along the stem are typical for star formation regions (e.g., Vrba et al. 1993; Whittet et al.
1994, 2001), while the values obtained for the bowl are unusually high. Another noteworthy result
presented in Paper I is the apparent general tendency of decreasing dispersion in polarization
angles along the filamentary structure of the Pipe nebula from B 59 toward the bowl, while the
mean degree of polarization increases toward this end. This effect is better visualized by inspection
of the image presented in Fig. 4.4, where we represented the obtained mean polarization degree
and dispersion of polarization angles by filled and open circles, respectively, scaled to the values of
these observational quantities. In fact, this figure is more instructive than the diagram introduced in
Fig. 2 of Paper I, because in addiction to the above mentioned anti-correlation between polarization
degree and dispersion of polarization angles seen along the main axis of the complex, one can also
see how these two quantities distributes spatially over the cloud. In general, one see that fields
toward lower infrared absorption have the tendency of presenting larger values of dispersion of
polarization angles. A noticeable exception is Field 26, located close to the center of the area
2
The uncertainty of the polarization angle is estimated by error propagation in the expression of the position angle
θ, which yields σθ = 21 σP /P, in radians, or σθ = 28.◦ 65 σP /P (see for instance, Serkowski 1974) when expressed in
degrees.
52
10o
10%
o
8
7o
Galactic Latitude
6o
5o
4o
3o
2o
4o
3o
2o
1o
0o
359o
Galactic Longitude
358o
357o
356o
Figure 4.4: Representation of the mean polarization degree (filled circles) and dispersion
of polarization angles (open circles) for the observed areas. The size of the symbols are
proportional to the scale indicated over the left-hand corner of the image. The anti-correlation
between dispersion in polarization angle and mean polarization is clearly seen.
displayed on Fig. 4.4, which presents the second largest dispersion value in our sample (∆θ =
32.◦ 5).
All fields, but three, having a rather broad distribution of polarization angles (∆θ ≥ 10◦ ) are
in the vicinity of B 59. The exceptions are: Field 15, laying in the stem almost middle way from
B 59 to the bowl, the already mentioned Field 26, and Field 27, both located in the eastern side of
the stem, close to the bowl.
4.3.2 Polarization maps
It is instructive to analyze the obtained polarization for each CCD field. In Figs. 4.5 to 4.9 the
obtained polarization is overlapped onto the dust extinction maps of the 5 large areas demarcated
in Fig. 4.1, which cover all observed CCD fields except Fields 39 and 45. The histograms give
the distribution of obtained position angles for each field, identified in the upper right corner. The
gaussians represent the best fit to the distribution and are showed for comparison purposes only –
they help us to visualize how the distributions of some fields depart from the “normal” distribution.
In a classical work, Chandrasekhar & Fermi (1953) obtained a reasonably accurate estimate for
4.3. Data Analysis
10
0
number of stars
20
07
20
10
0
120
160
20
60
160
20
20
05
10
0
120
160
20
60
02
number of stars
09
30
number of stars
13
number of stars
number of stars
40
53
10
0
120
160
20
60
10
0
140
0
40
80
10%
B59
03
number of stars
30
20
10
0
160
20
10
140
0
40
80
-27o 30’
30
40
30
20
10
0
30
20
10
0
11
20
10
0
160
20
14
100
08
80
60
40
20
0
160
20
12
0
160
20
20
10
06
10
01
0
140
0
40
80
10
04
number of stars
40
16
number of stars
30
14
number of stars
number of stars
50
17h 18m
number of stars
160
20
5
0
number of stars
50
number of stars
stem
00
40
Declination (2000)
number of stars
50
12
30
20
10
0
40 80 120 160 20
0
40
80
Figure 4.5: Polarization map for Fields 01 to 14 overlapping the dust extinction map of the
corresponding area (Lombardi et al. 2006). The overplotted contours are for AV = 2, 4 and 8
mag. The length of the vectors correlates linearly with the degree of polarization according to
the scale indicated over the left-hand corner of the image. The vertical dashed-line demarcates the limits between the stem (left) and B 59 (right), as defined in Paper I. Histograms for
the distribution of the polarization angles are shown individually for each field. The identification of the fields is given in the upper right-hand corner of the histograms. The overplotted
gaussian curves are for comparison purposes only. The ‘star’ symbols indicate the location
of the identified candidate YSOs by Forbrich et al. (2009). Note that the location of the young
stellar cluster identified by Brooke et al. (2007) in the heart of B 59 was omitted. The source
on the west side of B 59 core is the Herbig Ae/Be star KK Oph which is very likely associated
to the cloud. The two other objects at the east of B 59 are sources 11 (north) and 16 (south)
listed by Forbrich et al. (2009).
54
10%
19
60
15
-26o 30’
50
number of stars
number of stars
70
40
30
20
10
0
number of stars
10
160
20
20
20
10
20
10
70
30
20
10
0
120
160
20
0
40
18
18
40
number of stars
number of stars
17h 22m
30
0
120
0
40
17
0
140
-27o 30’
21
40
10
30
20
0
20
00
number of stars
number of stars
22
30
0
140
Declination (2000)
160
20
40
16
60
50
40
30
20
10
0
140
160
20
0
40
Figure 4.6: Same as Fig. 4.5 for Fields 15 to 19, 21, and 22. The ‘star’ symbols locate sources
24 (east) and 26 (west) listed by Forbrich et al. (2009).
10%
number of stars
20
10
-26o 30’
number of stars
30
36
26
20
-27o 00’
10
0
120
160
bowl
17h 30m
31
30
30
20
10
0
10
0
120
160
10
40 80 120 160 20
26
24
32
20
20
0
stem
28
number of stars
number of stars
40
20
0
40
80
number of stars
120
160
80
70
60
50
40
30
20
10
0
Declination (2000)
0
30
number of stars
number of stars
30
30
27
20
10
0
120
160
120
160
Figure 4.7: Same as Fig. 4.5 for Fields 20, 26, 27, 30 to 32, and 36. The vertical dashed-line
demarcates the limits between the bowl (left) and the stem (right), as defined in Paper I.
4.3. Data Analysis
55
number of stars
10%
28
50
40
bowl
00
stem
30
20
10
0
23
number of stars
70
60
50
40
30
20
10
0
Declination (2000)
160
20
-25o 30’
-26o 00’
160
20
17h 30m
20
29
number of stars
25
number of stars
number of stars
80
70
60
50
40
30
20
10
0
28
10
0
160
20
160
20
26
90
80
70
60
50
40
30
20
10
0
24
160
20
Figure 4.8: Same as Fig. 4.5 for Fields 23 to 25, 28, and 29. The vertical dashed-line demarcates the limits between the bowl (left) and the stem (right), as defined in Paper I.
10%
70
number of stars
number of stars
44
20
10
160
20
40
30
20
160
20
-25o 30’
41
60
0
number of stars
10
Declination (2000)
number of stars
50
10
0
0
40
30
20
10
0
00
50
number of stars
number of stars
160
20
40
-26o 30’
10
0
30
20
10
0
160
20
30
20
10
34
32
43
100
80
30
60
40
38
37
number of stars
number of stars
40
20
10
20
10
20
0
160
20
120
42
number of stars
50
46
36
number of stars
17h 38m
number of stars
35
40
160
20
80
70
60
50
40
30
20
10
0
33
50
160
20
20
34
60
0
160
20
0
160
20
0
160
20
160
20
Figure 4.9: Same as Fig. 4.5 for Fields 33 to 35, 37, 38, 40 to 44, and 46.
56
the field strength in the diffuse ISM by directly relating the dispersion in polarization position
angle to the ratio of two energy densities: the energy density of the uniform component of the
field and the energy density of turbulence. Since then, it is widely accepted that the mean value
of the distribution of polarization position angle obtained from a polarization map gives the angle
of the mean or uniform (large-scale structured) magnetic field for the region under investigation,
while the dispersion in the distribution gives information about the statistically independent nonuniform (turbulent or random) component of the magnetic field (a detailed discussion concerning
this subject can be found in Myers & Goodman 1991, and references therein).
The effects of the high interstellar absorption in some of the observed fields are clearly seen
on the distribution of the measured stars. For instance, our Field 03, with line-of-sight toward
one of the most opaque regions of the entire nebula, the B 59 region (Román-Zúñiga et al. 2007,
2009), is the observed field with the smallest number of stars with P/σP ≥ 5 (21 stars only). Its
histogram of observed polarization position angles and the obtained mean position angle, θhPi =
48.◦ 8 (Table 4.3), indicate that most of those stars belong to the right-hand tail of the polarization
position angle distribution given in Fig. 4.3 (left panel). Although the obtained large dispersion of
position angles – which is due to 6 stars – the distribution of the remaining stars is rather narrow, as
seen in the histogram for Field 03 shown in Fig. 4.5. The two polarization angles on the right-hand
side of the main distribution (θ = 64.◦ 9 and 70.◦ 1) correspond to [BHB2007] 2 and [BHB2007] 1,
respectively, supposed to be candidate young stars (Brooke et al. 2007; Forbrich et al. 2009). It
is noteworthy that high resolution optical images of the region show a “light cone-shaped” which
apparently emanates from these stars and illuminates the surrounding dust material. Interestingly,
both observed polarization vectors are almost perpendicular to the symmetry axis of this cone.
From the histograms shown in Fig. 4.5 we note that most of the fields presenting large dispersion of polarization angles suggest a multicomponent structure, in special, Field 06 presents
a very interesting geometry for the obtained distribution of the polarization vectors and deserves
further comments (see § 4.5). Fields 01 to 04 show distributions of polarization angles with many
stars having values between 0◦ and 40◦ , while the remaining fields given in Fig. 4.5, already show
distributions with polarization angles between 160◦ and 20◦ , likely what was obtained for most of
the other observed fields.
The area covered by Fig. 4.5 contains, apart from the young stellar cluster identified by Brooke
et al. (2007) embedded in B 59, three of the six candidate YSOs found by Forbrich et al. (2009).
One of them is the well known KK Oph, a pre-main-sequence binary with 1.6” separation and
suggested to constitute a Herbig Ae star with a classical T Tauri companion (e.g., Herbig 2005;
Carmona et al. 2007, and references therein). Although de Winter & Thé (1990) attribute a distance
of 310 pc to this star, it is commonly accepted a distance of 160 pc (e.g., Hillenbrand et al. 1992)
suggesting that this object may have been formed by material formerly associated to the Pipe
nebula. Carmona et al. (2007) estimate an age of about 7 Myr to this system, that is, from 5 to
6 Myr older than the estimated age of the YSOs in B 59. The two other objects are sources 11
and 16 in the Forbrich et al. (2009) candidate YSOs list, and have lines-of-sight toward Fields 09
4.3. Data Analysis
57
and 11, respectively, close to the transition between the B 59 and the stem regions, as defined in
Paper I. These sources were spectroscopically studied by Covey et al. (2010), who confirmed the
youthful character of the latter, and found that it is a visual binary, while the former presents an
ambiguous spectra, that is, it may either be a rather young object or a reddened giant/subgiant.
Figure 4.6 displays the middle portion of the stem. We observed seven fields in this area. The
obtained histograms seem to present a kind of transition between the characteristics observed for
the B 59 region and the ones for the bowl. That is, Field 15 (one of the fields with ∆θ > 10◦ ) have
a distribution that resembles the ones obtained for the fields in B 59, while very close to it one see
Field 16 which shows a distribution with a dispersion typical of the ones presented by fields in the
bowl, however, centered around 0◦ . On the left-hand side of this figure there is Field 22 showing
polarization properties with all the characteristics observed in the bowl, that is, low dispersion of
polarization angles and centered around 160◦ . Two of the Forbrich et al. (2009) YSO candidates
are located in this area. One of them very close to the center of our Field 17 (source 26), the other
one close to the border of Field 18 (source 24). None of these sources were studied by Covey et al.
(2010), who on the other hand, investigated two other sources that turned out to be OH/IR stars,
likely residing in the Galactic Bulge.
Figure 4.7 displays the “transition region” between the stem and the bowl, as denoted by the
vertical dashed-line. In this area we find two of the three fields presenting broad distribution of
polarization angles not belonging to the B 59 vicinity, Fields 26 and 27, the former shows a distribution of polarization vectors that resembles the one observed for Field 06, suggesting that there
may be some similarities between the physical properties of both cores, while the distribution for
the latter clearly shows a bimodal distribution of polarization vectors. All fields presenting particularly interesting polarization distribution are separately discussed in § 4.5. The four eastern fields
of this area present polarimetric characteristics of the bowl, that is low dispersion of polarization
angles, rather high polarization degree and a mean polarization angle centered around 160◦ . A detail that calls our attention is the polarization probed by Field 20 (upper right corner of the figure).
While all other fields shown in this figure present a distribution of polarization angles centered
around ∼160◦ , the distribution of polarization angles for Field 20 is centered around ∼30◦ . This is
the second less absorbed field (AV ≈ 1.m 5), so that the polarization mapped by these stars may be
mainly caused by a background medium.
The area displayed in Fig. 4.8 is located to the north of the one displayed in Fig. 4.7 and covers
mostly the more diffuse medium of the Pipe nebula, except for Field 29 with line-of-sight toward
a portion with higher extinction. Although this field presents a rather large dispersion of position
angles, as compared to the other fields in the bowl, its rather high mean polarization and mean
polarization angle centered around 160◦ , are characteristics of that part of the complex.
Figure 4.9 displays eleven fields observed in the bowl area. The main characteristics of the
fields observed toward this region of the Pipe nebula are the high degree of polarization and the
highly aligned polarization vectors, as testified by the low dispersion of polarization angles shown
by the histograms displayed on this Figure.
58
B59
Mean Polarization Angle (o)
60
stem
bowl
F03
40
F20
20
180
160
F06
F27
140
10
15
20
25
30
Right Ascension (17h + min)
35
40
Figure 4.10: Distribution of mean polarization angle, θhPi , as a function of the right ascension
of the observed field, which correlates quite well with its position along the long axis of the
Pipe nebula. Filled (blue) and open (red) dots represent values for fields associated to lower
and higher infrared absorptions, respectively. The former are mostly fields outside the main
structure of the Pipe nebula, namely, Fields 02, 04, 07, 08, 16, 19 to 21, 23 to 25, and 27.
The gray bars give the interval defined by θhPi ± ∆θ, where ∆θ is the dispersion of polarization
angles (see Table 4.3).
It is also interesting to analyse the distribution of mean polarization angle as a function of
the right ascension of the observed fields. Such distribution is shown in Fig. 4.10, and as already
mentioned, due to a fortuitous coincidence this celestial coordinate correlates quite well with the
field’s position along the long axis of the Pipe nebula. Most of the obtained mean polarization
angles are in the interval θhPi ∼ 180◦ ± 20◦ , indicating that the local uniform magnetic field is
somewhat aligned perpendicularly to the main axis of the cloud complex.
Apart from four fields, identified in Fig. 4.10, the distribution of the remaining mean polarization position angles seems to follow a pattern. The values obtained for fields toward directions
having lower infrared absorption, represented by open dots, present a rather constant value all
over the stem of the Pipe, including the B 59 region, except for two of the four mentioned fields
(Fields 20 and 27). On the other hand, the distribution shown by fields with rather large infrared
absorption, represented by filled dots, is more interesting. Again, apart from the other two identified fields (Fields 03 and 06, both in the B 59 region), which as we have mentioned earlier show
some kind of peculiar characteristic, one see that the mean polarization angles for these fields
seems to be rather constant (θhPi ∼ 180◦ ) from B 59 to almost the center of the stem, then decrease
slowly until close to our arbitrary border of the bowl region, and rise up again by a small value
and became almost constant (θhPi ∼ 170◦ ) in the bowl.
This behaviour somehow suggests that the uniform component of the magnetic field is “uniform” in the surrounding diffuse medium but presents small systematic variations along the dense
4.3. Data Analysis
59
parts of the complex. A remarkable point to be noted is the fact that the right ascension of Fields
20 and 27 somehow coincides with the one where the mean position angle of the fields associated
to cores seems to reach its smallest value. Unfortunately our observational data do not allow us to
investigate further this coincidence.
4.3.3 Deriving AV from 2MASS data
It is instructive to compare the obtained mean polarization with the interstellar extinction acting
on each observed line-of-sight. The mean extinction in each field could have been estimated by
the use of the extinction map obtained by Lombardi et al. (2006). In fact, we started using their
image with this purpose, however, as already mentioned, some of the observed fields contain areas
of high interstellar absorption that were not probed by our stellar sample. Thus, simply averaging
the infrared extinction over the observed field would provide a larger value for the reddening
than the one actually probed by our obsereved stars. Because of that, we decided to use another
approach, that is, the mean extinction in each field may be determined by assuming that the old
bulge population present in each observed volume has an upper giant branch similar to that found
in K, J − K color magnitude diagrams (CMD) of Baade’s window (see e.g., Frogel et al. 1999).
We proceeded assuming that the upper giant branch in each of our observed fields is comparable
to and has the same slope as the extinction-corrected template derived by Dutra et al. (2002), given
by
(KS )0 = −7.81 × (J − KS )0 + 17.83
(4.1)
This assumption is perfectly justified, because those authors applied this template to study the
interstellar reddening in a volume that partially contains the Pipe nebula. We also assumed that
the relation between extinction and reddening is given by
AKS = 0.670 E(J − KS ).
(4.2)
From the (KS , J − KS ) CMD values of each star in the field, we calculated the shift along
the reddening vector given by Eq. (4.2) required to make it fall onto the reference upper giant
branch, Eq. (4.1). Since the adopted template appropriately describes the upper giant branch locus
for stars with 8 ≤ (KS )0 ≤ 12.5, all star presenting a corrected KS magnitude outside this range
were excluded from our mean absorption estimate, and similarly to what we have done when
estimating the mean polarization, a 2-σ filter was applied to the obtained distribution of E(J − KS )
and the field’s extinction value was taken as the median of the distribution of stars passing the
clipping selection. The estimated mean AKS values were then converted to AV by the relation
derived by Dutra et al. (2002), i.e. AKS /AV = 0.118. To illustrate the method used to estimate
the mean interstellar absorption, we show in Fig. 4.11 the CMD obtained for our Field 43. It is
clearly noticeable that most stars brighter than KS ≈ 12m , in this field, are reddened by about
E(J − KS ) = 0.m 5. Stars used in our estimate of the mean interstellar absorption are represented,
60
6
FIELD 43
KS (mag)
8
10
12
14
0
1
2
J−KS (mag)
3
Figure 4.11: Color-magnitude diagram for stars in Field 43. Stars passing the selection criteria
(see text) and used to estimate the field’s mean interstellar absorption are represented by filled
(red) circles. The straight line represents the reference upper giant branch (equation 4.1). It is
clear the gap between the standard reference line and observed stars brighter than KS ≈ 12m ,
which corresponds to an interstellar reddening of about E(J − KS ) = 0m
. 5.
in Fig. 4.11, by filled circles. In general, an analysis of the (J − H, H − KS ) color indices shows
that most of the stars fainter than KS ≈ 12m in our diagrams are likely to be main-sequence stars
of earlier types (typically B–G).
The left panel of Fig. 4.12 shows the obtained CMD for all observed star, in our sample, with
P/σP ≥ 5 and identified in the 2MASS catalogue. For comparison, the (J − H) − (H − KS ) diagram
for the same stars is given in the right panel. As one can see, most of the observed stars seems
to occupy the area corresponding to normal reddened stars. The stars in this zone could also be
dereddened onto intrinsic color lines by extrapolation from the observed stellar locus along the
appropriate reddening vector.
The obtained values of AV and their estimated uncertainties are given respectively in columns
14 and 15 of Table 4.3. The later were estimated from the standard deviation of the obtained
distribution of E(J − KS ), before applying the 2-σ filter, being that the stellar photometric errors
have not been taken into account.
Although the extinction can reach very high values toward some of the observed cores, one see
in Table 4.3 that, as expected, our optical polarimetric survey is probing the less absorbed areas
only (e.g., from AV ≥ 0.m 6 to AV ≤ 4.m 6). It is important to note that although Román-Zúñiga et al.
(2007) found evidences that the extinction law prevailing in the densest regions of B 59 agrees
more closely with a dust extinction with a total to selective absorption RV = 5.5 we adopted the
typical values for the diffuse interstellar medium, since we are studying regions with extinctions
4.4. Polarizing efficiency toward the Pipe nebula
61
Figure 4.12: Left panel: KS − (J − KS ) CMD for all observed star with P/σP ≥ 5 identified in
the 2MASS catalogue. The straight line represents the reference upper giant branch, Eq. 4.1,
obtained by Dutra et al. (2002). Right panel: (J −H)−(H −KS ) color-color diagram for the same
stars. The theoretical locus for the main-sequence stars is represented by the continuous line,
while the white (red dashed-line) represents the giant branch stars. The absorption vector
indicated in both diagrams corresponds to AV = 5m .
well below AK . 2m .
As an independent control of the method used to evaluate the interstellar absorption towards
the observed areas, one may compare the results obtained for our example field, Field 43, with the
ones we would have obtained from the extinction map produced by Lombardi et al. (2006). As
one may verify from visual inspection of Fig. 4.9, our stellar sample covers rather uniformly the
area defined by Field 43 which means that, simply averaging the Lombardi et al. extinction over
this area will probably yield values that are representative of the mean extinction probed by the
observed stars. Such procedure give us AV = 3.m 28 ± 1.m 26, which agrees quite well with the value
given in Table 4.3.
4.4 Polarizing efficiency toward the Pipe nebula
The degree of polarization produced for a given amount of extinction is referred to as the
“polarization efficiency” of the intervening dust grains. This efficiency of polarization depends on
both the nature of the grains and the efficiency with which they are aligned in the line-of-sight. The
most efficient polarization medium conceivable is obtained by modeling the dust grains as infinite
cylinders (very long in comparison to their radii) with diameters comparable to the wavelength,
perfectly aligned with their long axes parallel to one another and perpendicular to the line of
sight. For such a model, Mie calculations for particles with dielectric optical properties, place a
theoretical upper limit on the polarization efficiency of the grains due to directional extinction at
62
visual wavelengths of p/AV ≤ 14 % mag−1 (see, for instance, Whittet 2003). The observations,
however, show that the upper limit predicted by this very idealized scenario is far from being
reached. In general, studies of interstellar polarization demonstrate that the efficiency of the real
Galactic interstellar dust as a polarizing medium is more than a factor of 4 less than predicted
for the ideal polarizing medium. The observational upper limit on the ratio of polarization to
extinction for the diffuse interstellar medium is given by p/AV ≈ 3 % mag−1 (Serkowski et al.
1975).
Considering that our sample contains a rather large number of objects, in the bowl region,
showing outstanding degrees of polarization, it is natural that we try to investigate if these observed
areas present unusual polarimetric properties as compared to the common Galactic interstellar
medium.
The diagrams shown in Fig. 4.13 were constructed in order to investigate the obtained ratio
between our estimated mean degree of polarization and mean total interstellar absorption for the
observed fields toward the Pipe nebula — error bars were omitted in these diagrams for the sake
of clarity. The plot of mean polarization versus total visual absorption given in the Fig. 4.13
(top panel) shows that basically all data points lie on or below the line representing the usual
relation p/AV ≈ 3 % mag−1 — the two points appearing above this line represent data obtained
for Fields 38 and 41, however, taking into account the estimated 1-σ uncertainties for the mean
degree of polarization and total interstellar absorption, these two fields may also obey the above
relationship. On the one hand, this result indicates that the interstellar material composing the
Pipe nebula follows the usual behaviour of the common diffuse interstellar medium. On the other
hand, as one can see from the values tabulated in Table 4.3 we have found levels of mean degree
of polarization that are unusual for the same interstellar material.
Several previous investigations have suggested that the polarizing efficiency of the interstellar
dust declines systematically with total extinction, as one probes progressively denser environments
within a dark cloud (e.g., Goodman et al. 1992, 1995; Gerakines et al. 1995). The obtained diagram of polarizing efficiency, p/AV , as a function of the interstellar absorption (Fig. 4.13 – middle
panel), does not show clearly this tendency, at least not for the covered interval of interstellar
absorption. In fact, on the contrary, if we exclude Field 02, which shows the lowest interstellar
absorption and a polarization efficiency of almost 3 % mag−1 , the other fields show a tendency of
increasing efficiency with the interstellar absorption.
More interestingly is the diagram shown in the bottom panel of Fig. 4.13, which shows the
distribution of the estimated polarization efficiency of the observed fields as a function of their
position along the long axis of the Pipe nebula. It is known that variations in polarization efficiency might result from changes in physical conditions that affect alignment efficiency, such as
temperature, density and magnetic field strength, or in grain properties such as their shape and size
distribution and the presence or absence of surface coatings. Most of the observed fields in the stem
(including its tip — the B 59 region), present a polarization efficiency around p/AV ∼ 1 % mag−1 ,
then it rises up and down when one move along the bowl from west to east, reaching values of
4.4. Polarizing efficiency toward the Pipe nebula
63
P (%)
15
10
5
0
P/AV (%/mag)
4
3
2
1
0
0
P/AV (%/mag)
4
1
B59
2
3
AV (mag)
stem
4
5
bowl
3
2
1
0
10
15
20
25
30
35
Right Ascension (17h + min)
40
Figure 4.13: Top panel: Plot of mean polarization (P) versus total visual absorption (AV ) derived from the 2MASS data for the observed stars with P/σP ≥ 5. The solid line represents
optimum alignment efficiency (P(%) = 3 × AV ). Middle panel: Polarization efficiency (P/AV )
versus visual absorption AV . Bottom panel: Distribution of the polarization efficiency as a
function of the right ascension of the observed field. Symbols have the same meaning as in
Fig. 4.10.
64
about p/AV . 4 % mag−1 . Summarizing, although showing an interesting behaviour, the global
properties of the probed dust material composing the Pipe nebula does not seem to present any
special peculiarity, when compared to the common diffuse interstellar medium, that could explain
the observed high degrees of polarization. However, one notice a clear difference between the
behaviour shown by the polarimetric properties presented by fields located in the stem and in the
bowl.
Although the division between the regions denominated B 59 and stem was chosen rather arbitrarily (in Paper I, it is characterized by a rising on the degree of polarization), one notice an
interesting feature in the bottom panel of Fig. 4.13. The polarization efficiency seems to increase
along the dust filaments probed by our sample when we move from the B 59 region to the stem.
It happens only for the fields of the stem shown in Fig. 4.5, after that, the ratio p/AV returns to
the typical value of ∼1 % mag−1 observed for B 59 and the remaining fields in the stem. This behaviour can be an indication that distinct physical regimes may be acting on different fragments of
the stem. For instance, variations of the value of p/AV may arise where the local magnetic field is
not orthogonal to or its direction varies along the line-of-sight, or where the processes responsible
for grain alignment change for some reason (grain composition, size, shape, etc). The interested
reader will find a good review on the efficiency of grain alignment in the work by Whittet et al.
(2008, and references therein). It is worthwhile to mention that the point where the polarization
efficiency returns to its typical value of ∼1 % mag−1 almost coincides with the place where one
noticed the value of the mean polarization angles started decrease (see Fig. 4.10).
All these results reinforce once more how interesting is the Pipe nebula and suggest that this
complex may be a testbed for different theories of dust grain alignment efficiency.
4.5 Fields showing interesting polarization distributions
Inspection of Figs. 4.5 to 4.9 shows that some of the observed fields present remarkable polarization geometries. For many of them one clearly note that the obtained polarization angles for
the objects in the field suggest a multicomponent, or in some cases a hoop-like, distribution. As
one have seen, in most cases the mean polarization vector is aligned perpendicularly to the long
axis of the Pipe nebula, but there is the case of Field 20 (see Fig. 4.10) where the distribution of
polarization angles does not follow the average behaviour for the region. Below we introduce three
of the most interesting observed fields, and comment on the fields having high mean polarization
(hPi ≥ 10%).
4.5.1 Field 06
The polarization map for Field 06 is shown in Fig. 4.14, one of the most interesting distribution
in our survey. This is one of the four fields we have identified in Fig. 4.10 as having a mean
polarization angle which seems to disagree from the pattern observed for the cloud complex. In
order to emphasize the geometry of the magnetic field in this region, all star for which polarization
4.5. Fields showing interesting polarization distributions
65
5%
5%
35
Declination (2000)
Declination (2000)
40
45
-27o 40’
-26o 50’
17h 12m 15s
00s
11m 45s
17h 26m 00s
25m 45s
30s
15s
Figure 4.14: Left panel: Polarization vectors overlaid on the optical image of Field 06. All
measured polarization for this field are represented in this figure and not only the ones having
P/σP ≥ 5. The observed orientation of the polarization vectors seems to embrace the dust
core whose existence is suggested by the scarcity of observable stars to the left of the center.
The length of the vectors correlates linearly with the degree of polarization according to the
scale indicated over the left-hand corner. Right panel: Same for Field 26.
has been measured are represented in the map. The polarization vectors seem to suggest that
the local magnetic field follows the border of the dust cloud evidenced by the higher interstellar
absorption noticed to the left of the center. Has this core been modeled by the field or, on the
contrary, was the field shaped by the core? In any case, this seems to be an interesting region
which deserves further investigation.
4.5.2 Field 26
The polarization map obtained for Field 26, Fig. 4.14, seems to be the result of a mixture of
two distributions, a main component centered around 160◦ (see also the histogram introduced in
Fig. 4.7), combined with an hoop-like component. An interesting point is that, as one may observe
in the polarization map, the surveyed area seems to show different characteristics toward directions
located northern and southern of the densest parts of the cloud — visually characterized by the
absence of stars. Apparently, at the south only the main component of the distribution (θ ∼ 160◦ ) is
present, while at the north we observe the presence of both distributions. An inspection of Fig. 4.7
shows that the northern part of this field probes a more diffuse part of the interstellar material, as
what happens in the case of Field 27 (see below), while the southern stars have line-of-sight toward
a volume presenting higher extinction. One of the cores studied by Frau et al. (2010), who used the
IRAM 30-m telescope to carry out a continuum and molecular survey toward four of the starless
66
5%
5%
40
Declination (2000)
Declination (2000)
00
05
45
-25o 50’
-27o 10’
17h 25m 45s
30s
15s
00s
17h 33m 30s
15s
00s
32m 45s
30s
Figure 4.15: Same as Fig. 4.14 for Field 27 (left) and 35 (right).
cores from the list of Alves et al. (2007), is Core 48, which is associated to the higher interstellar
absorption shown in Fig. 4.14. The radio data indicates that, although being very diffuse, this core
has a strong dust emission, and their molecular analysis suggests that chemically it seems to be in
a very early stage of evolution.
4.5.3 Field 27
There is no dense core associated to the volume probed by this field, and it is other of the fields
having mean polarization angle not fitting in the main pattern of mean position angles, as defined
in Fig. 4.10. The distribution of polarization vectors shown in Fig. 4.15 (see also the histrogram
of polarization angles shown in Fig. 4.7) clearly shows a bimodal distribution with mean angles
values centered on ∼135◦ and ∼155◦ . Both components seem to be well distributed all over the
surveyed field.
4.5.4 Distribution of polarization and position angles as function of the 2MASS KS
magnitude for Fields 26 and 27
The top panels of Fig. 4.16 display the measured polarization angles as function of the 2MASS
KS magnitude for Fields 26 and 27. An interesting result comes out from these diagrams. One
clearly notice that the distribution shown by Field 27 (right panel) is rather defined by the stellar
KS magnitude and occupies different regions of the diagram. Stars having KS & 12m , that is statistically populated by main sequence stars, as already mentioned in § 4.3.3, are mainly associated to
the component having higher mean angle, while stars having KS . 12m , statistically populated by
giant stars, are basically associated to the component having lower mean angle. This is indicated
by the horizontal and vertical dashed lines positioned at θ = 150◦ and KS = 12.m 0, respectively.
4.5. Fields showing interesting polarization distributions
FIELD 26
FIELD 27
180
180
67
120
60
150
120
0
4
polarization (%)
polarization (%)
6
3
2
1
0
6
4
2
0
8
10
K2MASS (mag)
12
14
8
10
12
K2MASS (mag)
14
Figure 4.16: Distribution of polarization degrees (bottom panels) and polarization angles (top
panels) as a function of the K magnitude. Data obtained for Field 26 is represented on the
left panels and for Field 27 on the right panels. All observed stars in each field were used to
construct these diagrams. The horizontal and vertical dashed lines, represented in both top
panels, were arbitrarily positioned at θ = 150◦ and K2MASS = 12m
. 0, respectively (see text).
Mean uncertainties of the quantities are indicated by the horizontal and vertical bars on the
lower left corner of each diagram.
The distribution presented by Field 26 is rather different but shows some of the characteristics
presented by Field 27. For the sake of comparison, we have represented the same horizontal
and vertical dashed lines in both diagrams. While the polarization angles observed for Field 27
are restricted between θ ∼ 120◦ and 170◦ , Field 26 presents basically all values of polarization
angles. However, as observed for Field 27, most of the stars in Field 26 fainter than KS = 12m has
polarization angle larger than ∼140-150◦ , suggesting that the same kind of interstellar structures
may be present toward both line-of-sights, which are separated about 20′ from each other.
It is also interesting to compare the distribution of degree of polarization as a function of the
stellar magnitude (bottom panels). First of all, one notices that although Fig. 4.7 seems to indicate
that the line-of-sight toward Field 27 is less affected by interstellar absorption than Field 26, the
measured polarization for the latter is generally smaller than the one obtained for stars in the former
field — it must be noted, however, that the estimated average interstellar absorption in § 4.3.3 is
essentially the same for both fields (see Table 4.3). The KS − (J − KS ) CMD for the observed
stars in Field 27 suggests that the interstellar absorption toward this line-of-sight is rather more
uniform than the one probed by stars in Field 26, as one should expect from the dust extinction
map obtained by Lombardi et al. (2006) and shown in detail by our Fig. 4.7. Thus, the estimated
68
average interstellar absorption for Field 27 is more representative of what we have all over the
surveyed volume, while the one estimated for Field 26 is a mean between regions showing rather
high absorptions, e.g. toward the southern area of the CCD field, with regions not so absorbed
probed by the stars located in the northern area of the CCD field.
4.5.5 Comments on the Fields with high mean polarization degree
Five of the observed fields present mean degree of polarization hPi ≥ 10%, they all lay in the
bowl and are Fields 35, 37, 38, 40, and 41. In Fig. 4.9 these fields are almost aligned along the
diagonal crossing the image from the upper left-hand to the lower right-hand corner. The main
characteristics of these fields, apart from the high value of observed polarization degree, is the
very low dispersion of polarization angles, which suggests that the turbulent energy prevailing
on the observed cores must be quite low (see § 4.6). In particular, it is noticeable the quite low
dispersion presented by Field 35 (see also Fig. 4.15, right panel), the lowest in our survey, with a
rather “normal” distribution.
Although also presenting a very low dispersion, Field 38, the one with the highest mean polarization in our survey, shows a fairly asymmetry in the observed distribution of polarization angles.
As shown in Fig. 4.17, it may be caused by two dust cloud components along the observed line-ofsight, each one subject to slightly different orientations of ambient magnetic fields. These clouds
may be associated to the two main velocity components that seem to characterize the kinematics of
the ‘bowl” (e.g., Muench et al. 2007), even though they have not detected two C18 O components
toward their observed line-of-sight through this field.
The distribution of polarization angles as a function of the 2MASS KS magnitudes does not
present any remarkable feature, unless for the fact that the 6 brightest stars in the field (KS . 8.m 0)
have polarization angles between 169◦ and 172.◦ 5, while the remaining stars present a rather normal
distribution between ∼ 165◦ and 180◦ .
Field 40 contains other of the cores observed by Frau et al. (2010), Core 109. The radio data
show that this object presents a strong dust continuum emission, is the densest among the four
investigated cores, and one of the most massive. The interstellar extinction experienced by the
observed stars is very nonuniform, ranging from AV ≈ 2m to AV & 5m . Interestingly the observed
13 CO molecular emission shows a double velocity component (Alves et al., in preparation), which
is not seen in C18 O (Muench et al. 2007, ratified by the work in preparation by Alves et al.), and
could explain the asymmetry of the distribution of polarization angles which, as observed for Field
38, is also noticed for this field but this time due to a small excess in the left wing of the distribution
(see distribution introduced in Fig. 4.9). Analyzing the distribution of the polarization angles as
function of the 2MASS KS magnitudes one obtained that this excess is due to stars brighter than
KS ∼ 11.m 5, which are in average more affected by the interstellar absorption and present higher
mean degree of polarization. Although located in the bowl, supposed to be the less evolved region
of the Pipe nebula, the molecular investigation conducted by Frau et al. (2010) indicated that the
core may be one of the chemically most evolved in their molecular survey.
4.6. The Structure Function of the polarization angles in the Pipe nebula
69
number of stars
30
20
10
0
160
170
180
10
Figure 4.17: The distribution of polarization angles for Field 38 is clearly asymmetric suggesting two components. Our best fitting represented by the full line (red) is the result of two
Gaussian components, one centered at 170◦. 2, σ std = 1.◦ 83, and other at 176◦. 2, σ std = 2.◦ 36,
represented by the dashed lines (blue). All observed stars in this field have P/σP > 11, being that most of them have a much larger signal-to-noise ratio, meaning that the theoretical
uncertainties of the estimated polarization angles are in general much smaller than 2◦. 6.
4.6 The Structure Function of the polarization angles in the Pipe
nebula
4.6.1 Basic definitions
The second–order structure function (hereafter S F) of the polarization angles, h∆θ2 (l)i, is
defined as the average of the squared difference between the polarization angles measured for all
pair of points separated by a distance l (e.g. see equation 5 of Falceta-Gonçalves et al. 2008). Thus,
the S F give information on the behavior of the dispersion of the polarization angles as a function
of the length scale in molecular clouds. Recently, it has been used as a powerful statistical tool to
infer information of the relationship between the large-scale and the turbulent components of the
magnetic field in molecular clouds (Falceta-Gonçalves et al. 2008; Hildebrand et al. 2009; Houde
et al. 2009). Given the large statistical sample of the polarization data in the Pipe nebula, it is
interesting to compute the S F along the Pipe nebula to scales up to few parsecs. For a qualitatively
discussion we will first use the square root of S F, also called the angular dispersion function or
ADF (Poidevin et al. 2010). The use of the ADF instead of the S F allows a more straightforward
comparison of the behavior of position angle dispersion as a function of the length scale. Then,
we use the S F to compare our statistical sample with the previous works (Falceta-Gonçalves et al.
2008; Houde et al. 2009).
70
4.6.2 Qualitative analysis
We have first computed the ADF for all the individual fields using a logarithmic scale between
(5.6 mpc) and 11.′ 8 (0.35 pc). This range was selected in order to have a good statistical sample.
Figure 4.18 shows the ADF for all the Fields but 3, 6, 26. These three fields, which are the ones that
exhibit the highest polarization angle dispersion (see Table 4.3), are shown separately in Fig. 4.19.
There is a clear trend in the distribution of the ADF along the Pipe nebula (see Fig. 4.18). On one
hand, fields in B 59 (1–8) not only show a higher polarization angle dispersion at all the observed
scales but the ADF slope is the highest. A steep slope is an indication that the large-scale magnetic
field orientation in the plane of the sky changes significantly. Fields 3 and 6 have dispersion values
at scales larger than ≃ 0.1 pc close to the expected maximum dispersion that would be obtained in
case of a purely random polarization angle distribution, ≃ 52◦ , (Poidevin et al. 2010). As pointed
in § 4.5.1 for Field 6 this is due to a strongly distorted field surrounding a core. On the other hand,
all the Fields in the bowl (28–46) not only have a remarkably small dispersion of the position
angles (Alves et al. 2008) but this trend is also observed in the ADF at all the observed scales.
Indeed and in contrast with B 59, the almost flat slope of the ADF in the bowl Fields indicate that
the projected magnetic field in the plane of the sky is very uniform. The ADF behavior of the stem
Fields is intermediate between that of B 59 and the bowl. However, the global ADF properties
of field 26 differ from the general trend found in the stem: it shows an unusual high dispersion,
≃ 40◦ at all scales. Compared with other Fields with also a high dispersion (e.g. 3 and 6) the ADF
slope of Field 26 is relatively flat. Field 27, the one with a bimodal distribution (see § 5.3), shows
a similar ADF behavior to Field 26 but a smaller level: ADF ≃ 17◦ at all scales. Because of the
peculiarities of these two Fields, we treat them as a distinctive region in the Pipe nebula for the
S F analysis. Here on, we call this region as the “stem–bowl border”. We also include Field 20
in this region because its average mean direction is quite different from the ones of the rest of the
stem (see Fig. 4.10) and it is relatively near to Fields 26 and 27.
Figure 4.20 shows the S F for the four distinctive regions within the Pipe nebula: B 59, the
stem (except Fields 20, 26 and 27), the bowl and the stem–bowl border. By combining the different
fields of each region, the S F can be computed at larger scales, up to few parsecs (see left panels
of Fig. 4.20). The general trend described in the previous paragraph for the ADF also applies for
the S F. For example, it is remarkable that the bowl shows very low S F values up to scales of few
parsecs, with position angle dispersion lower than ≃ 10◦ . Yet, B 59 and the “stem–bowl border”
show an abrupt increase of the S F at scales larger than 0.3–0.5 pc. For B 59 this is due to the
high PA dispersion Fields 3 and 6. Indeed, if these two fields are excluded, the resulting S F is
smoother at these scales.
8′′
4.6.3 Comparison with Houde et al. (2009)
The larger statistics obtained by dividing the Pipe in four region also allows to better sample
the smaller scales. The right panels of Fig. 4.20 show that at scales of few hundredths of a parsec
71
Figure 4.18: Square root of the second order structure function of the polarization angles,
h∆Φ(l)2 i1/2 , for all the individual fields (except for Fields 3, 6, and 26) observed in the Pipe
nebula. The units of h∆Φ(l)2 i1/2 are degrees. The upper row panels have a larger range of
values in the abscissa axis. Fields 1 to 8 are located in B 59. Fields 9 to 24 and 27 are in the
stem. The rest of the fields belong to the bowl. The dashed line shows the 16.◦ 6, which is the
value of the dispersion of the position angles for turbulent and magnetic equipartition (Troland
& Crutcher 2008).
Figure 4.19: Same as Fig. 4.18 but for Fields 3, 6 and 26, which show a higher dispersion.
72
Figure 4.20: Second–order structure function of the polarization angles, h∆Φ(l)2 i, for the five
distinctive regions in the Pipe nebula (the list of fields associated with each region is given
in Table 4.4). Right and left panels show the smallest and largest scales for each region,
respectively. The gray (red) histogram for B 59 shows the structure function without Fields 3
and 6. The dashed-lines (blue) indicates the best fit of equation 4.3 for distance up to 0.07 pc.
73
the S F increases linearly with length scale. Yet, at scales of . 0.01 pc, the S F drops fast when
approaching to the zero length scale. This is a clear indication that we are starting to resolve the
correlation length scale for the turbulent magnetic field component, which is the scale at which
the turbulent energy is dissipated. In order to approximately estimate the turbulent length scale,
we follow the recipe given in the detailed analysis carried out by Houde et al. (2009), where they
assumed a Gaussian form for the autocorrelation function for the turbulence. We use equation 44
from Houde et al. (2009) taking into account that the effective angular resolution of the optical
polarization data can be considered zero. Therefore, in that equation the angular resolution term
is W = 0. Thus, equation 44 from Houde et al. (2009) can be rewritten as:
2 /2δ2
t
h∆Φ(l)2 i ≃ a0 l + a1 [1 − e−l
]
(4.3)
The first term, a0 l, gives the large-scale magnetic contribution to the S F (note that we have
adopted a linear dependence instead of the original l2 dependence of the aforementioned Eq. 44).
The second term corresponds to the turbulent contribution to the S F. δt is the turbulent length
scale and a1 is a function of the large–scale magnetic field strength, B0 , the turbulent component
of the magnetic field, δBt , and of N, the number of turbulent correlation lengths along the line of
sight3 :
a1 = (2/N) (δB2t /B20 )
(4.4)
N can also be understood as the number of independent turbulent cells along the line of sight
(Houde et al. 2009). We have used equation 4.3 to fit the S F data in the four Pipe regions for the
scale range shown in the right panels of Fig. 4.20. These are the scales in which the large-scale
magnetic field contribution to the S F is basically linear. For each of the four Pipe regions a χ2
analysis was carried out to find the best set of solutions for the free parameters a0 , a1 and δt . The
best-fit solutions obtained are given in Table 4.4 and the 99% and 67% confidence intervals for a1
and δt are shown in Fig. 4.21. The dashed blue line in the right panels of Fig. 4.20 show the best
solution for each region. We find that the turbulent correlation length, δt , is in all cases of few
milliparsecs. Given that the assumption of the Gaussian form for the turbulence autocorrelation
function is not correct, the found values should be taken as an approximation. In any case, the
right panels of Fig. 4.20 show that the turbulent correlation length should be . 0.01 pc. Indeed, at
the 99% confidence level the χ2 analysis provides an upper limit for δt of ≃ 12 mpc (see Fig. 4.21).
This upper limit is slightly lower that the δt found for OMC-1, 16 mpc, from submm polarization
observations (Houde et al. 2009).
From Eq. 4.4 we can estimate the turbulent to magnetic energy ratio, δB2t /B20 , if the number of
independent turbulent cells, N, is known. For optical polarization data, the number of independent
√
turbulent cells is N ≃ ∆/( 2π δt ) (Houde et al. 2009), where ∆ is the cloud thickness. ∆ ≃
N(H2 )/n(H2 ), where N(H2 ) and n(H2 ) are the column and volume densities of the molecular gas
3
Note that this term is equivalent to number of the magnetic field correlation length along the line of sight introduced
by Myers & Goodman (1991)
74
Table 4.4: Structure function parameters for the Pipe nebula
Region
a0
2
( radian
pc )
B 59
stem
stem–bowl
bowl
a
0.44
0.08
0.38
0.01
a1
(radian2 )
δt
(mpc)
(δB2t /B20 )a
Fields
0.025
0.021
0.054
0.008
2.1
4.8
≤ 2.1
4.4
0.4
0.2
0.8
0.1
1–8
9–19, 21–25
20, 26, 27
28–46
Estimated for N = 30 (see text).
traced by the optical polarization data. N(H2 ) can be obtained from the typical visual extinction of
the observed fields. The average visual extinction for the bowl is 3.6 mag, whereas for the rest of
the regions is 2.1 mag. Using the standard conversion to column density (Wagenblast & Hartquist
1989), these values yields to N(H2 ) ≃ 4.5 × 1021 and 2.6 × 1021 cm−2 for the bowl and for the
rest of the regions, respectively. For the observed fields, Paper I estimated that the volume density
of the gas associated with the optical polarization is n(H2 ) ≃ 3 × 103 cm−3 . Therefore, the cloud
thickness of 0.5 pc for the bowl and of 0.3 pc for the rest of the regions. With these values and using
for δt the range at the 67% confidence interval (see Fig. 4.21) we obtain that N ranges between 25
and 100 for the bowl and 15 to 60 for the rest of the regions. Nevertheless, a high value of N will
also reduce significantly the observed polarization level. But all the bowl fields and many of the
stem fields have polarization levels of 4–15% and 3–4%, respectively. Therefore, it is unlikely the
case of a high N, at least, for these two regions. Indeed, Myers & Goodman (1991) estimated that
for optical polarization observations N is expected to not be larger than ≃ 14. Houde et al. (2009)
found N ≃ 21 for OMC-1 from submm dust polarization observations that trace significantly
larger column densities. Therefore, we tentatively adopt a relatively high value of N = 30. For
this case, the magnetic field appears to be energetically dominant with respect to turbulence in the
Pipe nebula except for the “stem–bowl border”, where magnetic and turbulence energy appear to
be in equipartition (see Table 4.4).
4.6.4 Comparison with Falceta-Gonçalves et al. (2008)
Falceta-Gonçalves et al. (2008) carried out simulation of turbulent and magnetized molecular
clouds computing the effect on the dust polarization vectors in the plane-of-the-sky for cases with
super-Alfvénic and sub-Alfvénic turbulence (i.e., clouds energetically dominated by turbulence
and magnetic fields, respectively). They computed the S F derived from dust polarized emission
as well as from optical polarization using background stars for the different sub and super-Alfvénic
cases, and for different angles of the magnetic field with respect to the line of sight (see Figs. 6
and 11 of this paper). The SF for super-Alfvénic turbulence is clearly higher than the one for subAlfvénic turbulence: The S F ranges from 0.4 at the smallest scales up to ≃ 1.0 to the highest scales
75
Figure 4.21: Plot of the set of the solutions for the δt and a1 parameters of the S F . The inner
and outer contours show the 63.3% and 99% confidence regions of the χ2 , respectively.
(see central panel of Fig. 6 from Falceta-Gonçalves et al. 2008). For the case of sub-Alfvénic
turbulence such a high values of the S F are reached only in the cases where the magnetic field
direction is close to the line of sight. For the other cases of sub-Alfvénic turbulence, S F . 0.5.
Comparing the S F obtained in the four Pipe nebula regions (Fig. 4.20) with the results of FalcetaGonçalves et al. (2008) it is clear that B 59, the stem, and the bowl are compatible with the presence
of sub-Alfvénic turbulence. The behavior of the S F for the stem–bowl border (S F from 0.1 at the
smallest scale to & 1.0 at the larger scales) may indicate the case of sub-Alfvénic turbulence with
a magnetic field near the line of sight rather than super-Alfvénic turbulence. Indeed, the only
individual field in the Pipe nebula that at all scales have a S F compatible with the super-Alfvénic
turbulence is Field 26.
4.6.5 Summary of the S F analysis
The comparison of the S F derived from our optical polarization data with the ones derived
in the works by Houde et al. (2009) and Falceta-Gonçalves et al. (2008), indicated that the Pipe
76
nebula is a magnetically dominated molecular cloud complex and that the turbulence appears to
be sub-Alfvénic. Only the region we call the stem–bowl border, in particular Field 26, appears to
have a behavior that is compatible with super-Alfvénic turbulence. A similar situation seems to
apply to the well investigated low mass star forming region in the Taurus complex where there is
evidence for a molecular gas substrate with sub-Alfvénic turbulence and magnetically subcritical
(Heyer et al. 2008; Nakamura & Li 2008). Hily-Blant & Falgarone (2007) also found that in
Taurus, the magnetic fields are dynamical important, although they found that they are transAlfvénic. In addition, analyzing the polarization angles at different scales using optical and submm
observations in several molecular cloud yield Li et al. (2009) to suggest that these clouds are also
sub-Alfvénic.
4.7 Summary
The Pipe nebula has proved to be an interesting interstellar complex where to investigate the
physical processes that forestall the stellar formation phases. The polarimetric survey analyzed in
this work covers a small fraction only of the entire Pipe nebula complex, and there is no doubt that
new data is highly desired in order to verify some of the speculations settled in this investigation.
In Paper I, we suggested that the Pipe nebula, a conglomerate of filamentary clouds and dense
cores, is possibly experiencing different stages of evolution. From the point of view of the global
polarimetric data alone, we proposed three evolutionary phases from B 59, the most evolved region, to the bowl, the youngest one, however, the real scenario seems to be much more complicated
than that. As demonstrated by Frau et al. (2010), from the point of view of the chemical properties
derived for four studied starless cores, there does not seem to be a clear correlation between the
chemical evolutionary stage of the cores and their position in the cloud.
In addiction, the polarimetric analysis conducted here suggests that,
1. Although the unusually high degree of polarization, observed for numerous stars in our
sample, the probed interstellar dust does not seem to present any peculiarity as compared
to the common diffuse interstellar medium. In fact, the fields where the high polarization
were observed show a polarization efficiency of the order of p/AV ≈ 3 % mag−1 , which is
the typical maximum value universally observed for the diffuse interstellar medium.
2. Basically all observed fields in B 59 and the Pipe’s stem present an estimated polarization
efficiency of the order of p/AV ≈ 1 % mag−1 , and all so far known candidate YSOs presumed
associated to the Pipe nebula were found in those regions.
3. While the value of the mean polarization angle obtained for fields toward volumes not associated to the densest parts of the main body of the Pipe nebula seems to remain almost
constant, the same does not happens for fields presenting large interstellar absorption, suggesting that the uniform component of the magnetic field permeating the densest filaments of
the Pipe nebula shows systematic variations along the main axis of the dark cloud complex.
4.7. Summary
77
4. Analysis of the second–order structure function of the polarization angles suggests that in
the Pipe nebula the large scale magnetic field dominates energetically with respect to the
turbulence, i.e. the turbulence is sub-Alfvénic. Only in a localized region between the bowl
and the stem turbulence appear to be dynamically more important.
Chapter 5
Infrared polarimetry with LIRIS:
scientific results for the low- mass
star-forming region NGC 13331
5.1 Introduction
Infrared polarimetry is the most suitable tool to observe magnetic fields within molecular
clouds at large scales. Like in the optical case, infrared polarized light is produced by differential absorption of background starlight. Davis & Greenstein (1951) proposed that some fraction
of non-spherical interstellar dust grains become aligned perpendicular to the local magnetic field
due to paramagnetic relaxation. Although this mechanism is commonly invoked in polarization
investigations, its efficiency within molecular clouds is controversial. Modern simulations provide much more realistic scenarios for the theory of grain alignment. Indeed, several authors have
successfully modeled the interstellar polarization by radiative torques propelled by anisotropic radiative fluxes (Draine 1996; Lazarian & Hoang 2007; Hoang & Lazarian 2008, 2009). Mechanical
alignment by anisotropic particle flux was also thought for particular environments like outflows
or jets (Gold 1952), although it has not been proven observationally yet. The interested reader
can find a complete discussion on grain alignment theory in the superb review by Lazarian (2007),
who claims radiative torques as the most promising mechanism to align dust grains with the local
magnetic field.
The dust grains behave like a polarizer to any incoming radiation, absorbing and scattering the
component of the electric field (E-vectors) parallel to their longer axis. Therefore, the observed
radiation will carry some degree of polarization with the transmitted E-vectors having a position
angle (P.A.) aligned to the magnetic field permeating the interstellar medium. The resulting po1
Alves, F. O., Acosta-Pulido, J. A., Girart, J. M., Franco, G. A. P. & López, R. 2011, submitted to The Astronomical
Journal
79
80
Chapter 5. Near-infrared polarimetry on NGC 1333
larization map outlines the geometry of the field lines which are projected onto the plane-of-sky
(POS). Near-infrared (near-IR) observations trace visual extinctions of a few tens of magnitudes,
providing deeper photometry than optical wavelengths. However, usually the increase in interstellar extinction is not accompanied by an increase of the degree of polarization, suggesting that
grains in higher densities environments have lower polarizing efficiency probably due to changes
in their structure (e.g., shape, roundness, or composition). The declining of polarization efficiency
with total extinction seems to be a global effect as has been reported by earlier investigations
(Goodman et al. 1992, 1995; Gerakines et al. 1995). Nevertheless, there is unequivocal evidence
that grains do align in dense environment (e.g., Whittet et al. 2008, and references therein). Alternatively, the observed infrared polarization in star-forming regions can be connected to dust
scattering rather than to differential absorption. In this case, the polarized light arises from infrared reflection nebulae associated to disks and envelopes of young stars. Maps of polarization
due to dust scattering have their pattern usually correlated to the distribution of the material around
these sources.
NGC 1333 is known as the most active site located in the Perseus molecular cloud. Several
signatures of star-forming activity are observed toward this region. Previous near-IR studies revealed a clustered stellar distribution with many sources associated or embedded to NGC 1333
and having a strong infrared excess (Lada et al. 1996). Lately, Wilking et al. (2004) showed that
a large portion of such a cluster is composed by low- and sub-stellar masses stars having less than
1 Myr. In addition, numerous protostars associated to bright IRAS sources are powering a large
number of molecular outflows (Knee & Sandell 2000), giving a complex dynamic scenario to this
cloud. Many of such outflows are traced by shock-induced emission, what led some authors to
propose that the dense molecular material is somehow being disturbed by their kinematics (Warin
et al. 1996; Sandell & Knee 2001; Quillen et al. 2005). All these observational features are related
to the youngness of this cloud, what reinforces that NGC 1333 possesses the expected physical
conditions for triggered star formation.
Due to the large interest rose by the intense activity presented by NGC 1333, the region has
been the subject of several polarimetric investigations. Measurements in optical wavelengths,
covering an area of about one square degree around the nebulous material associated to NGC 1333,
was conducted by Vrba et al. (1976) and latterly by Turnshek et al. (1980) in a larger area. An even
larger survey covering the full Perseus complex was done by Goodman et al. (1990), while Tamura
et al. (1988) used K-band polarimetry to measure infrared sources in the core of the reflection
nebula. In spite of the low spatial resolution of the optical surveys, all of them suggest a bimodal
distribution of P.A. for the observed polarization vectors indicating that the large scale magnetic
field presents two components, not necessarily coincident in spatial position.
NGC 1333 IRAS 4A (hereafter IRAS 4A), a low luminosity protostellar source in the region
of NGC 1333, has become the most representative case of a collapsing magnetized core. One of
the first polarimetric observations with a mm interferometer showed hints of a hourglass magnetic
field configuration (Girart et al. 1999). This morphology was further confirmed by Girart et al.
5.2. Observations
81
(2006), who obtained a hourglass field geometry at physical scales of a few hundred AU’s. Such
a geometry is foreseen by core collapse models based on magnetically controlled infall motions,
also known as ambipolar diffusion (Tassis & Mouschovias 2004; Mouschovias et al. 2006). In
such models, the gravitational energy generated by the collapsed material overcomes the magnetic
support produced by the large number of ionized particles initially connected to the field lines.
Gonçalves et al. (2008) constructed synthetic polarization maps of collapsing magnetized clouds
and reproduced quite well the magnetic field observed in IRAS 4A.
In the present paper, we report one of the first scientific results collected with the aid of the
near-IR camera LIRIS (Long-slit Intermediate Resolution Infrared Spectrograph: Manchado et al.
(2004); Acosta Pulido et al. (2003)) in its polarimetric mode. For testing the performance of
the instrument in this mode we collected J-band linear polarization for stars laying angularly
close (∼ 5′ ) to the region of IRAS 4A. The selected targets avoid the most active portion of the
NGC 1333 cloud so that the polarized light is supposed to be produced uniquely by differential
absorption, leading to a polarimetric pattern parallel to the POS magnetic field geometry.
Our scientific goal was to compare the local magnetic field in IRAS 4A with the larger scale
field associated to the cloud. Such comparison has already been done by Girart et al. (2006), however, due to the scarcity of measurements close to the protostellar source, their comparison was
done with angularly distant objects (∼14-20 arcmin) retrieved from the Goodman et al. (1990)
survey. Since our observed area is closer in projection to IRAS 4A we are able to describe how
the magnetic field evolves at different physical scales, departing from an uniform component associated to the large scale field down to core scales.
In order to ascertain the quality of the near-IR data, we also provide preliminary results for
some stars in an optical linear polarization survey performed toward NGC 1333.
5.2 Observations
5.2.1 Near-infrared observations
The observations were collected in December 2006 and December 2007 at the Observatorio
del Roque de los Muchachos (La Palma, Canary Islands, Spain). We used LIRIS attached to
the Cassegrain focus of the 4.2-m William Herschel Telescope. LIRIS is equipped by a Hawaii
detector of 1024 x 1024 pixels optimized for the 0.8 to 2.5 µm range.
LIRIS is capable to perform polarization observations by using a Wedged double Wollaston
device, WeDoWo, which is composed by a combination of two Wollaston prisms and two wedges
(see Oliva 1997, for detailed description). In this observing mode one obtains simultaneous measurements of the polarized flux at angles 0, 45, 90 and 135 degrees. An aperture mask of 4′ × 1′ is
used in order to avoid overlapping between the different polarization images. An example of a typical LIRIS image in polarimetric mode is shown in Fig. 5.1. The degree of linear polarization can
thus be determined from data taken at the same time and the same observing conditions. In order
82
0
90
135
45
Figure 5.1: A typical CCD image in polarization mode. The four strips correspond to the 0◦ ,
90◦ , 135◦ and 45◦ polarization vectors from which the Stokes parameters are calculated.
to have an accurate sky subtraction a 5-point dithern pattern was followed. Offsets of about 20′′
were adopted along the horizontal, long mask direction. During the 2006 campaign, the observing
strategy consisted of 7 frames per dither position, each having 20 seconds exposure time, while
in the second campaign the number of frames per dither position was reduced to 6. The 5-point
dither cycle was repeated several times until completion of the observation. The total observing
time for each field was 2800 s in 2006 and 2400 s in 2007.
We carried out J-band polarization observations of 10 fields, 6 of them with the telescope rotator at 0◦ and 4 of them with the rotator at 90◦ (see Table 5.1). Figure 5.2 indicates the observed
fields as black and red rectangles, corresponding to observations with rotator at 0◦ and 90◦ , respectively. The positions of the protostellar cores IRAS 4A and IRAS 4B are indicated as crosses,
and the zone where star formation is active is roughly delimitated by the ellipse. We excluded this
region from our science targets in order to avoid contributions of dust scattering to our polarization maps. Except for the two upper fields, we attempted to cover the fields observed at 0◦ with
the observations at 90◦ in order to compare both data sets and, consequently, to achieve higher
precision in the estimated polarization parameters.
5.2.2 Optical observations
R-band linear polarimetry was performed using the 1.6 meter telescope of the Observatório do
Pico dos Dias (LNA/MCT, Brazil) in missions conducted in 2007 and 2008. A specially adapted
CCD camera composed by a half-wave rotating retarder followed by a calcite Savart plate and
a filter wheel was attached to the focal plane of the telescope. The half-wave retarder can be
5.2. Observations
83
F6
Declination (2000)
15
IRAS 4A
F5
31o 10’
IRAS 4B
F4p F3p F2p
F1p
F1
F2
F3
F4
03h 29m 45s
30s
15s
00s
28m 45s
Figure 5.2: DSS optical image of our science targets. Black boxes are observed fields with
rotator at 0◦ while red boxes are observed fields at 90◦ . Crosses mark the positions of the
protostars NGC 1333 IRAS 4A and NGC 1333 IRAS 4B. The ellipse in the upper right corner indicates the star-forming region, where no science targets were select in order to avoid
polarization data due to dust scattering.
rotated in steps of 22.◦ 5 and one polarization modulation cycle is fully covered after a complete
90◦ rotation. The birefringence property of the Savart plate divides the incoming light beam into
two perpendicularly polarized components: the ordinary, fo , and the extra-ordinary, fe , beams.
From the difference in the measured flux for each beam one estimates the degree of polarization
and its orientation in the plane of the sky. For a suitable description of this polarimetric unit,
we refer the interested reader to the work by Magalhães et al. (1996). The obtained optical data
is part of an ongoing large scale (about 1 square degree) survey whose results will be discussed
elsewhere. Therefore, no detailed description of the reduction and calibration of these data will be
provided here. The area covered by the optical survey overlaps the portion of the sky investigated
in this work, and in order to make a comparative analysis of the obtained near-IR quantities we
included the optical results gathered for stars lying in this overlapped area.
84
Table 5.1: Log of the observationsa
Target
α2000
δ2000
ID (hh:mm:ss.ss) (dd:mm:ss.ss)
F1
F2
F3
F4
F5
F6
F1p
F2p
F3p
F4p
a
03:29:22.01
03:29:25.24
03:29:23.98
03:29:22.90
03:29:34.26
03:29:20.52
03:29:15.44
03:29:19.59
03:29:25.70
03:29:30.95
+31:09:42.12
+31:08:41.88
+31: 07:49.41
+31:06:54.62
+31:12:50.08
+31:15:59.63
+31:08:12.82
+31:08:28.20
+31:08:17.24
+31:08:30.44
Obs. date
Rotator
(◦ )
2006 Dec 26
2006 Dec 26
2006 Dec 26
2006 Dec 26
2007 Dec 13
2007 Dec 13
2006 Dec 26
2007 Dec 13
2007 Dec 13
2007 Dec 13
0
0
0
0
0
0
90
90
90
90
The night of 2006 December 27 had very limited weather conditions and only calibrators were observed.
5.3 Data Analysis
The near-IR data reduction was done using the package lirisdr developed by the LIRIS team
under IRAF environment1 . Given the particular geometry of the frames (see Fig. 5.1) when the
WeDoWo is used one of the first processing steps consists of the image slicing into four frames.
Each set of frames corresponding to a given polarization stage is processed independently. The
data reduction process comprises sky subtraction, flat-fielding, geometrical distortion correction
and finally coaddition of images after registering. A second background subtraction was included
in order to avoid the residuals introduced by the vertical gradient due to the reset anomaly effect.
An approximate astrometric solution was performed based on the image header parameters.
5.3.1 Photometry
Aperture photometry of the field stars in each slice was obtained using the task Object Detection, available within Starlink Gaia software2 . The aperture radius was taken as ∼ 4 arcseconds,
which corresponds to 3.1-times the median seeing of the night. The background was extracted
from an annulus with radii 4.6 arcseconds. The astrometric solution of each slice was tweaked
using the astrometric tools available within the Starlink Gaia software. We used the 2MASS catalogue to perform the photometric and astrometric calibrations. In our sample, we reached J
magnitudes as faint as ∼17. The next step consisted basically in searching the correspondence
of each object in all four slices in order to compute the polarization properties. In some cases,
matching of stars observed with rotator at 0◦ and 90◦ was also necessary since some objects were
present in both sets of observations.
1
IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of
Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.
2
GAIA is a derivative of the Skycat catalogue and image display tool, developed as a part of the VLT project at ESO
5.3. Data Analysis
85
5.3.2 Polarimetric analysis
Using the WeDoWo, we measured simultaneously four polarization states in each of the strips
as,
i0 [PA = 0] =
i90 [PA = 0] =
i45 [PA = 0] =
i135 [PA = 0] =
1
t0 (I∗ + Q∗ )
2
1
t90 (I∗ − Q∗ )
2
1
t45 (I∗ + U∗ )
2
1
t135 (I∗ − U∗ )
2
(5.1)
(5.2)
(5.3)
(5.4)
where I∗ , Q∗ and U∗ are the Stokes parameters of the object to be measured, and the factors
t[0,90,45,135] represent the transmission for each polarization state. In this case, the normalized
Stokes parameters can be determined by,
q∗ =
u∗ =
i0 − i90 t0/90
i0 + i90 t0/90
i45 − i135 t45/135
i45 + i135 t45/135
(5.5)
(5.6)
where the factors t0/90 and t45/135 measure the relative transmission of the ordinary and extraordinary rays for each Wollaston. These factors were calibrated using non-polarized standards and
resulted in the values: t0/90 = 0.997 and t45/135 = 1.030, with an uncertainty of about 0.002 in
both cases.
In LIRIS the rotation of the whole instrument by 90◦ causes the exchange of the optical paths
for the orthogonal polarization vectors. Now, the resulting polarization states are given by
i0 [PA = 90] =
i90 [PA = 90] =
i45 [PA = 90] =
i135 [PA = 90] =
1
t0 (I∗ − Q∗ )
2
1
t90 (I∗ + Q∗ )
2
1
t45 (I∗ − U∗ )
2
1
t135 (I∗ + U∗ )
2
(5.7)
(5.8)
(5.9)
(5.10)
This effect can be used in order to get a more accurate estimation of the Stokes parameters
because combining both measurements, PA=0◦ and 90◦ , results in the cancelation of the transmission factors and reduces flat-fields uncertainties. The normalized Stokes parameters are then
computed by
86
q∗ =
u∗ =
RQ − 1
i0 [PA = 0]/i90 [PA = 0]
, being R2Q =
RQ + 1
i0 [PA = 90]/i90 [PA = 90]
i45 [PA = 0]/i135 [PA = 0]
RU − 1
, being R2U =
RU + 1
i45 [PA = 90]/i135 [PA = 90]
(5.11)
(5.12)
Finally, after estimation of the q and u Stokes parameter, the degree of linear polarization and
the position of polarization angle (measured eastwards with respect to the North Celestial Pole)
are calculated as,
p =
θ =
q
q2∗ + u2∗
(5.13)
!
u∗
1
tan−1
.
2
q∗
(5.14)
Flux errors in i0 , i90 , i135 and i45 are dominated by photon shot noise while the theoretical
error in polarization fraction were estimated performing error propagation through the previous
equations. In addition, we calculated the errors in p using a Monte Carlo method, which returned
values of the same order of the theoretical errors, meaning that they are coherent.
Figure 5.3 shows the obtained dependence of the polarization uncertainty as a function of the
J-band magnitude achieved for our observations with LIRIS. Uncertainty measurements for observations with rotator at 0◦ (green triangles), 90◦ (red circles) and a combination of both (crosses) are
shown. This plot contains only stars whose signal-to-noise ratio of the combined setup (crosses) is
better than 1. Objects with no combined positions correspond to stars where only 0◦ observations
were performed (again, only stars with signal-to-noise ratio better than 1 are shown). The observed
distribution suggests that the uncertainties are dominated by photon shot noise, as expected for a
sample collected with fixed exposure time. It is noticeable that the uncertainty decreases when
data taken at 0◦ and 90◦ are combined. The uncertainty in polarization degree establishes a natural
limit at the polarization degree which is due to the polarization bias. Bias in the degree of linear
polarization (p) comes from the fact that this quantity is defined as a quadratic sum of q and u,
which will produce a non-zero polarization estimate due to the uncertainties on their measurement
(for a suitable discussion see for instance, Simmons & Stewart 1985; Wardle & Kronberg 1974).
In order to correct the observed polarization degree and compute the true polarization we used
the prescription proposed by Simmons & Stewart (1985) for low observed polarization, that is,
the true polarization degree can be approximated by the expressions ptrue = 0 if pobs /σ p < Ka ,
otherwise ptrue = (p2obs − σ2p · Ka2 )1/2 . We adopted Ka = 1 which corresponds to the estimator
defined by Wardle & Kronberg (1974).
The 1σ uncertainty in θ was estimated (i) by applying the relation derived by Serkowski (1974),
that is, σθ = 28◦ .65 σ p /p, when ptrue /σ p ≥ 5; or (ii) graphically with the aid of the curve proposed
by Naghizadeh-Khouei & Clarke (1993) when ptrue /σ p < 5..
5.3. Data Analysis
87
10
9
0
8
90
Combined
7
σ
6
5
4
3
2
1
0
10
11
12
13
14
15
16
17
18
J (LIRIS)
Figure 5.3: Distribution of polarization errors (σP ) with J magnitudes obtained for each field
star with telescope rotator at 0◦ (green triangles), 90◦ (red circles) and a combination of both
(crosses). The estimated errors are dominated by photon statistics. Note that uncertainties
are lower when the combination of images taken with the telescope rotator at 0◦ and 90◦ is
used. The large discrepancy observed between 0◦ and 90◦ errors for some stars are due to
the distinct observation epochs of each data set.
5.3.3 Standard stars
Observations of polarized and unpolarized standard stars were taken in order to calibrate the
instrumental characteristics of the LIRIS in its polarimetric mode. Table 5.2 summarizes the general information of each of these objects. Identification in the SIMBAD Astronomical Database,
equatorial coordinates (epoch J2000), type, polarization degree and position angle as found in
the literature, the filter used for such observations, and each corresponding reference are given in
columns 1 to 8, respectively. The polarization degree and position angle provided by Whittet et al.
(1992) for the polarized standard star (CMa R1 No. 24) is the only one measured in the J-band,
the same filter used in our observations. Data from Schmidt et al. (1992), for the two unpolarized
stars, are a compilation of optical calibration data collected with the Hubble Space Telescope.
Usually, observations of unpolarized standard stars have the main goal to check if some degree
of instrumental polarization is added to the results. Despite of the low signal-to-noise ratio of
our data, the results are consistent with objects having a very low degree of polarization. The
unpolarized stars Gl91B2B and BD+28d4211 were observed with rotator at 0◦ and 90◦ , being
that the later was measured in both observing runs. The Stokes parameters for each object proved
to be relatively small. Averaging over both observing runs, the normalized Stokes q resulted to
be equal 0.051 and -0.117 per cent for observations with rotator at 0◦ and 90◦ , respectively, and
correspondingly, the normalized Stokes u resulted to be 0.226 and 0.119 per cent for 0◦ and 90◦ ,
respectively.
The observed polarization degrees, although of being low, are slightly higher than the ones
previously published (see Table 5.3). However the true polarization degree (after bias-correction)
88
Table 5.2: Standard stars
ID
α2000
δ2000
(hh:mm:ss.sss) (dd:mm:ss.ss)
CMa R1 No. 24 07:04:47.364
BD+28d4211 21:51:11.070
G191B2B
05:05:30.621
Type
P
(%)
-10:56:17.44 Polarized
2.1± 0.05
+28:51:51.80 Unpolarized 0.041 ± 0.031
0.067 ± 0.023
0.063 ± 0.023
0.054 ± 0.027
+52:49:51.97 Unpolarized 0.065 ± 0.038
0.090 ± 0.048
0.061± 0.038
θa
(◦ )
Filter
Ref.
86 ± 1
38.66
135.00
30.30
54.22
91.75
156.82
147.65
J
Nb
U
B
V
U
B
V
Whittet et al. (1992)
Schmidt et al. (1992)
a
Position angles measured from North to East.
b
“Near-UV” filter centered in 3450 Å and with full width at half maximum (FWHM) bandpass of 650 Å. For
details, see Schmidt et al. (1992).
Table 5.3: Observational results for the unpolarized standard stars.
a
ID
Mission
Pobs
(%)
P/σ
Ptrue
Pmin /Pamax
(%)
G191B2B
BD+28d4211
BD+28d4211
2007
2006
2007
0.41
0.09
0.15
1.38
0.60
1.17
0.28
0.00
0.08
0.00/1.10
0.00/0.41
0.00/0.45
Lower/upper value for the degree of polarization at 99% confidence level (Simmons & Stewart 1985).
indicates a maximum value of 0.076% for BD+28d4211 and 0.28% for G191B2B. Both measurements of BD+28d4211 returned values of polarization degree which are consistent with each
other. Applying the method proposed by Simmons & Stewart (1985) for a 99% confidence level,
on the observed unpolarized standards, results a small, if there is any, instrumental polarization.
The polarized standard star CMa R1 No 24 was observed in order to verify the zero point of the
polarization position angles. Table 5.4 summarizes the results obtained for the four measurements
conducted for this object. As expected, high quality data are less sensitive to biasing, and the
unbiased polarization has basically the same values of the observed polarization. Taking into
account the uncertainties, we see that our J-band data matches perfectly the result obtained by
Whittet et al. (1992). Moreover, the difference between our average P.A. obtained for these four
measurements and the one obtained by Whittet et al. (1992) is only ∼6◦ , discarding any further
correction for the calibration of this quantity, given the uncertainties.
5.4. Polarization properties
89
Table 5.4: Observational results for the polarized standard star.
a
ID
Pobs
(%)
σP
(%)
P/σ
Ptrue
(%)
Pmin /Pamax
(%)
θobs
(◦ )
σθ
(◦ )
CMa R1
No 24
2.10
2.04
2.33
2.05
0.26
0.26
0.26
0.22
7.98
7.99
9.06
9.43
2.08
2.02
2.31
2.04
1.39/2.78
1.35/2.70
1.62/3.00
1.45/2.61
92.7
94.3
93.5
86.8
4
4
3
3
Lower/upper value for the degree of polarization at 99% confidence level (Simmons & Stewart 1985).
5.4 Polarization properties
5.4.1 Infrared data
Table 5.5 contains a summary of the obtained near-IR polarization data. The columns give, for
stars which resulted in a signal-to-noise, P/σP , better than 1.0, the star’s identification number in
our catalogue, the equatorial coordinates (epoch J2000), magnitude in J-band, polarization degree,
its uncertainty and the unbiased polarization degree, the polarization angle and its uncertainty
(estimated as previously mentioned), the rotator position used to acquire the data, and the object’s
type as found in the Simbad Astronomic Database, respectively. The histogram of position angles
for stars having P/σP > 1, shown in Fig. 5.4, presents a clear concentration of objects, which,
excluding star number 13, shows an almost normal distribution represented by a mean position
angle of 160◦ and a standard deviation of only 11.◦ 6. Interestingly, we note that this value is
about twice as smaller as the mean 1-σ estimated error for this quantity (ninth column in Table
5.5), indicating that we may have overestimated the near-IR polarization uncertainties. Indeed,
the good agreement shown by the near-IR and optical data (see next section) corroborates that
the uncertainties for the former data may be smaller than estimated. Figure 5.5 shows the spatial
distribution of the near-IR polarization vectors overlaid on the 2MASS J-band image. Each vector
is scaled according to the vector scale shown in the left upper corner of the image and is centered
on the star’s position. Green vectors indicate stars with P/σP > 3 while red vectors have 1 <
P/σP < 3. Circles show the position of stars whose the degree of polarization was determined
with poor signal-to-noise, that is, these objects have P/σP < 1.
Inspection of Fig. 5.5 reveals a trend of larger polarization degree for objects located at lower
declinations (δ < 31:10:00.00) where P̄ is ∼ 3.5%. In the upper half part of our image, only three
stars present P/σP greater than 1.5. Among them, two stars (number 6 and 22 in Table 5.5) have
P.A. ≃ 135◦ , which is slightly lower than the value obtained for the dominant ordered map in the
lower half part of the image, while star number 13 is the one whose P.A. deviates considerably
(by ∼100◦ ) from the main distribution shown by the histogram given in Fig. 5.4. Our results are in
agreement with several previous works in the literature. Optical polarization measurements from
Vrba et al. (1976) has in common two objects among the ones investigated here: stars number 2
90
Table 5.5: J−band polarization data
ID
α2000
(hh:mm:ss.ss)
δ2000
(dd:mm:ss.ss)
J
(mag)
pJ
(%)
σp
(%)
J
ptrue
(%)
θa
(◦ )
σbθ
(◦ )
Rotator position
(◦ )
Classc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
03:29:14.58
03:29:14.89
03:29:15.05
03:29:16.08
03:29:16.20
03:29:16.68
03:29:17.52
03:29:17.91
03:29:18.21
03:29:18.64
03:29:20.01
03:29:20.10
03:29:21.87
03:29:23.50
03:29:24.70
03:29:25.60
03:29:27.04
03:29:27.16
03:29:28.99
03:29:29.60
03:29:30.80
03:29:32.41
31:06:38.20
31:09:27.50
31:08:06.90
31:07:31.40
31:07:34.00
31:16:18.30
31:07:33.20
31:07:07.70
31:07:55.70
31:09:59.60
31:09:54.30
31:08:54.00
31:15:36.30
31:07:25.00
31.07:27.00
31:08:43.00
31:08:04.60
31:06:48.20
31:10:00.30
31:08:47.90
31.06:33.00
31:13:01.10
14.70
12.67
16.06
12.99
13.83
10.74
15.04
15.34
14.50
12.50
12.45
16.08
11.33
16.57
17.16
17.00
12.39
14.92
13.36
16.30
17.97
13.34
1.74
3.10
3.16
2.32
1.88
1.67
1.82
2.70
2.55
4.68
4.89
3.15
1.60
4.54
4.56
4.90
3.53
3.32
4.01
3.17
7.01
1.90
1.27
0.64
2.43
0.74
0.97
0.60
1.45
1.91
1.43
0.65
0.64
2.44
0.75
3.46
4.42
3.99
0.66
1.79
0.93
2.71
6.51
1.21
1.41
3.03
2.02
2.20
1.61
1.56
1.10
1.90
2.11
4.63
4.85
1.99
1.41
2.94
1.12
2.85
3.47
2.80
3.90
1.64
2.61
1.47
173
157
160
172
167
135
171
169
163
155
160
155
49
167
167
172
169
173
142
156
160
135
27
7
33
10
18
11
37
29
20
4
4
33
16
33
24
23
6
20
7
42
25
24
0,90
0,90
0,90
0,90
0,90
0
0,90
0,90
0,90
0,90
0,90
0,90
0
0,90
0,90
0,90
0,90
0,90
0,90
0,90
0,90
0
IR source
Star
IR source
IR source
IR source
IR source
IR source
IR source
Star
Star
CTTSd
IR source
IR source
IR source
IR source
IR source
IR source
IR source
a
Position angles are counted from North to East.
b
1σ uncertainty of the position angle (see text for explanation on how it was estimated).
c
Type of object as found in the Simbad Astronomic Database. Objects without a correspondent class do not
present any previous report available on literature.
d
Classical T-Tauri Star (Lada et al. 1974)
and 13 in our catalogue. The latter has also been observed by Menard & Bastien (1992). Tamura
et al. (1988) obtained a bimodal distribution in their K-band polarimetry toward NGC 1333. Both
the dominant distribution in our map and the misaligned polarization vector associated to star
number 13 are also seen in their maps. In all cases, polarization degree and P.A. are in good
agreement with our data. Discrepancies, which may arise from distinct responses between distinct
wavebands, are smaller than the measured uncertainties.
5.4.2 Comparison to optical data
The R-band polarimetry introduced in Sect. 5.2.2 has 12 stars in common with our near-IR
data. Table 5.6 provides the equatorial coordinates and the polarization parameters measured for
stars in a radius of ∼ 11′ around the line-of-sight studied here. Objects that were also observed in
5.4. Polarization properties
91
Number of objects
8
6
4
2
0
30
60
90
120
Position Angle (o)
150
180
Figure 5.4: Distribution of polarization angles of the near-IR data. The histogram is binned in
10◦ .
near-IR are marked with a “check mark” in the last column of this Table.
Figure 5.6 shows a comparison between the obtained polarization vectors, at both bands, plotted over a DSS image. It is noticeable the good correlation between them, not only in a global
aspect but also for each individual star. Figure 5.7 illustrates the difference between the measured
P.A. in both bands, where the discrepancies averages only in 6.◦ 5. The bimodal distribution previously reported by Tamura et al. (1988) is reinforced by the R-band data set since six other objects,
in addition to star number 13 of the near-IR catalogue, also present position angles perpendicular
to the dominant orientation.
With the polarimetric parameters for two distinct bands we can use the Spectral Energy Distribution (SED) of the observed linear polarization to check if it is consistent with the physical
properties of NGC 1333. As proposed by Serkowski (1973), Coyne et al. (1974) and Serkowski
et al. (1975), such SED is described by the empirical formula
λ p(λ)
max
,
= exp −Kln2
pmax
λ
(5.15)
where p(λ) is the percentage polarization at wavelength λ, pmax is the maximum polarization at
wavelength λmax , and K is a parameter that in principle was assumed to have a constant value but
later was deduced to vary linearly with λmax in such a way that when the latter is expressed in
µm, K = −0.1 + 1.86λmax (Wilking et al. 1982). From the literature, we find that typical values
of λmax for the interstellar medium are around 0.55 µm. In particular, for the case of NGC 1333,
Whittet et al. (1992) found that λmax reaches values as high as 0.86 µm. Figure 5.8 represents the
obtained PNIR × Pvisible diagram. Lines of constant λmax equals to 0.55 and 0.86 µm are plotted.
Take into account the error bars, practically all points respect the limits imposed by the Serkowski
Law (Equation 5.15), being under the highest slope line of maximum wavelength for NGC 1333,
and concentrated around the locus of the typical interstellar value of λmax of 0.55 µm.
92
5%
Declination (2000)
15
10
31o 05’
03h 29m 40s
30s
20s
10s
Figure 5.5: J -band polarization vectors in NGC 1333 plotted over a 2MASS J -band image.
Vector length scale is shown on the upper left corner. Green vectors indicate stars with P/σP >
3 while red vectors have 1 < P/σP < 3. Open circles indicate positions of observed objects
with P/σP < 1.
5.5. Extinction and efficiency of alignment
93
Table 5.6: R-band polarization data
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
a
α2000
δ2000
PR
(hh:mm:ss.ss) (dd:mm:ss.ss) (%)
03:29:02.87
03:29:03.74
03:29:04.04
03:29:07.39
03:29:09.57
03:29:12.16
03:29:14.59
03:29:14.90
03:29:16.08
03:29:16.25
03:29:16.61
03:29:17.54
03:29:17.84
03:29:18.24
03:29:18.65
03:29:20.02
03:29:20.59
03:29:21.75
03:29:27.08
03:29:27.19
03:29:29.11
03:29:34.24
03:29:39.77
03:29:40.43
31:16:00.82
31:16:03.60
31:17:06.66
31:10:49.02
31:09:08.68
31:08:10.91
31:06:37.34
31:09:27.35
31:07:30.30
31:07:33.89
31:16:17.62
31:07:32.57
31:05:37.40
31:07:55.21
31:09:59.57
31:09:54.25
31:06:11.48
31:15:36.43
31:08:04.41
31:06:47.75
31:06:08.77
31:07:53.33
31:14:51.61
31:12:46.38
0.68
7.58
1.38
3.11
4.61
0.39
4.04
4.53
4.51
3.92
0.87
3.88
4.35
3.32
4.40
5.75
5.13
0.94
4.61
5.20
5.36
2.15
1.38
0.34
σP
(%)
θa
(◦ )
0.15
0.54
0.52
0.17
0.61
0.08
0.75
0.06
0.12
0.21
0.14
0.25
0.45
0.48
0.04
0.10
0.93
0.09
0.29
0.51
0.32
0.39
0.19
0.06
66.4
57.7
86.3
167.0
161.1
71.8
151.5
157.8
166.2
157.6
117.5
163.3
164.4
167.2
156.4
164.0
174.5
49.4
157.6
166.1
167.3
153.7
13.6
41.4
P/σP NIR
4.62
14.1
2.29
8.68
5.94
3.78
5.39
37.2
23.1
11.4
6.38
5.93
9.71
6.88
40.7
46.4
5.3
10.4
5.50
10.3
16.8
5.58
6.10
3.47
X
X
X
X
X
X
X
X
X
X
X
X
Position angles are counted from North to East.
5.5 Extinction and efficiency of alignment
The alignment efficiency of the dust grains due to the local magnetic field can be estimated
by the ratio of the polarization degree to the visual extinction (P/AV ). In order to estimate AV
we have retrieved from the 2MASS catalogue the measured colors J − H, H − K and J − K
for common objects. By comparing the observed colors with the intrinsic colors of stars with
different spectral types we have assigned a spectral type and an extinction value by minimizing
the following function:
χ2 = ((J − K)obs − (J − K)mod )2 + ((H − K)obs − (H − K)mod )2
(5.16)
(J − K)mod = (J − K)int [SpTyp] + (A J − AK )
(5.17)
where
and a similar expression was addopted for (H − K)mod . The intrinsic colors of different spectral
94
5%
Declination (2000)
15
IRAS 4A
IRAS 4B
31o 10’
03h 29m 45s
30s
15s
00s
28m 45s
Figure 5.6: Comparison between optical (blue vectors) and near-IR (red vectors) data. The
polarimetric map is plotted over a DSS optical image. The vector length scale is shown on
the upper left corner. Orange vectors represent the averaged magnetic field of IRAS 4A and
IRAS 4B, as obtained by submillimeter observations of Attard et al. (2009).
types and luminosity classes were taken from Tokunaga (2000). The extinction curve through
which the fit was performed was extracted from Cardelli et al. (1989). After the best pair of values
for the spectral type and AV is obtained, the errors in these parameters are determined by bootstrapping techniques. As a final check, the fit is considered successful only when the difference
between observed and modeled colors is below the measurement errors and the uncertainty in AV
is below 1.5 times its value. Otherwise, the star was discarded and the value of its extinction was
not considered in our analysis.
Figure 5.9 shows the dependence of the efficiency of grain alignment with the visual extinction obtained for the selected stars. The upper observational limit on the polarizing efficiency
is indicated by the horizontal dashed-line. It corresponds to the visible limit given by 3%/mag
(Serkowski et al. 1975) corrected by the empirical formula given in Equation 5.15. This correction was done assuming that the maximum of polarization occurs in the wavelength of the V-band
5.6. Intrinsic polarization from YSO’s
95
PAVIS − PAIR (o)
30
0
−30
60
90
120
PAIR (o)
150
180
Figure 5.7: Comparative diagram of the position angles obtained for the visible and near-IR
data sets.
(∼ 0.55 µm). The figure shows that, except for two stars, all data points appear under this maximum polarizing efficiency. Both exceptions, however, present large uncertainties in their estimated
ratio between observed polarization and interstellar absorption. In addition, the plot suggests the
depolarization phenomenon, i.e., there is a systematical declining of the polarizing efficiency from
≃ 1.8%/mag at extinctions of ≃ 1.5 visual magnitudes to 0.5 %/mag at higher values of AV . Within
the uncertainties, the data follow a a quadratic relation between those two quantities (solid line of
Fig. 5.9). These two effects are also observed in other very active star formation clouds like Taurus
and Ophiuchus (Arce et al. 1998; Whittet et al. 2001, 2008). For the molecular clouds observed
so far, a general relation is successfully described by the following power law: pλ /τλ ∝ (AV )−0.52 ,
where τλ is the optical depth at the observed wavelength λ (Whittet et al. 2008). Nevertheless,
this may not be a general trend. Thus, an extensive optical polarimetric survey conducted in the
Pipe nebula molecular cloud showed an increasing dependence of grain alignment efficiency with
visual extinction (Franco et al. 2010). At some line-of-sights, the ratio P/AV may be even higher
than the current observational upper limit. However, this unexpected behavior is observed at zones
of strong magnetic field, where it is supposed to be projected almost entirely against the POS.
5.6 Intrinsic polarization from YSO’s
Our near-IR and optical maps are characterized by an uniform component predominant to the
south of the IRAS 4A/4B double system, and by an almost perpendicular configuration associated
with few stars to the north of the IRAS 4A/4B system and closer to the region of active star formation (Fig. 5.6). Although there is a well established existence of a bimodal distribution of P.A. for
the large scale region of NGC 1333 (e.g., Vrba et al. 1976; Turnshek et al. 1980; Goodman et al.
96
.86
λ max
PJ (%)
6
=0
Pmax = 6.0
4
55
λ max
= 0.
Pmax = 4.0
2
Pmax = 2.0
0
0
2
4
PR (%)
6
Figure 5.8: Spectral Energy Distribution of the observed linear polarization in near-IR and
visible. Solid lines indicate constant λmax of 0.55 and 0.86 µm from bottom to top, respectively. Dashed lines represent constant pmax of 2, 4 and 6% from the origin going outwards,
respectively.
1990), this second component is more likely to be related to the Young Stellar Objects (YSO’s)
found in this active zone. The polarization vectors of this component are probably produced by
intrinsic scattering within circumstellar disks rather than by interstellar absorption. Therefore, no
information about the ambient magnetic field can be inferred from these data. Instead, intrinsic
polarization reveals the optical depth of circumstellar disks. Several authors have studied the physical properties of YSO’s by means of polarimetry (e.g., Brown & McLean 1977; Mundt & Fried
1983) and, in general, observations suggest that near-IR polarization vectors, when produced by
single scattering, are oriented perpendicularly to optically thin disks, while multiple scattering
within optically thick disks generate polarization vectors whose P.A. are parallel to their long axis
(Angel 1969; Bastien & Menard 1990; Pereyra et al. 2009).
The YSO’s showing intrinsic polarization in the near-IR and/or R-band sample are:
• Lkhα 271, a Classical T-Tauri Star (Lada et al. 1974) which corresponds to star number 13
in Table 5.5. The near-IR polarization angle and degree are in excellent agreement with the
R-band data (star number 18 in Table 5.6). Tamura et al. (1988) attribute the polarization to
anisotropic reflection nebulosity. Optical data from Menard & Bastien (1992) also support
this idea. These authors claimed that the polarization comes from an optically thick circumstellar disk surrounding the source but that outbursts or inhomogeneities in circumstellar
shell make the polarization of this source to vary considerably.
• SVS 13A, star number 2 in Table 5.6, not observed in our near-IR survey. It matches perfectly in polarization degree and P.A. with the K-band data collected by Tamura et al. (1988)
(PK = 7.2 ± 0.9% and P.A. = 56 ± 4◦ ). This object is a well-studied source (Rodrı́guez et al.
5.6. Intrinsic polarization from YSO’s
97
PJ/AV (%/mag)
3
2
1
0
0
2
4
6
AV (mag)
8
10
12
Figure 5.9: Dependence of efficiency of alignment with the visual extinction for the nearIR polarization data. The horizontal dashed line represents the observationally determined
upper limit for the efficiency of grain alignment corrected to be representative for the J -band
(see text). The solid curve represents P J /AV ∝ A−0.52
and is shown for comparison purposes
V
only.
2002; Anglada et al. 2004; Chen et al. 2009) which powers a bipolar and collimated outflow associated to the well-known Herbig-Haro objects HH 7-11 (Herbig 1974; Strom et al.
1974). The polarization is associated with internal scattering in the nebular material of the
disk (Tamura et al. 1988).
• 2MASS J03290289+3116010 (ASR 2), an object angularly close to SVS 13A. This object
is the star number 1 in Table 5.6, an infrared source with a very low degree of polarization,
however, with a measured P.A. which is almost parallel to the one obtained for SVS 13A. As
inferred by its Spectral Type retrieved from the SIMBAD Astronomical Database, K-type,
and its bright magnitude (J ≃ 12.8), this star could be a foreground object, thus not carrying
any information about the ambient field. In fact, previous spectral analysis and photometric
studies place this star at a distance of only ∼50 pc from the Sun (Aspin et al. 1994; Aspin
2003).
• ASR 8, is the star number 3 in Table 5.6. Although this object is classified as a brown dwarf
at SIMBAD, an extensive survey on the evolutionary state of stars in NGC 1333 identifies
this object as a T-Tauri star with a mass of 0.7 M⊙ (Aspin 2003), which is reinforced by
the presence of X-ray emission (Getman et al. 2002). We therefore attribute the optical
polarization measured for this star due to intrinsic scattering.
In addition, there are two other low polarization stars in the optical data set with P.A. belonging
to the supposedly second component (stars number 6 and 24 in Table 5.6). Both are bright infrared
98
sources (J . 13.0), and apparently not associated with YSO’s, as no star formation or nebulosity
signs have been reported in the literature related to them. Their 2MASS color indices suggest they
may be unreddened M-type dwarf stars, supposition that is verified by the measured low degree of
polarization. We therefore attribute those objects to foreground stars.
5.7 The magnetic field in NGC 1333
5.7.1 The distribution of dust and molecular gas in NGC 1333
The most detailed picture of the distribution of gas and dust in the Perseus cloud was achieved
by COMPLETE (Ridge et al. 2006a; Pineda et al. 2008), a survey of near/far-infrared extinction
data compiled with atomic, molecular and thermal dust continuum data obtained over a large area
(Perseus and Ophiuchus molecular clouds). These data show a wide dynamical range in visual
magnitudes for NGC 1333, and a non-Gaussian CO spectral profile consistent with multi-velocity
components for this direction. These results are consistent and likely related to a layered cloud
structure along the line-of-sight. This morphology was proposed by Ungerechts & Thaddeus
(1987) after CO line data showed two distinct cloud velocity components. At smaller scales,
interstellar extinction studies of field stars toward NGC 1333 also presented multi-components
(Černis 1990).
According to the column densities maps of the Perseus cloud (Ridge et al. 2006b), the region
studied here lies in the lower density envelope of NGC 1333. The maps of high density molecular
tracers (N2 H+ , HCO+ ) as well as of the 870 µm dust emission show that around IRAS 4A the dense
gas has a filamentary distribution oriented in the NW-SE direction, with the long axis positioned
at ≃ 142◦ (Sandell & Knee 2001; Olmi et al. 2005; Walsh et al. 2007).
5.7.2 The field morphology as traced by the diffuse gas
Considering uniquely the polarization vectors produced by interstellar extinction, the near-IR
map of Fig. 5.5 suggests that the POS component of the magnetic field suffers a smooth change
in orientation from ∼163◦ in the lower portion of the image to ∼135◦ in the upper part. Both
directions are consistent with the Perseus field of Goodman et al. (1990) and the local field derived
by Tamura et al. (1988). In Section 5.5, we have shown that the interstellar extinction associated
to our polarization data ranges between 2 and 4 magnitudes. According to the selection criteria
of Ridge et al. (2006b), our data belong to the group of objects having AV > 0.7 magnitudes and,
therefore, mean P.A. of 145◦ ± 8◦ .
The magnetic field orientation derived by our near-IR data is roughly parallel to the filamentary
structure traced by the molecular data from Walsh et al. (2007) and the dust continuum data of
Sandell & Knee (2001). However, the magnetic field direction associated with the dense filament
is approximately perpendicular to the filament’s major axis, as derived from submm polarization
maps towards IRAS 4A and IRAS 4B (Girart et al. 1999, 2006; Attard et al. 2009). The local
5.7. The magnetic field in NGC 1333
Figure 5.10: Averaged spectra of the
99
12 CO
lines obtained over a region of about
5′
1–0 (solid line) and the
13 CO
1–0 (dashed line)
centered at the position α(J2000)=3h 29m 24s and
δ(J2000)=31◦ 8′ . This region covers the F1–F4 and F1p–F4p observed fields with the William
Herschel Telescope (see § 5.2.1). The CO spectra was retrieved from the COMPLETE data
archive (Ridge et al. 2006a; Pineda et al. 2008). The dotted vertical line show the systemic
velocity of the IRAS 4A core (Choi 2001).
field around those protostars does not seem to carry any information of the large-scale ambient
field traced by the near-IR vectors. However, the single-dish polarization data from Attard et al.
(2009), which trace a more diffuse gas when compared with the interferometer data of Girart
et al. (2006), are associated with visual extinction as low as ∼10 magnitudes, as estimated from
their faintest dust continuum contours. Since our near-IR survey reaches visual extinctions as
deep as ∼11 magnitudes, the single-dish and near-IR data seem to reveal substantial changes in
the magnetic field topology throughout the in-between scales. Such sharp twist on the field in
a multi-scale scenario is hard to explain by means of structural changes on the magnetic field
only, because within the observed field, the position angle of the optical and near-IR polarimetric
data is quite uniform (see Fig. 5.4). Instead, the two data sets may be simply tracing distinct
gas components. As explained in § 5.7.1, there is observational evidence of a multi-component
structure for the NGC 1333 molecular cloud. Figure 5.10 shows the 12 CO (solid line) and 13 CO
(dashed line) spectra extracted from a box containing the region studied here. These spectra have
a non-Gaussian profile, and they have at least three distinguishable velocity components: a faint
emission centered at vLSR ≃ 2 km s−1 (seen more clearly in the 12 CO data), the peak of the
13 CO data centered at ∼7.6 km s−1 and the peak of the 12 CO data at ∼6.7 km s−1 . This last
component has the same vLSR of the IRAS 4A dense core (Choi 2001). Therefore, whereas the
submm polarization measurements trace only the molecular cloud component associated with the
IRAS 4A dense core, the near-IR and optical polarimetric data are probably tracing the mean
100
magnetic field of the different velocity molecular cloud components observed in the CO maps.
Nevertheless, further observations are needed in order to obtain a more complete description of
the magnetic field in this region.
5.8 Conclusions
Our near-IR data is one of the first polarimetric set collected with the infrared camera LIRIS.
We observed an area of ∼6′ × 4′ over the region of NGC 1333 in order to measure the starlight
polarization of background stars in that FOV. The main conclusions of this investigation are:
• The infrared polarization map derived for the surveyed area is perfectly consistent with the
visible map obtained with a totally distinct instrument, as well as with earlier results obtained by other authors. The distribution of polarization P.A. of our both data sets (visible
and infrared) are significantly similar, and the corresponding Spectral Energy Distribution
is consistent with the physical conditions found in NGC 1333. Therefore, the near-IR polarimetric capabilities of LIRIS has proved to be scientifically trustful for the astronomical
community, and guarantees that this mode will be useful to gather measurements for objects
unaccessible to optical instruments.
• Similar to what has been previously established for other active clouds, like Taurus and
Ophiuchus, our results seem to show that depolarization, that is, a declining of polarizing
efficiency, occurs for the interstellar medium along the observed lines-of-sight. This effect,
however, may not be as global as expected. The Pipe nebula, a molecular complex harboring
magnetically supported dust cores, shows an increasing dependence of polarizing efficiency
with visual extinction.
• The obtained polarization map for the surveyed area is dominated by a well ordered component produced by dichroic interstellar absorption. However, there are objects, some of them
catalogued as YSO’s, showing a transversal component which may be generated by internal
scattering within circumstellar disks.
• The magnetic field configuration as traced by the near-IR map is not aligned with the field
morphology obtained with the submillimeter data at the position of IRAS 4A/4B. The fainter
dust continuum emission of the previous single-dish submm data traces similar visual extinctions as this work, what implies that the field could be suffering structural changes inbetween scales. However, these two data sets may be associated with distinct gas components.
• Our near-IR data trace the field morphology of the diffuse gas which is known to be composed by a multi-velocity structure. That is, the traced field geometry can be the averaged
magnetic field over several distinct velocity components of the cloud. CO molecular data
5.8. Conclusions
101
obtained for this line-of-sight show non-Gaussian line profiles which are consistent with this
hypothesis.
102
Chapter 6
The magnetic field in the NGC 2024
FIR 5 dense core4
6.1 Introduction
Understanding the evolution of molecular clouds and protostellar cores is one of the outstanding concerns of modern astrophysics. Particularly, efforts are concentrated in determining which
physical agents are mainly responsible for controlling the dynamical properties of the dense cores.
It is widely accepted by the astronomical community that magnetic fields must be taken into account in evolutionary models of collapsing protostellar cores (Shu et al. 1999). Although some
theories claim that turbulent supersonic flows drives star formation in the interstellar medium
(Elmegreen & Scalo 2004; Mac Low & Klessen 2004), others demonstrate that the ambipolar diffusion collapse theory reproduces properly observed molecular cloud lifetimes and star formation
timescales (Tassis & Mouschovias 2004; Mouschovias et al. 2006).
One way to resolve these open issues in star forming theory is to increase the number of highquality observations which resolve the core collapse structure. Sampling several protostellar cores
with distinct physical properties can provide better constraints to improve simulations. Particularly, the number of observations of magnetic fields in molecular clouds and dense cores has been
increasing rapidly with the advent of new instruments with high sensitivity. In polarimetry, it is
globally accepted that non-spherical dust grains are aligned perpendicular to field lines (Davis &
Greenstein 1951) producing linearly polarized thermal continuum emission (Hildebrand 1988).
Which mechanism mainly contributes to the alignment of interstellar dust grains is still a matter
of debate (Lazarian 2007). However, very recently Hoang & Lazarian (2008, 2009) have successfully modeled the polarization by radiative torques propelled by anisotropic radiation fluxes.
Those torques act to align spinning non-spherical dust grains with their largest moment of inertia
axis parallel to the field lines. The polarized flux is usually only a small fraction of the total inten4
Published in Alves, F. O., Girart, J. M., Lai, S. -P., Rao, R., & Zhang, Q. 2011, The Astrophysical Journal, 726, 63
103
104
Chapter 6. The magnetic field in the NGC 2024 FIR 5 dense core
sity (usually a few percent) and for this reason the study of the magnetic field is highly limited by
the instrumental sensitivity.
Cold dust emits mainly at far-IR and submm wavelengths. In the submm regime, the emission
is optically thin and, therefore, it is not affected by scattering or absorption. For this reason, the
SMA has been extensively used to study thermal emission from dust and cool gas. Several authors
reported polarization observations of different classes of protostellar cores. The textbook case is
the low mass young stellar system NGC 1333 IRAS 4A (Girart et al. 2006). The supercritical state
is reflected in the SMA polarization maps which indicates a clear hourglass morphology for the
plane-of-sky magnetic field component in a physical scale of 300-1000 AU. This remarkable result not only was predicted by theories of collapse of magnetized clouds (Fiedler & Mouschovias
1993; Galli & Shu 1993) but is commonly used to test models of low-mass collapsing cores (Shu
et al. 2006; Gonçalves et al. 2008; Rao et al. 2009). In the regime of high mass protostars, recent
investigations performed with the SMA also provided observational constraints on the physics
involved during the core collapse stage. Two recent works exemplify distinct magnetic field features within this class of objects. The polarimetric properties of G5.89–0.39 are consistent with
a complex, less ordered field likely disturbed by an ionization front (Tang et al. 2009), while the
hourglass morphology expected for magnetically supported regimes was observed at large physical scales (∼ 104 AU) for the protostellar core G31.41+03 (Girart et al. 2009). Despite the distinct
energy balance and timescales of the two regimes (low and high mass), both results imply that the
magnetic support must not be ignored in the models.
NGC 2024 is the most active star forming region in the Orion B giant molecular cloud. The gas
structure in this region has an ionized component surrounded by a background dense molecular
ridge and a foreground dust and molecular component visible in the optical images as a dark lane.
Recently, the new ESO telescope VISTA (Visible and Infrared Survey Telescope for Astronomy)
released a high sensitivity near-infrared image of NGC 2024 (Figure 6.1). In this large scale view,
the foreground dust lane which optically obscures the Hii region is almost transparent. Scattered
light produced by the ionization front is seen as bright emission in the top of the image, and a cluster of hot young stars is revealed. Kandori et al. (2007) used near-infrared polarimetry to study the
scattered light from the Hii region. Several reflection nebulae associated with young stellar objects
(YSO) were discovered in their polarization maps. The overall centro-symmetric pattern suggests
that the ionizing source is IRS 2b, a massive star located 5′′ north-west of IRS 2, in agreement
with a previous near-infrared photometric study carried out by Bik et al. (2003). The submillimeter continuum emission arising from the dense molecular ridge was first observed by Mezger et al.
(1988, 1992). Several far infrared cores (so the acronym “FIR”) at distinct evolutionary stages
were identified and catalogued in a North-South (NS) distribution. In fact, the chain of FIR cores
could have been generated by the interaction between the nearby Hii region and the surrounding
molecular cloud. Fukuda & Hanawa (2000) performed numerical simulations of sequential star
formation trigged by an expanding Hii region near a filamentary cloud. In their models, isothermal expansion and magnetohydrodynamic effects are considered. Their simulations preview that a
6.1. Introduction
105
Figure 6.1: VISTA image of the Flame Nebula (NGC 2024). The obscuring dust lane that
exists foreground to the bright Hii emission is seen almost transparent in this near infra-red
image. The glow of NGC 2023 and the Horsehead Nebula are seen in the lower portion of the
image.
chain of cores is formed from this interaction, each pair of cores belonging to a distinct generation
though. Comparison between model and the dynamical parameters observed in NGC 2024 are
quite good. In particular, they state that FIR 4 and FIR 5 belong to the first generation of cores,
what is confirmed by the observed dynamical ages of their outflows. In this paper, we center our
discussion on FIR 5, the brightest and most evolved of them, with a strong and collimated unipolar
outflow (Richer et al. 1992). Continuum observations at 3 mm performed by Wiesemeyer et al.
(1997) suggest that FIR 5 is a double core embedded in an envelope. However, higher angular resolution observations from Lai et al. (2002) (LCGR02 from now on) resolved the dust emission in
one strong component surrounded by several weaker components in a radius of a few arcseconds.
Several authors have conducted polarimetric investigations toward FIR 5. Crutcher et al.
(1999) used the Very Large Array (VLA) to carry out Zeeman observations of OH and Hi absorption lines in order to trace the line-of-sight (LOS) component of the magnetic field. These
authors found a LOS field gradient of ∼ 100 µG across the northeast-southwest direction. Dust
emission polarization in the surroundings of FIR 5 was mapped in 100 µm by Hildebrand et al.
(1995) and Dotson et al. (2000) with the Kuiper Airborne Observatory. At longer wavelengths,
Matthews et al. (2002) used the SCUBA polarimeter to observe the 850 µm emission with at the
James Clerk Maxwell Telescope (JCMT) and obtained polarization patterns consistent with those
106
derived with the 100 µm data. Their single-dish dust polarization maps trace a relatively ordered
magnetic field along the ridge of emission containing FIR 4 and FIR 5 (Fig. 4 in their paper).
Based on the spatial coverage of their observations, this ordered field must extend over a distance
of at least ∼ 0.5 pc (for the assumed distance of 415 pc to the Orion B cloud). Matthews et al.
(2002) modeled this field using a helical-field geometry threading a curved filament, since this
configuration suited fairly to a 2-dimensional projection accordingly to the SCUBA maps. However, they found that this geometry is not consistent with the LOS Zeeman data of Crutcher et al.
(1999) because no reversed fields are seen at both sides of the chain of cores. Instead, those authors offer another interpretation based on a compression zone created due to the expansion of
the foreground ionization front. In this scenario, the magnetic field lines are stretched around the
ridge of dense cores in a physical morphology consistent with LOS field gradient observed in the
Zeeman data of Crutcher et al. (1999).
Concerning the local field associated with FIR 5, the work of LCGR02 has the best resolution for the dust continuum emission so far. These authors used the Berkeley-Illinois-MarylandAssociation (BIMA array) interferometer and obtained an angular resolution of 2.′′ 4 × 1.′′ 4. The
polarized flux of the BIMA maps extends in a N-S direction, perpendicular to the putative protostellar disk. The corresponding field lines were fitted with a geometric model consisting of a set
of concentric parabolas, indicating that the polarized flux trace a partial hourglass morphology for
the magnetic field. In this paper, we report SMA dust continuum polarization toward FIR 5. The
higher sensitivity of this instrument provides new information on the detailed field morphology of
the FIR 5 core.
6.2 Observations and Data Reduction
The high angular resolution of the SMA allows us to trace the thermal emission of dust grains
at physical scales of few hundred astronomical units1 (for objects in the Orion molecular cloud
complex) and, therefore, is able to spatially resolve compact dust cores. A detailed description of
SMA is given in Ho et al. (2004). The observations were carried out in 2007 November 24 and
December 19 with the SMA in its compact configuration. The number of antennas available for the
observations were 7 and 6, respectively. The atmospheric opacity at 225 GHz was 0.11 and 0.07 for
the first and second day, respectively (values measured by the Caltech Submillimeter Observatory
tau meter). Observations were done in the 345 GHz atmospheric window, what corresponds to
a wavelength of 870 µm. The SMA receivers operate in two sidebands separated by ∼ 10 GHz.
The central observed frequencies for the lower and upper side bands were 336.5 GHz and 346.5
GHz, respectively. The SMA correlator had a bandwidth of 1.9 GHz (for each sideband) divided
in 24 “chunks” of 128 channels each. In total, the full-band spectrum contains 3072 channels for
each sideband and a spectral resolution of 0.62 MHz, which corresponds to a velocity resolution
1
The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia
Sinica Institute of Astronomy and Astrophysics, and is funded by the Smithsonian Institution and the Academia Sinica.
6.3. Results
107
of 0.7 km s−1 . SMA receivers are single linearly polarized. By using a quarter-wave plate in
front of each receiver, the incoming radiation is converted into circular polarization (L, R). The
SMA correlator combines the signal into circular polarization vectors: RR, LL, RL, LR. In order
to obtain the full four Stokes parameters for all the baselines, the visibilities have to be averaged
on a time scale of 5 minutes. A description of the SMA polarimeter and the discussion of the
methodology (both hardware and software aspects) are available in Marrone et al. (2006) and
Marrone & Rao (2008).
The phase center (α2000 = 05h 41m 44.s 3, δ2000 = −01◦ 55′ 40.′′ 8) was set according to the peak
of emission obtained for FIR 5 in LCGR02. Uranus and Titan were observed as flux calibrators
in both tracks. The resulting visibility function for each calibrator is consistent with the expected
flux estimated by the SMA Planetary Visibility Function Calculator during the observing runs.
The quasar J0528+134 was used as the gain calibrator. The quasar 3c454.3 was used for bandpass and polarization calibration. The first track had a much better parallactic angle coverage for
3c454.3 than the second track, thus the 3c454.3 data from the first track were used to solve for
the instrumental polarization or “leakages”. The minimum and maximum UV distance for both
tracks was 16 and 88 kλ, respectively. Antenna 3 was used only in the second track, so no leakage
solution could be derived. Thus, antenna 3 was not used to obtain Stokes Q and U maps. After
the calibration steps, data from upper and lower sidebands for each track were synthesized into a
single data set. Calibrated visibilities for each track were combined into a final data set. Removal
of continuum contamination from the line data set was done. The main contribution arose from
the CO (3 → 2) transition at the chunk # 4 of the upper sideband (∼ 345.76 GHz)2 .
All the calibration and reduction steps were done with MIRIAD configured for SMA data
(Wright & Sault 1993). The science target was strong enough and self-calibration was performed
in order to increase the signal-to-noise ratio in the final maps. Imaging of the Stokes parameters
I, Q and U was performed. Maps of polarized intensity (IP ), polarized fraction (P) and position of
polarization angles (θ) were obtained by combining Q and U images in such a way that P = IIP =
√
Q2 +U 2
and θ = 21 tan−1 ( UQ ). The resulting synthesized beam of Stokes I maps has 2.′′ 45 × 1.′′ 48,
I
with a position angle (PA) of −39.8◦ . Table 6.1 summarizes the technical parameters of continuum
and line observations.
6.3 Results
6.3.1 Dust Continuum Emission
Figure 6.2 shows the contour map of the 878 µm dust emission in FIR 5 obtained with a quasiuniform weighting (a robust of −1), which provides a better angular resolution of 1.′′ 96×1.′′ 41. The
overall submillimeter emission resembles the 1.3 mm dust continuum maps obtained with BIMA
2
Since our interest in the line data set concerns only Stokes I emission, antenna 3 is unflagged in the deconvolved
CO (3 → 2) maps.
108
Table 6.1: Parameters of the continuum and line observations
Observations
Continuum
CO (3→2)
a
b
Rest
frequency
(GHz)
345.8000
345.7960
HPBW
PAa
(arcsec)
2.45 × 1.48
2.87 × 1.67
(◦ )
Spectral
resolution
km s−1
Peak of
emission
(Jy beam−1 )
rms
noise
(Jy beam−1 )
-39.8
-37.6
–
0.7
1.19
9.5
0.019b
0.57
Position angles are measured from North to East.
The rms noise of Stokes I emission, obtained with a robust weight of 0.5
by LCGR02, although the latter has a rms a factor of 3 lower. Our observations (with shortest
baseline equal to 16 kλ) allow us to only measure structures smaller than ∼ 5.7 arcseconds (see
Equation A.5 of Palau et al. (2010)). In LCGR02, they find extended emission at scales of 5−7
arcsec. The brightest emission arises around FIR 5: Main (following LCGR02 notation), which
is resolved into two components, 5A and 5B. Those components correspond to the double source
detected in 3 mm by Wiesemeyer et al. (1997) and indentified as FIR 5-w and FIR 5-e. However,
not all the fainter sources observed in the FIR 5: Main core of LCGR02 have been detected with the
SMA. FIR 5: Main appears more extended in the BIMA maps, attributable to the better sampling
of shorter baselines with the BIMA array. In particular, the N-S direction contains emission of the
dust condensations LCGR2, LCGR3 and LCGR5 (according to LCGR02 nomenclature). These
sources are missing in our SMA maps probably due to the absence of antenna 3 in the deconvolved
maps (see section 6.2). Antennas 3 and 6 cover a short baseline in the UV plane which is parallel
to the U axis and close to V = 0 kλ. In equatorial coordinates, it corresponds to features parallel
to the declination axis, close to the phase center. Therefore, by flagging antenna 3 we lost this flux
component which should be produced by the missing sources. However, several faint peaks (at the
4 and 7–σ level; 1 σ = 18 mJy beam−1 ) seen by LCGR02 out of FIR 5: Main were also detected
in our SMA data.
Tables 6.2 and 6.3 give the dust emission properties for the two condensations associated
with FIR 5: Main and for the fainter dust condensations, respectively. The intensity peak and the
position of the sources were derived using the Miriad task “maxfit”. For the two bright sources
associated with FIR 5: Main, a two Gaussian fit (using the AIPS’s “imfit” task) was used to
estimate the flux density of each component and its size. The two sources appear resolved but
in different directions. Source 5A has a full width half maximum (FWHM) size of 2.′′ 8 × 2.′′ 4
elongated close to the NE–SW axis (PA = 67◦ ), while source 5B has a deconvolved FWHM size
of 3.′′ 6 × 2.′′ 8 but is elongated along the SE–NW direction (PA = 124◦ ).
In order to estimate the column density and mass of the cores, we need to assume a value
for the cores’ temperatures. Different molecular line observations have established that the NGC
2024 cores are warm with temperatures between 40 and 85 K (Ho et al. 1993; Mangum et al.
1999; Watanabe & Mitchell 2008; Emprechtinger et al. 2009). Here we adopt a temperature of
6.3. Results
109
FIR 5: NE
FIR 5: MAIN
5A
5B
FIR 5: SW
FIR 6n
FIR 6c
Figure 6.2: Dust continuum map of FIR 5 with quasi-uniform weighting (robust = −1). Con-
tours are drawn at −3, 3, 4, 6, 9, 13, 19, 25, 32, 42, 52, 62 σ (1–σ ≃ 18 mJy beam−1 ). The
half power beam width (HPBW) of the synthesized beam is 1′′
. 96× 1′′
. 41 and the position angle
is −70.6◦ . The crosses indicate the dust continuum sources detected by Lai et al. (2002) with
BIMA.
60 K. We assume a dust opacity at 878 µm of 1.5 cm2 g−1 , which approximately is the expected
value for dust grains with thin dust mantles at densities of ∼ 106 cm−3 (Ossenkopf & Henning
1994). Using the previous FWHM sizes derived from the Gaussian fit, a beam-averaged column
density of ∼ 4.7 × 1023 and 2.2 × 1023 cm−2 for sources 5A and 5B were derived, respectively.
Similarly, masses for these two components are 1.09 and 0.38 M⊙ , respectively. The total mass of
FIR 5:Main, 1.5 M⊙ , is consistent with the value derived by Chandler & Carlstrom (1996).
6.3.2 Distribution of the polarized flux
For better sensitivity to the weak polarized emission, maps of Stokes I, Q and U were obtained
with a robust weight of 0.50. Figure 6.3 shows the Stokes Q and U emission, which have different
distributions. The Stokes Q emission arises from a negative compact spot about one arcsecond
north of source A. The Stokes U is quite extended along FIR5: Main, with the brightest emission
around source 5A. Source 5B has only weak polarized emission at 3–σ level. It is noteworthy that
significant positive Stokes U emission appears west of source 5A without dust emission associated. However, this spot of polarized emission coincides with the BIMA continuum source FIR
5: LCGR 1 (catalogue of LCGR02). The non-detection by the SMA could occur because dust
110
Table 6.2: FIR 5: main component
Dust
condensation
α2000 b
δ2000 b
Peakb
of intensity
(Jy beam−1 )
Totalc
flux
(Jy)
FWHM
Gaussian fit
(arcsec)
Deconv.c
size
(arcsec)
Deconv.c
PA
(◦ )
FIR 5A
FIR 5B
05 41 44.258
05 41 44.510
−01 55 40.94
−01 55 42.35
1.16(2)
0.40(2)
2.44(6)
1.26(8)
2.8 × 2.4
3.6 × 2.8
2.31(6)×1.58(8)
3.1(2)×2.3(1)
47(5)
130(11)
a
b
c
Units of right ascension are hours, minutes and seconds, and units of declination are degrees, arcminutes, and
arcseconds.
Fit error of the last digit in parenthesis.
Estimated using Miriad’s “MAXFIT” task.
Values derived with AIPS’s “IMFIT” task.
Table 6.3: Sub-millimeter dust condensations
Dust
condensation
α2000 b
δ2000 b
Peak
of intensity b
(mJy beam−1 )
Flux
density
(mJy)
FIR 5-sw
FIR 5-ne
FIR 6n a
FIR 6c a
05 41 43.667
05 41 45.043
05 41 45.193
05 41 45.134
-01 55 49.05
-01 55 31.60
-01 56 00.50
-01 56 04.01
77(18)
131(18)
70(18)
124(18)
81(21)
202(30)
40(15)
116(22)
a
b
According to Lai et al. (2002) numbering.
Estimated using Miriad’s “MAXFIT” task.
emission has been resolved out by the interferometer (approximately 30% of the flux is filtered
out, see section 6.3.1). Thus, we tentatively associated this polarized spot to this source. A cutoff
p
of 2–σ (1– σ ≃ 5 mJy beam−1 ) in polarized intensity ( Q2 + U 2 ) is used to obtain the linear
polarization emission and to derive the position angle in the plane of the sky of the polarization
vectors.
The polarization intensity and the polarization fraction in our maps achieve values as high as
54 ± 6 mJy beam−1 and 15% ± 2%, respectively, at the northern portions of the core, where the
polarized emission is brighter. Figure 6.4 (left panel) shows the dust continuum emission from
the protostar overlaid with the dust polarization vectors. Using the position of the continuum
peak as reference, three main components can be distinguished: a northern component, where the
highest polarization degrees are obtained, a southwestern component and an eastern component
offset by ≈ 5′′ from the continuum peak. This distribution is well represented in the histogram of
polarization angles shown in the right panel of Figure 6.4. There is a change of roughly 90◦ in
the position angles of vectors associated with FIR 5A and the eastern vectors associated with FIR
5B. Concerning only vectors associated with FIR 5A, position angles have a gradual rotation of
approximately 40◦ from north to south. Table 6.4 summarizes our polarization data. Note that the
distribution of the polarized flux of the SMA data is remarkably consistent with the BIMA maps
of LCGR02. Although the structure of emission in both the BIMA and SMA data sets has the
6.3. Results
111
Figure 6.3: Maps of Stokes Q (top panel) and U (bottom panel) emission. Dashed and solid thin
contours correspond to negative and positive polarized emission, repectively. The contours
start at −2–σ and 2–σ level with steps of 1–σ (1–σ = 5.3 mJy beam−1 ). The absolute Q and U
peak fluxes are 0.056 Jy beam−1 and 0.047 Jy beam−1 , respectively. The thick grey contours
show the Stokes I emission. Crosses indicate the position of the two dust intensity peaks. The
synthesized beam of the maps is shown in the bottom left corner of the bottom panel.
same overall pattern, the latter has a larger area of polarized flux. Compared to the JCMT maps
of Matthews et al. (2002), the mean direction of our SMA polarization field is consistent with the
lower resolution single-dish data, which do not resolve the structure of FIR 5 and traces a larger
physical scale associated with the diffuse gas found at the core envelope.
6.3.3 CO (3 → 2) emission
Our SMA CO (3 → 2) maps reveal a very complex morphology possibly related to multiple
outflows. Figure 6.5 shows the channel maps of the CO (3 → 2) emission with a velocity resolution
of ∼ 2.1 km s−1 . At blueshifted velocities the emission arises from an elongated but wiggling
structure in the East-West direction. This blueshifted component appears to be associated with
112
Figure 6.4: Left: Contour map of the dust continuum emission overlapped with the linear
polarization vectors (black vectors) towards NGC 2024 FIR 5. Gray scale correspond to the
polarized dust intensity. Contours levels are −3, 3, 4, 7, 11, 16, 22, 32, 42, 52, 62–× the rms
noise of the dust emission (∼ 19 mJy beam−1 ). The length of each segment is proportional
to the degree of polarization. The synthesized beam is of 2′′
. 45 × 1′′
. 48 with a position angle
of −40◦ . Vectors are sampled as 2/3 of a beam. Right: Histogram of position of polarization
angles. The three polarized components of FIR 5 polarization map are clearly seen in this plot
FIR 6. The distribution of the molecular gas at the cloud systemic velocity (vLSR ≃ 10 km s−1 ) is
basically associated with the FIR 5 main core. At redshifted velocities (vLSR >∼ 14 km s−1 ) there are
two main elongated features almost parallel extending in the North–South direction and observed
over a wide range of velocities (up to vLSR ≃ 30 km s−1 ). One of these features is associated
with the well studied outflow powered by FIR 5A (Sanders & Willner 1985; Richer et al. 1992;
Chandler & Carlstrom 1996) and the other one is located about 10′′ to the west and seems to
arise from FIR 5-sw. These two lobes have their brightest emission located near their associated
dust components (FIR 5A and sw). The emission presents a clumpy morphology, with an average
angular size of ∼ 5′′ , corresponding to a physical size of 0.01 parsecs. It is worth noting that the
three possible CO high velocity features have no counterpart at the opposite flow velocities. Thus,
the North-South redshifted lobes have no blueshifted counterpart, and the East–West blueshifted
lobe does not have a redshifted counterpart.
Figure 6.6 shows the Position-Velocity (PV) diagram centered in FIR 5A with a PA = 0◦.9
(along the brightest redshifted lobe). The outflow powered by FIR 5A has a wide distribution of
velocities which prevails until ∼ 30 km s−1 . An extended spatial distribution is observed up to
∼ 35′′ south of the source, although only low velocity components are observed at such distances.
No blue lobe is seen and only residual emission is measured in the northern counterpart. The blue
component observed at the offset position of −14′′ is part of the outflow associated with FIR 6. In
section 6.4.4 we provide a detailed discussion about the molecular distribution in this region.
6.3. Results
113
Table 6.4: SMA polarization data from NGC 2024 FIR 5
∆ RA a
(arcsec)
∆ Dec
(arcsec)
P
(%)
ǫP
(%)
σP b
IP c
(Jy beam−1 )
θd
(◦ )
ǫθ
(◦ )
5.4
0
5.4
4.5
1.8
0.9
0
-0.9
1.8
0.9
0
-0.9
1.8
0.9
0
-0.9
3.6
1.8
0.9
0
-0.9
2.7
1.8
0.9
0
-0.9
1.8
0.9
0
-0.9
0.9
0
0.9
0
-2.1
-2.1
-1.5
-1.5
-1.5
-1.5
-1.5
-1.5
-0.9
-0.9
-0.9
-0.9
-0.3
-0.3
-0.3
-0.3
0.3
0.3
0.3
0.3
0.3
0.9
0.9
0.9
0.9
0.9
1.5
1.5
1.5
1.5
2.1
2.1
2.7
2.7
6.00
13.4
9.20
3.40
3.60
3.30
5.20
8.00
2.00
1.70
1.80
3.40
1.50
2.10
1.40
1.60
4.80
2.40
4.00
2.80
1.70
3.90
3.90
6.70
6.30
3.30
6.80
9.40
11.7
8.60
11.1
15.0
14.2
12.6
2.0
3.1
2.8
1.4
1.6
1.2
1.1
1.9
1.0
0.7
0.6
1.0
0.7
0.6
0.5
0.8
2.4
0.7
0.5
0.5
0.7
2.1
0.9
0.6
0.7
1.0
1.7
0.9
1.1
2.0
1.5
1.7
3.1
2.7
3.00
4.32
3.29
2.43
2.25
2.75
4.73
4.21
2.00
2.43
3.00
3.40
2.14
3.50
2.80
2.00
2.00
3.43
8.00
5.60
2.43
1.86
4.33
11.2
9.00
3.30
4.00
10.4
10.6
4.30
7.40
8.82
4.58
4.67
0.018
0.027
0.019
0.013
0.013
0.016
0.027
0.025
0.012
0.014
0.017
0.019
0.012
0.022
0.016
0.012
0.012
0.019
0.042
0.031
0.013
0.011
0.023
0.061
0.051
0.018
0.023
0.061
0.063
0.025
0.043
0.054
0.028
0.029
35.723
-34.364
27.954
24.122
-48.573
-47.342
-35.171
-34.346
-49.173
-55.723
-39.46
-37.513
-60.593
-64.888
-52.705
-47.955
32.233
-64.96
-67.692
-58.781
-56.207
-10.944
-62.435
-70.852
-63.767
-58.229
-57.537
-73.461
-69.462
-61.584
-71.543
-72.681
-61.117
-71.458
9.194
6.093
8.355
12.244
12.838
10.207
6.1
6.549
13.955
11.734
9.757
8.696
13.363
7.45
9.965
13.225
13.901
8.479
3.88
5.187
12.44
15.247
6.924
2.667
3.165
8.806
7.051
2.66
2.569
6.407
3.729
2.981
5.685
5.554
a
b
c
d
Offset respect to the peak of total intensity (same for declination).
Signal-to-noise ratio of polarization.
Polarized intensity ×10−2 .
Position angles are measured from North to East.
114
B
A
Figure 6.5: Channel maps of the CO (3 → 2) emission associated to FIR 5 and FIR 6 dust
cores. Contours levels are -4, 4, 8, 12, . . . to 36 × 0.25 mJy beam−1 (the rms noise of the
map). The value of the VLS R is shown in the top left corner of each panel. Source positions
are indicated as crosses and labelled in the first panel. Magenta, green, red and brown
arrows indicate the position of the FIR 6, FIR 5A, the precessing and the FIR 5-sw outflows
respectively (see section 6.4.4). An ellipse indicates the supposedly cavity produced by the
high-velocity components of the main FIR 5 outflow component.
6.4 Discussion
6.4.1 Polarization properties
In this section, we focus our analysis on the northern and southwestern polarization features,
which are the brightest components and scientifically more interesting since a less uniform pattern
is observed. At 2-σ level, these two regions are connected and surround the peak of total intensity.
From the left panel of Figure 6.4, it can be noted that the peak of polarized and total intensities are
approximately 2.′′ 6 apart. Figure 6.7 shows the dependence of the polarization fraction with Stokes
I flux and with respect to the distance to source A. In both cases, there is a clear depolarization toward the center, where the highest density portions of the core are located. The left panel of Figure
6.7 suggests that the distribution of polarization with respect to the Stokes I emission seems to be
composed by two subsets: the highest polarization fraction data that has a slower growing curve
and corresponds to the northern component, and the subset with a linear dependence, which arises
from the southwestern component. The right panel of Figure 6.7 was produced by performing
averaging over polarization data for concentric annuli of 0.′′ 4 each.
The depolarization effect is observed not only at the brightest component, source A, but also
6.4. Discussion
115
Figure 6.6: Position-Velocity plot of the CO (3 → 2) emission centered close to source FIR 5A
(one arcsecond to the west) and along the North (positive offsets) to South (negative offsets)
direction. Contours levels are −5, −3, 3, and then steps of 3 times 0.3 Jy beam−1 , the rms
noise of the channel maps where the cut was obtained. The position of the driving source of
the redshifted outflow, FIR 5A, is indicated with a dashed line. The spatial overlap with the
East ouftflow associated with FIR 6 is also shown with a dashed line.
for the second dust component, source B, represented by a “hole” at r ≃ 4.′′ 5 in the right panel of
Figure 6.7. Those diagrams are consistent with the left panel of Figure 6.4, where the polarization
fraction increases with distance from the peak of emission, but there is a lack of overall polarized
emission toward source B.
The depolarization observed at higher values of Stokes I seems to be part of a global effect
observed at different wavelengths (Goodman et al. 1995; Lazarian et al. 1997). In the mm/submm
range, this phenomenon was also observed in the BIMA data published by LCGR02, as well as
far-infrared observations with single dishes (Schleuning 1998; Matthews et al. 2001) . The anticorrelation between Stokes I and polarization fraction can be caused by different mechanisms. On
one hand, it may be the result of changes in the grain structure at higher densities. Those changes
may be responsible for a decrease in the efficiency of dust grain alignment with respect to the local
magnetic field (Lazarian & Hoang 2007). In the case of FIR 5B, the embedded source may be in
a very early stage of formation, prior even to collapse (since no clear evidence of star-forming
signatures like outflows has been assigned to it). In this case, the lack of internal infrared radiation
could provide no radiative torque to the dust grains and, therefore, no polarized flux is observed.
Another explanation for this effect could be a twisted magnetic field or the superposition of distinct
field directions along the LOS resulting in a reduction of the net polarization degree (Matthews
0.12
0.1
Pol (%) x 0.01
Pol (%) x 0.01
116
0.08
0.04
0.01
1
0.2
Stokes I (Jy/beam)
0
0
1
2
3
4
Radius (arcsec)
5
6
Figure 6.7: Distribution of polarization toward NGC 2024 FIR 5. Left panel: Polarization intensity versus total intensity. Right panel: Polarization intensity versus radius with respect to the
peak of Stokes I emission.
et al. 2001). Observations at higher angular resolution would be necessary to resolve the small
scale structure.
6.4.2 Magnetic field properties
In section 6.1 we briefly introduce the physical mechanisms associated with the alignment
of dust grains with respect to the magnetic field lines. Although some works propose that grain
alignment could be independent of magnetic fields (e. g.: mechanical alignment by particle flux,
Gold (1952)), it has not been proven yet observationally. Dust grains are believed to have at
least a small fraction of atoms containing magnetic momentum in their compositions, so some
interaction with the ambient magnetic field is expected. The most stable energy state is achieved
when the grain longest axis rotates perpendicularly to the field lines. Consequently, dust emission
polarization vectors as observed in submillimeter polarimetry have to be rotated by 90◦ in order to
be parallel to the plane-of-sky (POS) component of the magnetic field. The LOS field component
adds no information to the 2D polarization map because the spinning dust grains produce zero
polarization flux. If a strong LOS component is expected, a decrease in net polarization flux is
observed, and alternative techniques must be used to measure it (e.g., Zeeman effect observations:
Troland & Heiles (1982); Crutcher et al. (1993)). Therefore, the polarization map of Figure 6.4,
when rotated by 90◦ , traces the projection of the 3D magnetic field morphology on the plane-ofsky (see Figure 6.8). For FIR 5A, the field geometry is described by curved lines centered on
the protostellar core. Toward the elongated emission associated with FIR 5B, the field lines are
parallel to the core’s major axis, implying a 90◦ change in the direction with respect to the FIR 5A
mean direction. By relaxing the signal-to-noise level down to 1–σ, one can see that this change
in the magnetic field direction is not abrupt, and an hourglass morphology can be roughly derived
for the main component (Figure 6.8, upper right box). Several theoretical works have performed
6.4. Discussion
117
Figure 6.8: Plane-of-sky field geometry for NGC 2024 FIR 5. Contours and beam size are the
same than in Figure 6.4. Vectors are plotted at 2σP level and relaxed to 1σP in the upper right
corner.
3D simulations of collapsing magnetized clouds. They all agree that the POS projection of the
magnetic field morphology in those class of objects is a hourglass shape (Ostriker et al. 2001;
Gonçalves et al. 2008). Our results, and many others (e.g. Girart et al. (2006); Rao et al. (2009))
provide observational support to these models.
So far, the CF relation developed by Chandrasekhar & Fermi (1953) is still the most straightforward method to estimate the plane-of-sky component of the magnetic field. Assuming energy
equipartition between kinetic and perturbed magnetic energies as
1 2
1
2
ρδVLOS
δB ,
≃
2
8π
(6.1)
(where δVLOS is the observational rms velocity along the line-of-sight and ρ is the average density), this method compares the fraction of uniform to random components of the field under
√
effects of Alfvénic perturbations (δv ∝ δB ρ) taking into account isotropic velocity dispersions.
The CF formula uses the dispersion of position of polarization angles and molecular line widths as
observational inputs for the gas motions in the core. However, recent works showed that this approximation overestimates the magnetic field for coarser resolutions (Heitsch et al. 2001; Ostriker
et al. 2001). These authors constrained the application of this method to data sets with relatively
low dispersion of position angles (∆θ ≤ 25◦ ), which means strong-field cases. By statistical studies of magnetic turbulent clouds, these authors showed that the CF formula is accurate only if this
118
condition is applied. Using the small angle approximation δφ ≈ δB/Buni f orm, the CF formula can
be stated as follows:
p
δVLOS
,
(6.2)
Buni f orm = ξ 4πρ
δφ
where δφ is the angle dispersion. The correction factor ξ (≃ 0.5) arises from the previously
mentioned strong field conditions to which this case applies (Ostriker et al. 2001).
Unlike LCGR02, we opted for not applying any geometric model to the observed field due
to the low statistics of our data set. The observed dispersion in our data (main component in
the histogram of Figure 6.4, right panel) is 12.2◦ . According to δφobs = (δφ2int + σ2θ )1/2 , the
observed dispersion depends on the intrinsic dispersion δφint plus the measurement uncertainty of
the position of the polarization angles σθ , resulting from the contributions of both effects. Since
that no geometric models were used to remove the systematic field structure, changes on the largescale field directions are included in the intrinsic dispersion, together with turbulent fields due to
Alfvénic motions. In our data set, the position angle uncertainties average to 7.52◦ , which gives us
an intrinsic dispersion of 9.61◦ . Some extra observational parameters are needed to compute the
magnetic field strength with equation 6.2. The average density and the rms velocity in FIR 5 can be
obtained from previous works. Emprechtinger et al. (2009) modeled the morphology of NGC 2024
based on APEX observations of CO isotopologues. The various line profiles obtained for different
transitions are consistent with a complex structure composed by a Photo Dominated Region (PDR)
foreground to the molecular gas where the far infrared cores are found. In their models, the dense
molecular cloud must be warm (75 K) and dense (9×105 cm−3 ) to reproduce the velocity gradients
observed for distinct cloud components. These results agree with the previous work of Mangum
et al. (1999), based on formaldehyde observations. These authors derived a kinetic temperature
of T K > 40 K for FIR 3-7 and estimate densities at the same order of magnitude (nH2 ≈ 2 × 106
cm−3 ). We adopt nH2 = 1.5 × 106 cm−3 as an average value for the density. For the velocity
dispersion, we adopt δVLOS of 0.87 ± 0.03 km s−1 , which is the value derived by Mangum et al.
(1999) from the formaldehyde observations. This molecule is a good tracer of dense gas, and for
the single-dish data of Mangum et al. (1999), it traces the gas kinetic temperature in a scale of
∼ 8000 AU, hence it is well correlated to the turbulent motions of the core. Finally, applying
those inputs to the equation 6.2, together with the δφint previously obtained, we estimate that the
POS magnetic field strength is 2.2 mG, which is in good agreement with the value estimated in
LCGR02. The uncertainty in the magnetic field strength is determined mainly by the error in the
volume density n, which is a factor of ∼ 2 due to the distinct assumptions on the cloud temperature.
This factor implies an uncertainty of 40% for the derived field strength. As mentioned earlier, the
dispersion used as input in equation 6.2 carries the combined effects of changes on the large-scale
field directions plus turbulent motions. In this case, the derived field strength is only a lower
limit since the angle dispersion is not generated purely by Alfvénic motions. On the other hand,
beam averaging and line-of-sight effects due to field twisting of multiple gas components usually
underestimates the real value of the turbulent component, and the estimated field strength in this
case would be an upper limit. So, we can assume that both effects cancel out and 2.2 mG is a fair
6.4. Discussion
119
estimation for the POS field strength.
The mass-to-flux ratio gives information on whether the magnetic field can support the cloud
against the gravitational collapse and, therefore, it provides clues about the evolutionary state of
the source. Specifically, this quantity compares the pressure produced by an amount of mass M
in a magnetic tube of flux Φ. A critical value, reached when the magnetic pressure is no longer
√
able to support the gravitational pulling, is given by (2π G)−1 (Nakano & Nakamura 1978).
Observationally, this parameter is defined by (Crutcher et al. 1999):
λ=
√
(M/Φ)observed
N(H2 )
= (mN(H2 )A/BA) × (2π G) = 7.6 × 10−21
,
(M/Φ)critical
B
(6.3)
where (M/Φ)critical is the mass-to-flux ratio of an uniform disk where gravity is balanced by magnetic pressure, m = 2.8mH allowing for He, A is the cloud area covered by observations, N(H2 ) is
the column density and B is the magnetic field strength. Applying the POS magnetic field strength
obtained in the previous paragraph, B = 2.2 mG, and the column densities derived in section 6.3.1,
we estimate a mass-to-flux ratio for FIR 5A of 1.6 (for T = 60 K), which corresponds to a core
in a supercritical stage. In any case, those calculations are restricted to the dust envelope, without
taking into account the mass contribution of the embedded protostar. We consider that the derived
mass-to-flux values are only a lower limit for this quantity and therefore it is in agreement with
the observed star-forming signatures.
We can also derive the ratio between turbulent and magnetic energies. From the autocorrelation
function of the polarization position angles, it is possible to measure how the dispersion of PA’s
varies with respect to the distinct length scales within the cloud. This function provides an indirect
calculation of the turbulent to magnetic energy as (Hildebrand et al. 2009):
βturb ≈ 3.6 × 10−3
δφ 2
1◦
(6.4)
For the angular dispersion obtained from our sample, δφint = 9.61, we compute the turbulent
to magnetic energy ratio as βturb = 0.33. This value agrees with the ratio estimated in LCGR02,
which reinforces that the turbulent motions are magnetically dominated. The turbulent-to-magnetic
energy ratio found for FIR 5 is consistent with what was measured for other low-mass protostellar
cores like NGC 1333 IRAS 4A and IRAS 16293 − 2422 (Girart et al. 2006; Rao et al. 2009).
6.4.3 Magnetic field around FIR 5A: gravitational pulling or Hii compression?
In this section, we try to elucidate which mechanism is mainly responsible for the curved
magnetic field morphology in FIR 5. One possibility is that the gravitational pulling overcomes
the local magnetic support and drags the ionized material toward the center, warping the field lines
in such a way that they assume an hourglass morphology. This is consistent with the previous
result that the protostellar core is in the supercritical regime. However, if this is the case then only
the hourglass component west of FIR 5A is observed. The lack of detected vectors east of FIR 5A
could be due to the overlap in the line of sight of the dust polarization associated with both FIR
120
5A and FIR 5B cores. The magnetic field direction associated with FIR 5B is perpendicular to the
FIR 5A main direction. Alternatively if the two cores are connected, then it could be due to an
abrupt change in the magnetic field direction. In both cases, the net polarization flux is expected
to decrease significantly. Another possibility is that the grain alignment efficiency associated with
source B is smaller. Indeed, Figure 6.7 (right panel) show that the second polarization “hole”
matches quite well to the position of FIR 5B. Of course, the cause could also be a combination of
these possibilities.
If the tension generated by the magnetic field curvature is produced by the gravitational collapse, then we can make a rough estimation of the mass required to produce the observed curvature.
This magnetic force can be expressed as B2 /R, where R is the radius of curvature of the field lines.
According to the equations derived by Schleuning (1998), we have
#−1
"
"
# #2 "
#−1 "
M
R
n(H2 )
B 2 D
(6.5)
=
100M⊙
1mG
0.1pc
0.5pc
105 cm−3
where D is the distance of the field lines from the protostar. At D = 1.′′ 9 (789 AU) the field lines
have a radius of curvature R of 17′′ (7055 AU). At the selected radius of curvature, the estimation
of magnetic tension force is ∼ 10−23 dyne cm−3 . Applying these values to equation 6.5, we find
that the mass inside the radius of 1.′′ 9 is ≃ 2.3 M⊙ . Although this value is almost a factor of two
higher than the mass estimation done for FIR 5A in section 6.3.1, it is within the same order of
magnitude of the first estimation, even with the large uncertainties in the assumptions of D and the
radius of curvature R. This method is an alternative approximation to test if gravitational pulling
is the responsible for the magnetic field curvature.
Given the situation of the FIR 5 core, the external agents may also interfere in the protostellar
physical environment. Previous observations proved that the molecular ridge and the chain cores
in NGC 2024 are located at the far side of the Hii region (Barnes et al. 1989; Schulz et al. 1991;
Chandler & Carlstrom 1996; Crutcher et al. 1999). The distribution of molecular and ionized
gas proposed by Matthews et al. (2002) for NGC 2024 (Figure 8 in their paper) has the western
portion of the ionization front expanding toward the background molecular ridge and stretching the
magnetic field lines around the ridge of dense cores. At large scales (∼ 0.5 pc), this morphology
is corroborated not only by the LOS field obtained from the Zeeman observations (Crutcher et al.
1999) but also by the POS field from the single-dish dust polarization data. At smaller scales
(∼ 0.02 pc), this could have an effect of compressing the magnetic field lines, bending them
toward the east, as observed around the FIR 5 core. In order to check if the radiation pressure can
be large enough to compress the molecular gas, we have studied the distribution of the ionized
gas in NGC 2024. For this purpose, we accessed the NRAO Data Archive System to search for
centimeter emission that could reproduce this morphology. We found an extended emission in
6 cm related to the Hii region produced by the star IRS 2b. Figure 6.9 shows that the hot gas
has an extended component to the west and is roughly flattened to the south (although slightly
curved to the southwest). FIR 5A and FIR 5B, indicated as crosses in Figure 6.9, lie in the border
of the Hii region. The bright southern pattern near FIR 5 could trace the compressed ionized
121
Declination (2000)
6.4. Discussion
Figure 6.9: VLA 6 cm emission from the Hii region in NGC 2024 (data from the VLA Archive).
Grey scale-filled contours are 0.5, 1.5, 2, 3, 4, 5, 6, 7, 9, 11, 13.1σ (1σ ≃ 9 mJy beam−1 ).
The beam size of 8.6′′ × 7.5′′ and PA of 37◦ is shown in the lower left corner. Crosses indicate
the location of FIR 5A and FIR 5B sources. The star indicates the position of the ionization
source.
gas resulting from the interaction between hot/diffuse and cold/denser components. The radiation
L
pressure produced by the illuminating star (Prad ) can be calculated by cA
, where L is the luminosity
of the ionization source, c is the speed of light and A is the area of the expanding shell. Bik et al.
(2003) found that the spectral type of IRS 2b is in the range O8 V–B2 V, which is consistent with
the intensities of radio continuum and recombination lines observed in the Hii region (Kruegel
et al. 1982; Barnes et al. 1989). Therefore, we can assume L = 105.2 L⊙ , which is representative
of such a spectral type. A first estimation for the radius of the Hii region was done by Schraml
& Mezger (1969) through low resolution (∼ 2′ ) radio observations of NGC 2024. These authors
measured a radius of 0.2 pc (≃ 41 × 103 AU) inferred from the observed emission. However,
from Figure 6.9, the radius of the centimeter emission can be fairly estimated in ∼ 1′ , which is
approximately the distance between FIR 5 and IRS 2b. As a result, the radiation pressure Prad
is calculated as 1.16 ×10−8 dyne cm−2 . The ionization pressure (Ne × T e × k) also accounts for
the energy produced by the PDR. We assume an electron density of 5.94 ×103 cm−3 as derived
from the emission parameters of the centimeter VLA map. The recombination line studies of
Reifenstein et al. (1970) provide an electron temperature of 7200 K for this Hii region. To be
conservative, we adopt a range of 7200–15000 K for T e . With these parameters, the ionization
122
pressure is estimated to range between 5.9 × 10−9 and 1.2 × 10−8 dyne cm−2 . On the other hand,
2
the magnetic pressure is defined by Pmag = B8π , where B is the total magnetic field strength. Since
our SMA maps provide a two-dimensional picture of the total field, we are able to calculate only
a lower limit for the magnetic pressure. Therefore, applying the previous equation for the field
strength obtained in section 6.4.2, we have Pmag ≥ 1.96×10−7 dyne cm−2 . This value is at least one
order of magnitude higher than the radiation and ionization pressures. Even if we add the thermal
pressure to the calculations (Pther ≃ 1.4 × 10−9 dyne cm−2 , Vallee (1987)), the energy injected by
the ionization front is still lower than the magnetic force. Therefore the expanding Hii region is
not enough to compress the magnetic field lines into the observed geometrical configuration, and
the bending is produced by the gravitational pulling.
6.4.4 Multiple Outflows
Previous works reported that FIR 5 has an associated (redshifted) unipolar and highly collimated outflow with a mass of ∼ 4 M⊙ and density of ∼ 102 cm−3 (Sanders & Willner 1985; Richer
et al. 1992; Chandler & Carlstrom 1996). However, a rather complex morphology was proposed
by Chernin (1996) as indicated by their interferometric (BIMA) and single dish (NRAO 12 m
telescope) combined maps of CO (1 → 0). In those, in addition to the unipolar lobe associated
to FIR 5, there are two other redshifted features along the North-South direction and practically
parallel to the FIR 5 molecular outflow, but neither of them associated with it. These two components were named ns1 and ns2 and are detected at vLSR velocities between 15 and 25 km s−1 .
ns2 is associated with FIR 6. They also identified a blueshifted feature, ew1, extending east of
FIR 6. Chernin (1996) proposed that the brightest outflow component apparently powered by FIR
5A has a layered velocity structure. Their lower resolution combined molecular maps (∼ 4.′′ 5)
are dominated by an unipolar red lobe composed by two parallel outflows at lower velocities (∼
20 km s−1 in their Figure 1) which merge into only one at high velocities . This redder emission,
referred as ns1 in their paper, is more collimated than the lower velocity components and arises
10′′ west of FIR 5A. The author suggests that the ns1 outflow is widened by jet-wandering or
internal shocks (Chernin & Masson 1995) and is powered by a deeply embedded and undetected
source rather than FIR 5A due to its misalignment with it.
In this work, we offer a different interpretation for this scenario. The SMA CO (3 → 2)
maps have an angular resolution a factor of 2 higher than the combined maps of Chernin (1996).
Contrary to his proposal, our maps show that this outflow is clearly powered by FIR 5A instead
of by a faint, undetected low-mass star. The overall morphology described by Chernin (1996)
is also observed in our maps. The main difference is that we detect high velocity gas which is
offset by 10′′ west of FIR 5A, coinciding in position with the previously undetected FIR 5-sw dust
condensation.Then, two interpretations can be derived from those features. Firstly, it is possible
that all components are part of a single but velocity-layered outflow, the two low velocity lobes
tracing the cavity where the highest velocity outflow is located. The presence of the high velocity
lobe not only at the center of the cavity but also displaced from it could suggest that the outflow
6.4. Discussion
123
Figure 6.10: Superposition of contours from 15.6, 19.2 and 29.7 km s−1 velocity channels
(black contours) over 7.2 km s−1 channel (red contours). Intensity contours are -3, 3, 4, 5, 7,
9, 12 σ (1 σ ≈ 0.57 mJy beam−1 ). Source positions are maked as crosses.
is precessing. Alternatively, the presence of the FIR 5-sw dust source associated with the western
red shifted lobe, and in particular at high outflow velocities, suggest that this lobe could be an
independent molecular outflow. As in the case of FIR 5A, this outflow would be also an unipolar
outflow.
Our CO (3 → 2) maps seem to indicate a possible interaction between the different outflows.
In the blue lobe of Figure 6.5, there is extended emission centered in the dust condensation FIR
6n (using the LCGR02 nomenclature) with an EW orientation. The emission is associated with an
unipolar outflow detected from ∼ 1.0 to 7.8 km s−1 and is characterized by a wandering/wiggling
morphology. The outflow suffers structural changes in its shape, represented by drastic rotations
in PA. From being powered initially toward the NW direction, it assumes an almost horizontal
distribution (PA = 94◦ ) which corresponds to its brightest emission. Then, another structural
change seen at 7.8 km s−1 results in an u−like shape. Both the bending from NW to the EW
direction and the u−like structure coincide spatially with the projection of the red-lobe NS outflows
124
Figure 6.11: Spectrum of the interacting zone between the EW outflow, powered by FIR 6,
and the high velocity feature apparently powered by FIR 5-sw. The spectrum was obtained
for a velocity range of 0 to 33.2 km s−1 . The three peaks correspond to the emission from the
EW outflow (the blue shifted peak at ∼ 7 km s−1 ), the main lobe powered by FIR 5A at ∼ 18
km s−1 and the high velocity lobe arising from FIR 5-sw at ∼ 30 km s−1 .
powered by FIR 5A and FIR 5-sw. Figure 6.10 shows contours of velocity channels 15.6, 19.2
and 29.7 km s−1 (black contours) overlaid with the 7.2 km s−1 channel (red contours) in the upper,
middle and bottom panels, respectively. The variations in PA of the EW outflow may be somehow
due to the interaction with the main outflow powered by FIR 5A and the high velocity emission
from FIR 5-sw. Global inspection of these three panels tentatively leads to the hypothesis of a
shock interaction between distinct outflows in such a way that the gas structure is modified. The
spectrum exhibited in Figure 6.11 was obtained for the supposedly interacting zone of the panels of
Figure 6.10. A box of −6′′ < ∆α < −18′′ and −9′′ < ∆δ < −24′′ was used to select a region where
all three outflows components (EW, main and high velocity features) contribute to the emission.
The lack of CO emission seen at ∼ 25 km s−1 is probably due to the cavity previously mentioned
and corresponds to the velocity interval between low and high red velocity components. The blue
emission is associated with the EW outflow.
6.4.5 Unipolar molecular outflow
Previous observations of NGC 2024 fail to detect a blue counterpart for the bright outflow
powered by FIR 5A (Richer et al. 1992; Chernin 1996). However, other studies claim a bipolarity
for this outflow (Sanders & Willner 1985; Barnes et al. 1989). In all cases, the red shift lobe
which is ejected toward the south has a brighter, more extended and collimated emission than the
putative blue counterpart. These works all identify this feature as the main component of this
outflow, making the morphology of the blue lobe, if it really exists, of unclear nature.
This asymmetrical pattern of the outflow powered by FIR 5A could be explained by the cloud
morphology proposed by Matthews et al. (2002), illustrated in Figures 6 and 8 in their paper.
6.5. Conclusions
125
They indicate how the NGC 2024 Hii region could be seen from the west and north directions,
respectively. In this scenario, the dust cores appear in the dense molecular cloud behind the Hii
expanding front (using the line-of-sight as reference), with FIR 5 projected right below the interface zone. Consequently, the bipolar molecular outflow ejected from this core will have the blue
molecular component destroyed by the UV photons produced in the Hii region, since it points right
toward it, but the red lobe would remain intact. Despite the fact that Barnes et al. (1989) did not
know accurately which core is the driving source of the supposedly blue outflow, these authors
found that the total luminosity of the nebula is comparable to the flow energy. Therefore, some
interaction between both could be expected.
6.5 Conclusions
In this paper, we report SMA polarization observations of the intermediate-mass protostellar
core NGC 2024 FIR 5. Data acquisition was done using the polarimetric capabilities of the SMA
combined with wide spectral window receivers. The polarized flux appears distributed in three
components: two of them around the peak of total intensity (Stokes I) and another component
arising from the elongated portion of the core. The overall polarization portion resembles a partial
hourglass morphology due to a possible ambipolar diffusion phenomenon taking place in the core.
The magnetic field strength was estimated in 2.2 mG. The estimates of turbulent-to-magnetic
energy and mass-to-flux ratio are consistent with a supercritical highly magnetized core. In previous works, magnetized collapsing cores were also observed in high-mass protostars. In general,
ambipolar diffusion seems to affect core evolution globally, independent of the mass range.
The absence of a symmetrical field morphology gives rise to different interpretations for the
field structure in the core. The dust cores in NGC 2024 may be affected by an expanding ionization
front compressing the molecular gas. It could be perturbing the field structure at smaller scales.
The bended lines observed in our SMA maps could be the consequence of the radiation pressure
of the hot component. Previous VLA 6 cm observations trace the foreground Hii region as an
extended emission produced by the O2–B2 ionization source IRS 2b. However, our estimations of
radiation pressure due to the expanding shell does not overcome the magnetic pressure generated
by the field lines. Therefore, the bent field lines result from the gravitational pulling, and the
asymmetric hourglass is more likely due to depolarization effects arising in the position of the
previously unresolved FIR 5B source.
A complex outflow morphology was observed toward FIR 5. Several collimated features were
detected toward FIR 5, FIR 6 and FIR 5-sw. We speculate about a possible flow interaction between distinct components. It could explain the structural changes observed in some outflows. The
brighter emission powered by FIR 5A has a clumpy structure and arises highly collimated in a NS
orientation. The absence of a blue lobe counterpart can be attributed to the expanding Hii region
to the north of the core. The UV radiation field may be responsible for dissociating the molecular
structure of the outflow, destroying this component.
Chapter 7
Spectro-polarimetric observations of
H2O masers toward IRAS 16293-2422:
tracing magnetic fileds at very high
volume densities5
7.1 Introduction
Spectro-polarimetric observations of masers is a powerful tool to study with accuracy the magnetic field properties in the maser pumping zone. Water masers are unique because they are found
in all type of star-forming regions. In contrast, methanol and OH masers are found associated with
high-mass star formation sites. Despite the fact that the H2 O molecule has a complex rotational
structure, some of the rotational lines are well known to emit as masers. The most ”popular” water
maser line is the (616 − 523 ). This is because it emits the frequency of 22 GHz, which has been easily accessible to the radio telescopes for the last few decades. This line splits in different hyperfine
components, which have a small Zeeman splitting factor (∼ 10−3 Hz µG−1 ). Yet, this emission
is usually very strong, so with the present powerful radio telescopes it is possible to measure the
circular polarization and from this measurement to derive the magnetic field strength in the lineof-sight. If the linear polarization is also measured, then the full 3-D magnetic field configuration
can be derived. The 22 GHz water maser line is an excellent probe of molecular gas at very high
volume densities (n(H2 ) in the 108 to 1010 range, Elitzur et al. 1989). The 22 GHz water maser
emission is often associated with active star forming regions, and in particular with the earliest
stages of protostellar evolution (Torrelles et al. 1996; Sarma et al. 2002; Vlemmings et al. 2006b),
but it is also found in some circumstellar envelopes of evolved stars (Vlemmings et al. 2002).
Recently, several studies have appeared in the literature reporting the efficiency of the spectro5
Work in progress: Alves, F. O., Vlemmings, W. H. T., Girart, J. M., Torrelles, J. M., 2011, in preparation.
127
128 Chapter 7. Spectro-polarimetric observations of H2 O masers toward IRAS 16293-2422
polarimetric technique using masers. These studies have allowed the study the magnetic field
properties in very dense molecular environment around circumstellar envelopes of evolved stars
and of young stars (Vlemmings et al. 2002; Vlemmings & van Langevelde 2005; Vlemmings
et al. 2006a,b; Fiebig & Guesten 1989; Sarma et al. 2001, 2002). For example, Vlemmings et al.
(2006b) carried out VLBA circular and linear polarization observations of H2 O masers around
the Cepheus A HW2 high-mass young stellar object. They derived a magnetic field strength of
several tens of mG at scales of several tens of AU around the protostar. Interestingly, their data
point to an enhancement of the magnetic field within ∼ 25 AU of the massive protostar, where it
strengths up to 600 mG within the putative protostellar disk. Their results emphasize the major
role of magnetic fields in the cloud collapse phase and in shaping the protostellar outflows in very
active high-mass star-forming regions.
The goal of this investigation is to obtain information on the magnetic field properties at high
volume densities (n(H2 ) ≃ 109 cm−3 ). At these densities and with the present telescopes it would
be difficult to detect the dust polarization emission (and the feasibility would be limited toward a
handful list of objects). In addition, it is possible that at such high densities and at submillimeter
wavelengths the emission suffers from depolarization effects (Goodman et al. 1992, 1995; Lazarian
et al. 1997). On the other hand, water masers, which are excited at these densities, can provide an
alternative technique to study the magnetic field properties.
We performed water maser observations toward IRAS 16293-2422 (hereafter, IRAS16293),
a prototypical low-mass protostellar system located in ρ Ophiucus molecular cloud at a distance
of 150 pc from the Sun (Rao et al. 2009). This source is a well-studied binary system, usually
referred as source A and source B, with separation of 5′′ (750 AU) and very embedded in a dense
molecular core (Wootten 1989; Looney et al. 2000). Both sources have a very rich chemistry which
is typically found in hot cores (Ceccarelli et al. 2000; Kuan et al. 2004; Bisschop et al. 2008). High
resolution maps resolve source A, the southern and and brighter one, in two dust submillimeter
components and two compact centimeter components (Chandler et al. 2005). IRAS 16293 has
two large scale bipolar CO outflows, one of them associated with source A while the powering
source of the other CO outflow is a matter of debate (Walker et al. 1988; Stark et al. 2004; Yeh
et al. 2008). Recently, observations of the SiO (8–7) emission have revealed a compact molecular
outflow also associated with source A (Rao et al. 2009). IRAS 16293 has strong water maser
emission that has been well monitored (Wilking & Claussen 1987; Terebey et al. 1992; Claussen
et al. 1996). The strongest features appear typically between a vLS R of 0 and 10 km s−1 , and very
often have intensities of more than 100 Jy.
Tamura et al. (1993) performed observations of the 1.1 mm dust polarized emission toward
IRAS 16293 at an angular resolution of 19′′ . They found that the magnetic field lines are perpendicular to the major axis of the circumstellar disk. This configuration was corroborated recently
by Rao et al. (2009), who used the SMA and obtained a polarization map at an angular resolution
of ≃ 2′′ (≃ 300 AU), resolving both sources A and B. The mean volume density traced by the
SMA maps is ≃ 6 × 107 cm−3 . The polarization pattern around source A is compatible with a
7.2. Observations
129
Figure 7.1: Left panel: 1.3 mm polarization vector and the orientation of the ambient field of the
cloud. The direction of the core magnetic field as inferred from the mm data is perpendicular to
the electric vector (Tamura et al. 1993). Arrows indicate the position of the two bipolar outflows.
Right panel: Submm magnetic field lines overlaid to the 345 GHz continuum emission of the
SMA maps (Rao et al. 2009). Crosses show the position of the three resolved condensations.
The continuum submm map has an angular resolution a factor of 2 smaller than the mm map.
hourglass morphology for the magnetic field. The estimated magnetic field strength was 4.5 mG.
The SMA maps show that there is a considerable misalignment between the outflow direction and
the magnetic field axis, and this is roughly in agreement with model predictions where the magnetic energy is comparable to the centrifugal energy. In contrast, source B is associated with an
uniform and apparently undisturbed magnetic field (Fig. 7.1).
In this work, we report spectro-polarimetric Very Large Array (VLA) observations of H2 O
masers toward IRAS16293. In section 7.2, the details of the observational setup are described.
In section 7.3, the results obtained from the maser spectroscopy are shown. In section 7.4, we
report a description of the radiative model through which an estimation for the line-of-sight (LOS)
magnetic field strength is provided and finally in section 7.5 our conclusions are reported.
7.2 Observations
The observations were done with the Very Large Array (NRAO, New Mexico, USA) in its
more extended configuration, A, in 2007 June 25th and 27th . The tracks lasted ∼ 5.5 hours each. A
total of 27 antennas were used, with 10 of them already retrofitted with the new system, resulting
in a combined VLA/EVLA (Extended VLA) observation. We used the K band receivers (2224 GHz) to tune at the frequency of the water maser the (616 − 523 ) rotational transition, which
has a rest frequency of 22.23508 GHz. We used the full polarization capability of the correlator,
selecting a bandwidth of 0.7813 MHz (∼ 10.5 km s−1 in velocity). This spectral setup provides
a total of 128 channels, which allows to cover most of the velocity range of the strongest water
maser features (observed around the ambient cloud velocity, vLS R ≃ 4km s−1 ) at the high spectral
resolution of 0.08 km s−1 . Quasar J1626-298 was used as gain calibrator . Quasars J1331+305 and
the radio source J1751+096 were used for polarization calibrations in order to obtain corrections
in the instrumental feed polarization and the proper calibrate the position angle of the polarization.
All three calibrators were also used for bandpass corrections. We performed self–calibration using
the channel with the strongest intensity. Since the emission detected is unresolved, we performed
phase and amplitude self–calibration and applied the solutions to the other channels.
Data reduction was done with the Astronomical Image Processing Software package (AIPS).
Imaging of Stokes parameters I, Q and U were generated with a quasi-uniform weighting (robust
= -1). Maps of polarized fraction (P) and position of polarization √
angles (PA) were obtained by
Q2 +U 2
and PA = 12 tan−1 ( UQ ).
combining Stokes Q and U images in such a way that P = IIP =
I
The resulting synthesized beam has 0.14′′ × 0.08′′ , with a position angle of PA = −5.7◦ . The
rms noise for channels where no emission is detected is ∼ 8 mJy beam−1 , and it increases up to 23
mJy beam−1 at the peak emission channel. A slightly lower rms is observed for polarized intensity
(the Stokes Q, U and V maps).
7.3 Results
7.3.1 H2 O maser emission
The contour channel maps of the H2 O emission observed with the VLA/EVLA data are shown
in Figure 7.2 at a 50σ level. The emission extends over a wide range of velocities (4.5 < vLSR
< 9 km s−1 ). Most of the emission appears at redshift velocities with respect to the cloud systemic
velocity. The water maser line has peak intensity of ∼ 167 Jy beam−1 , detected at a vLSR velocity
of ≃ 7.4 km s−1 . Some channels present double emission features (channels at vLSR velocities
around ≃ 6.0 and 8.5 km s−1 ). The secondary features are significantly less brighter (two orders
of magnitude weaker) and appear at a distance of ≃ 0.2′′ (30 AU in projection).
The Stokes I spectrum of the stronger spot is shown in Figure 7.3, left panel. The non-Gaussian
line profile indicates that there are several components not resolved both spectroscopically and
spatially. Apart of the peak intensity at 7.4 km s−1 , unresolved emission seems to be present
at velocities closer to the systemic cloud velocity (vLSR ≃5.5 km s−1 ) with a strong flux of ∼20
Jy beam−1 . Fainter emission (∼ 5 Jy beam−1 ) is also observed at higher velocity channels (vLSR
≃9.2 km s−1 ). Therefore, there are at least three unresolved components (Table 7.1). A Gaussian
fit on each of those components provides a mean spatial separation of ∼ 22 milli-arcseconds,
which is higher than the precision on the position determination, ≃ 2 milli-arcseconds (estimated
from the ratio between the width of the synthesized beam and the the signal-to-noise ratio of the
fainter component). The right panel of Figure 7.3 shows that the maser features may be distributed
linearly and could be related a shock zone created by outflows or to the putative circumstellar disk
7.3. Results
131
Figure 7.2: Channel maps of the deconvolved H2 O emission toward IRAS 16293-2422. Contours are -50, 50, 500, 3×103 , 1×104 , 2×104 times 8 mJy beam−1 , the rms noise of the map.
The peak flux of 167 Jy beam−1 occurs at channel 41 (∼ 7.4 km s−1 ). The deconvolved beam
is shown in the lower left corner of the first channel. The vLSR velocity of each channel is
shown over the emission structure.
of submillimeter source Aa. The velocity gradient observed between vLSR ≃ 5.7 km s−1 and higher
velocities follows the straight distribution in a roughly E-W sense (PA ≃ 110◦ ).
A scheme of the distribution of dust and molecular outflows in IRAS16293 is shown in Figure
7.4. The maser spot detected in our observations is associated with source A. They are located
≃ 0.25′′ (≃ 38 AU in projection) to the South-East of the dusty condensation Aa detected by
Chandler et al. (2005) from subarcsecond submm continuum observations. At this distance, it
is likely that the maser emission is produced in the dense circumstellar material around the Aa
protostar. Source A is associated with a powerful and possibly very young molecular outflow
(traced by the SiO 8–7 emission) extending toward the NW-SE direction (Rao et al. 2009), with
the SE lobe being redshifted. Our maser spot is also detected at redshifted velocities and lies at
the same PA as the SiO outflow with respect to source Aa. Therefore, it is possible that the water
masers may trace a region where the very dense and hot molecular outflow interacts with the
circumstellar material around the protostars embedded in source A. VLBI water masers detections
were also reported toward source A (Imai et al. 2007). However, their milliarcsecond angular
Table 7.1: Possible H2 O maser components in IRAS 16293-2422
vLSR
(km s−1 )
I peak a
(Jy beam−1 )
α (2000)
(h m s)
5.7
7.4
9.2
26.52 (0.01)
180.00 (0.02)
4.96 (0.01)
16 32 22.88298
16 32 22.88084
16 32 22.88183
a
160
δ (2000)
(o ′ ′′)
-24 28 36.4952
-24 28 36.4869
-24 28 36.4933
Peak intensities and equatorial coordinates derived with JMFIT
of AIPS.
Spectrum of
H2O maser emission
Stokes I
140
Possible independent maser features
120
JY/BEAM
100
80
60
Position of the emission
peak of intensity
40
20
0
10
9
8
7
Kilo VELO-LSR
6
5
4
Figure 7.3: Left panel: Stokes I spectrum obtained in the peak flux position at RA =
16h 32m 22.88s and Dec = -24◦ 28m 36.50s . Right panel: Possible independent maser features
(stars) as derived by gaussian fits. The numeric labels are the systematic velocity of each
component. The circle indicates the position from which the spectrum of the left panel was
extracted.
resolution found a spot exactly over the Aa dusty condensation and another one to the south-west
of it. While the former may have been excited in the circumstellar disk of source Aa, the latter
could be associated with the CO E-W red lobe outflow.
7.3.2 Polarized emission
The spectrum of linearly polarized intensity is very similar Stokes I line profile (see the left
panel of figure 7.3) except for the flux scale, which is much weaker: It peaks at the same systemic
velocity as the Stokes I spectrum, although it reaches ∼ 4.5 Jy beam−1 . The dependence of the
polarization intensity, polarization fraction, position angle and Stokes I with systematic velocity
is shown in Figure 7.5. The polarization fraction is observed to be 2.5 ± 0.2%. The polarization
position angle is θ = −23◦ and shows only small changes across the maser (σθ = 2◦ ), implying
that the polarization vectors at different velocities trace basically the same region. The formal
7.4. Modeling the polarized emission of the water maser
133
-24 28 32
B
33
SiO blue
DECLINATION (J 2000)
34
35
36
CO blue
Ab
Aa
VLA maser
CO red
VLBI maser
37
A
38
SiO red
39
16 32 23.1
23.0
22.9
22.8
22.7
RIGHT ASCENSION (J 2000)
22.6
Figure 7.4: Scheme of the distribution of dust and molecular material in IRAS16293. The plus
signal is the position of the peak intensity of our maser data. The ellipse is the deconvolved
size of source A as derived by Rao et al. (2009). Triangles denote the position of the submillimeter condensations observed by Chandler et al. (2005). Stars denote the VLBI water
maser detections of Imai et al. (2007) and straight lines denotes the direction of the CO and
SiO outflows associated with this core (Rao et al. 2009).
◦
◦
error in PA (σθ = 12 σIPP 180
π , Wardle & Kronberg 1974) is remarkably small: 0.14 . The linear
polarization as derived from Stokes U and Q maps is exhibited in Figure 7.7, which shows the
distribution of polarization vectors in the brightest channel (see Section 7.4). The peak of polarized
intensity is offset 0.05′′ with respect to the Stokes I peak. The polarization vectors can be parallel
or perpendicular to magnetic field orientation in the plane of the sky. In the next section, we
discuss which assumptions must be considered in order to solve this ambiguity.
The line profile of the circular polarization (Stokes V) has an inverse P-Cygni shape (see
Fig. 7.6). The Stokes V spectrum is proportional to the first derivative of the Stokes I spectrum
and to the line-of-sight magnetic field component (see section 1.5.4). The fraction of circular
polarization, calculated as (Vmax − Vmin )/Imax , is ∼ 0.45% for the brightest component. The other
hypothetical components show only residual Zeeman profiles with amplitudes at the rms level.
The red line in Fig. 7.6 indicates the fit which best represents this derivation, and which reveals
the intensity of the line-of-sight magnetic field (see next section).
7.4 Modeling the polarized emission of the water maser
In this section, we model the water maser line data in order to derive the line-of-sight (LOS)
magnetic field strength in IRAS16293. A complete analysis of the maser theory on magnetized
zones is provided in Nedoluha & Watson (1992). For our work, a non-LTE radiative transfer
Figure 7.5: Stokes I (black line) and polarized intensity (multiplied by a factor of 10, red line)
spectra of the water maser emission (upper panel). The Dependence of polarization fraction
(black line) and position angle (dashed line) with vLSR .
model from Vlemmings et al. (2002) was applied to the data. A detailed description of the model
used can be found in Vlemmings (2006). Exemples of applications of this model on high-mass
star-forming regions are reported in Surcis et al. (2009) and Vlemmings et al. (2010) for methanol
masers and Vlemmings et al. (2006b) and Surcis et al. (2011) for water masers.
Some basic definitions must be introduced previously to the code description. An important
property of a maser spot is the degree of saturation. It relates the stimulated emission rate R and the
loss rate Γ through which the molecular states return from their inverted population. In this sense,
the saturation level of a maser is given by R/Γ. The masers begin to saturate at R/Γ ≃ 0.5 s−1 and
approach full saturation for values larger than 100 s−1 . Another important quantity is the crossrelaxation rate Γν , which describes the formation rate of excited states through recombination of
pump photons trapped in an optically thick medium. Nedoluha & Watson (1992) have shown that
the maser brightness temperature T b of a maser is linearly proportional to (Γ + Γν ). For 22 GHz
water masers, Γ is typically assumed to be . 1 s−1 while Γν depends on the masing gas temperature
T.
Masers are pumped along path lengths which are usually much smaller than their parent clouds.
Those preferential paths provide exponential gain to the maser brightness. This effect is called
beaming and is represented by the solid angle ∆Ω. Therefore, the maser temperature brightness
can be conveniently redefined as T b ∆Ω. The angle θ between the maser propagation direction
135
Figure 7.6: Stokes I (upper panel) and Stokes V (lower panel) spectra of the water maser
emission.
(assumed to be the LOS) and the magnetic field lines is also an important parameter since several
factors like the degree of linear polarization Pl and the field topology depend on it. Finally, the
intrinsic thermal linewidth of the maser region, which is the Maxwellian distribution of particle
velocities given by ∆νth ≈ 0.5(T/100)1/2 , is used to estimate the masing gas temperature T .
The radiative transfer code models the observed total intensity I and polarization fraction Pl
spectra by performing a least-square fit to the intrinsic thermal linewidth ∆νth along several values
of T b ∆Ω. The best χ2 value of T b ∆Ω is used to calculate θ considering the dependence between
both quantities reported by Vlemmings (2006) and shown in Figure 7.8. Both outputs, together
with ∆νth , are then included in the full radiative transfer code to produce synthetic Stokes I and V
spectra that are used for fitting the observed I and V cubes.
In Fig. 7.9 we show the χ2 fit contours obtained for the brightness temperature and the intrinsic
thermal linewidth. Unfortunately, the linewidth of the best χ2 value (∆νth ≃ 3.5 km s−1 ) is larger
than than the values found in other sources (typically between 0.9 and 2.4 km s−1 , e. g. Surcis
et al. 2011). This occurs because our line is a blend of unresolved features. Nevertheless, from
the Zeeman splitting formalism, the magnetic field strength can be correlated to the fraction of
7.4 KM/S
-24 28 36.1
36.2
DECLINATION (J2000)
36.3
36.4
36.5
36.6
36.7
36.8
36.9
16 32 22.91
22.90
22.89
22.88
22.87
22.86
RIGHT ASCENSION (J2000)
22.85
Figure 7.7: Distribution of H2 O linear polarization vectors in the brightest emission channel
(vLSR ≃ 7.4 km s−1 ). Contours are -50, -30, 30, 50, 500, 3 × 103 , 1 × 104 , 2 × 104 × 8
mJy beam−1 , the rms of the map. Only polarization vectors whose P > 1% are plotted.
Vectors are sampled as 2/2 of a beam.
circular polarization by (see, for instance, Fiebig & Guesten 1989)
PV
= (Vmax − Vmin )/Imax
(7.1)
= 2 × AF−F′ × (B cos θ)/∆vI ,
(7.2)
where the AF−F′ coefficient depends on the maser rotational levels (F and F ′ ), the intrinsic thermal linewidth ∆νth and the maser saturation degree, while ∆vI is the FW H M of the total power
spectrum. For the AF−F′ coefficient, we adopted the range of 0.012 to 0.018. The first is the value
found for the water masers in the Cepheus A star-forming region (Vlemmings et al. 2006b), and
the second one is the typical found in other star forming regions. The water maser spectrum is
probably a blend of different velocity components, so we adopt a line width from 0.75 km s−1 , a
typical value found in other regions (Vlemmings et al. 2006b), to 1.0 km s−1 , the observed value in
IRAS 16293. For these values, we find that BLOS range from −90 to −180 mG. The negative signal
is inferred from the Stokes V shape and means that the field is pointing away from the observer.
Since that the linear polarization fraction in our data is about 3%, this maser is likely unsaturated
and the field strength determination is a fair approximation.
Figure 7.7 shows the linear polarization vectors at the channel with the brightest emission.
There is a degeneracy between the position angle of the linear polarization vectors and the magnetic field direction projected in the plane-of-sky (POS). The position angle of the polarization
will be parallel or perpendicular to the magnetic field in the POS for θ > θcrit or θ < θcrit = 55◦ ,
respectively (Goldreich et al. 1973). θcrit is the so called Van Vleck angle and depends of several
factors, such as the saturation degree and the brightness temperature of the maser emission. De-
137
Figure 7.8: Dependence of linear polarization Pl with the angle θ between the maser propagation direction and the magnetic field orientation (extracted from Vlemmings (2006)). The
dependence is shown for difference values of brightness temperature. The thick solid line is
the theoretical limit for fully saturated masers (Goldreich et al. 1973).
spite that we could not constrain the magnetic field strength from the fit and that we were unable
to solve this ambiguity we can claim that the POS field topology is quite ordered in both cases as
shown by the linear polarization vectors (which would keep ordered if rotated by 90◦ ).
This work is the first determination of the field strength in a low-mass young stellar object at
densities larger than 108 cm−3 using the H2 O maser as a tool. We can compare the magnetic field
strength derived from the water maser to the previous values found at lower volume densities. Rao
et al. (2009) estimated the magnetic field strength in the plane-of-sky from SMA submm polarization observations toward IRAS16293. These observations trace the dense molecular envelopes
around the protostars at a mean volume density of 107 cm−3 . At this density they found that the
magnetic field component in the POS is 4.5 mG. In a magnetically dominated environment, we
should expect the observed that the magnetic field strength increases with the volume density as
n0.47 (Fiedler & Mouschovias 1993) . In this case, the expected magnetic field strength at densities
of n(H2 ) ≃ 109−10 cm−3 would range from 40 to 116 mG. These values are perfectly compatible
with the values derived from the water maser circular polarization. Indeed, for BLOS estimations
with narrow linewidths (∼ 0.75 km s−1 ), which is the typical case for water masers, we obtained a
mean field of ∼ 115 mG.
The H2 O maser emission of IRAS16293 is very strong and very stable over several epochs, as
shown by many surveys performed toward this source (Wilking & Claussen 1987; Claussen et al.
1996; Furuya et al. 2003). We are then encouraged to carry out very long baseline interferometry
observations. With this technique, the blended maser components found in this work will be likely
resolved both spatially and spectroscopically. This will allow to properly use the Vlemmings et al.
Figure 7.9: ∆χ2 output contours for the intrinsic thermal linewidth ∆νth and brightness temperature T b ∆Ω.
(2002) model to the different maser components and derive the full 3-D magnetic field properties
as already done in Cepheus A HW2 (Vlemmings et al. 2006b).
7.5 Conclusions
This work reports very preliminary results of the H2 O (616 −523 ) maser emission observed with
the VLA/EVLA toward the low-mass source IRAS 16293-2422. This is the first time that water
maser emission of a low-mass protostar is used to calculate the LOS magnetic field at densities
larger than 108 cm−3 . However, higher resolution data are necessary since that the full description
of the water maser emission was impossible to model due to the unresolved blended features. Our
main conclusions are:
• We detect an extremely strong emission which is likely associated with the submm source
Aa, resolved from the main source A of IRAS 16293-2422 in previous high-resolution maps.
• The maser spectrum has a non-Gaussian profile, which indicates that the spot harbors several unresolved components. At least three components can be detected within a velocity
gradient of ∼ 3.5 km s−1 distributed in a roughly linear configuration. Those components
could be associated with the presence of a circumstellar disk or with a shock region.
• The obtained Stokes V spectrum is consistent with Zeeman emission. The LOS magnetic
field strength estimated is ∼ 115 mG. This value is consistent with the value found at lower
volume densities by Rao et al. (2009) for a magnetically dominated molecular environment.
The POS field topology has an ordered pattern consistent with larger scales field morphologies.
Chapter 8
Conclusions
This thesis is mostly based on the science extracted by using the astronomical polarimetry. The
observation of polarized light from astrophysical objects, which is usually only a small fraction
of the total flux, is strongly limited by the instrumental sensitivity and by the lack of polarimeters
in most astronomical facilities. Fortunately and as a result of the crescent interest of the astronomical community on this observational technique, many of the new generation of telescopes
include polarization in their observing mode. In this thesis we have taken advantage of the new
polarimetric capabilities of the 4.2 m William Herschel Telescope, where a setup optimized for
near-infrared CCD-polarimetry was used, and the Submillimeter Array, where the high sensitivity
receivers improve the detection of continuum polarization at 345 GHz. The use of different polarimetric techniques at different wavelengths (optical, near-IR, submm and cm) has allowed to trace
different physical regimes within molecular clouds. In particular, we were able to study the magnetic field properties at distinct densities and physical scales in a selected sample of star forming
regions at different evolutionary stages. The specific summarized conclusion for each chapter are:
1. Optical polarimetry as a distance ruler (Alves & Franco 2007). Although polarimetry is in most cases associated with magnetic field studies, very recently (Alves & Franco
2006) has shown that polarimetry is also a powerful tool to determine distances in nearby
molecular clouds. This is thanks to the high sensitiveness of the optical polarization to the
visual extinction. Polarization data of stars with well determined distances can be used to
obtain the distribution of interstellar dust. Moreover, it has the advantage that no previous
knowledge is necessary about the target photometric classification. Using this technique,
we derived the distance to the molecular cloud Pipe nebula with much higher accuracy than
previous visual extinction investigations toward the same line-of-sight. Polarization observations of Hipparcos stars in a wide range of distances (10 . d . 200 pc) present a sharp
increase in the degree of polarization at ∼ 145 pc. Evidences of a lower diffuse material
foreground to the cloud is observed around ∼ 100 pc, where a few stars show some degree of polarization. The plane-of-sky magnetic field revealed by the highest polarized stars
show a dominant component perpendicular to the cloud main axis, while the low-polarized
139
140
Chapter 8. Conclusions
objects trace an orthogonal component likely associated to the previously mentioned foreground material. It is noteworthy to mention that the polarization map of the Pipe nebula
was selected for the cover image of the Astronomy and Astrophysics issue of August, 2007.
Moreover, this work was awarded as highlight in the same issue.
2. The global magnetic field of the Pipe nebula (Alves et al. 2008). The results of the optical
polarimetry of Hipparcos stars are corroborated by a much more extensive survey performed
in the whole cloud (we observed more than 10,000 stars in 46 fields). The global polarization
properties are described by a rise in polarization fraction from the north-western end, where
B59 is located (the only active star forming region), to the south-eastern portion of the
cloud (the “bowl”), where we measured the highest degrees of interstellar polarization ever
observed for a molecular cloud. On the other hand, this rise in the polarization degree is anticorrelated with the dispersion of polarization angles. The global magnetic field direction in
the plane-of-sky is perpendicular to the cloud long axis, suggesting that the cloud collapse
takes place along the field lines. We found that the Pipe can be subdivided in three regions
with distinct evolutionary states: the B59 region, where the lowest polarization degrees and
highest dispersion in polarization angles may be connected with the star formation activity,
the “stem” of the Pipe, whose filamentary gas distribution may result from an ambipolar
diffusion process; and the “bowl”, whose polarization properties suggest a very strong and
uniform magnetic field. The latter could be in a very early evolutionary state. Once more,
this impressive result was awarded as highlight in the Astronomy and Astrophysics issue of
August, 2008.
3. The magnetic field of the Pipe nebula at core scales (Franco et al. 2010). The core-tocore analysis of the polarization survey reveals some distinct features when compared with
the global scale. Despite of the high degree of interstellar polarization observed in the Pipe,
the polarizing efficiency P/AV are close to the expected observational limit seen in other
molecular clouds. Among the observed fields, the ones with no associated cores have a
mean polarization angle constant, independently of their position in the cloud. On the other
hand, higher extinction fields show systematic variations along the main axis of the cloud.
It is also important to emphasize the results of Frau et al. (2010), an investigation performed
in coordination with the polarimetric one. They found a correlation between the magnetic
activity of some cores and their chemical abundances, in the sense that chemically rich
cores possess a very strong field and vice-versa. We obtained the Second Order Structure
Function for our data, which revealed that the Pipe is sub-Alfvénic (magnetically dominated
with respect to turbulence) at almost all scales. The only exception is the interface “stembowl” region, where magnetic and turbulent energies appear to be in equipartition.
4. The intricate magnetic field of NGC 1333 The J−band polarimetry toward NGC 1333
confirmed LIRIS as a very reliable instrument when operated in this mode. The new nearIR data were collected toward the relatively diffuse gas around the dense core NGC 1333
141
IRAS 4A, reaching visual extinctions as deep as ∼ 11 magnitudes. The near-IR data are
perfectly consistent with visible band data obtained by other instrument. The polarization
results show that the polarizing efficiency of NGC 1333 is similar to the one observed in
other molecular clouds like Taurus and Ophiuchus, although much smaller to what was
observed for the Pipe nebula. The magnetic field topology derived from the interstellar polarization map is dominated by an ordered component. Few of the observed stars are YSO’s
and the observed polarization is produced by scattering. The magnetic field associated with
the diffuse gas is not aligned with the magnetic field associated with the dense envelope
around the protostar IRAS 4A. This suggests that the field morphology may be suffering
structural changes from large to small scales. However, a different interpretation arises from
CO spectra obtained toward the same line-of-sight, which show multiple velocity components. The observed near-IR field might be the average field along the multiple molecular
components in the line-of-sight.
5. The magnetic field in the NGC 2024 FIR 5 dense core (Alves et al. 2011). In this work,
we studied the magnetic field properties at much smaller scales than in the previous chapters. The intermediate-mass protostar NGC 2024 FIR 5, which shows a very ordered field
morphology and an intricate ambient kinematics, was selected for high-resolution SMA investigations. The dust continuum emission from this core is resolved into two components
with the brightest one powering a collimated unipolar (and redshifted) CO outflow. The
molecular gas from the missing blue lobe is probably dissociated in the nearby Hii region.
The magnetic field configuration presents an asymmetric hourglass shape which is likely
due to depolarization effects toward the source FIR 5B (the weaker dust condensation). The
estimated field strength is 2.2 mG, consistent with previous works. We estimated that the
radiation pressure of the Hii region is not enough to disturb the magnetic field lines at core
scales, differently of what is seen at larger scales in the NGC 2024 cloud.
6. H2 O masers: probing the magnetic field at high density environments. This investigation provided preliminary results on the magnetic field strength at very high densities toward
the class 0 protostar IRAS 16293-2422. The VLA/EVLA observations at 22 cm detected
a strong water maser emission which seems to be associated with the submillimeter condensation Aa. The spectrum has a non-Gaussian line profile, and there are at least three
different velocity components that could be tracing a velocity gradient of ∼ 3.5 km s−1 .
We detect the Zeeman splitting in the Stokes V spectrum toward the main component. We
derive a line-of-sight field strength of 115 mG. The comparison between the field strength
derived by previous submillimeter data (which trace densities as large as 107 cm−3 ), and the
field derived by our centimeter data (n ≃ 109 cm−3 ) are in agreement with a magnetically
controlled core collapse.
It would be interesting to combine all the data compiled in this thesis to estimate the magnetic
field dependence with the volume density. Figure 8.1 shows the derived magnetic field strength
142
Chapter 8. Conclusions
3
10
IRAS 16293−2422
2
10
1
B (mG)
10
κ=
7
0.4
NGC 2024 FIR 5
0
10
NGC 1333
.66
0
κ=
-1
10
Bowl
Stem
B59
-2
10
2
10
4
10
6
10
-3
Gas Density (cm )
8
10
10
10
Figure 8.1: Observational dependence between B and volume density for the results achieved
with this thesis. The dotted line represents this dependence for a magnetized object (κ ≈ 0.47)
while the dashed line represents a turbulent cloud (κ ≈ 0.66).
with respect to the volume density regime where it was measured for the targets of this thesis: Pipe
nebula, NGC 1333, NGC 2024 FIR 5 and IRAS 16293−2422. For the Pipe, due to the distinct
properties observed for B59, the stem and the bowl, the three regions are plotted separately. For
NGC 1333 the plane-of-sky magnetic field strength was calculated applying the ChandrasekharFermi formula to the near-infrared data. The angle dispersion was derived from our polarization
map (∆θ ≃ 11.6◦ ). The volume density sampled by the near-IR polarization was assumed to be
a value in-between the typical values traced by submm single-dish data and optical polarimetry
(n(H2 ) ≃ 104 cm−3 ). The linewidth was estimated from the 13 CO line profile shown in Chapter 5
as ∼ 2.7 km s−1 . The value derived in NGC 1333 should be taken as a rough estimation due to the
small statistics of the polarization sample.
Globally, from our multi-wavelength study we can see that the magnetic field strength clearly
increases with the volume density of the region observed, as it is shown in Figure 8.1. The lines
show the expected behavior for a magnetically dominated molecular cloud (dotted line) and a turbulent molecular cloud (dashed line). If we take into account that the magnetic field measurement
for IRAS16293 trace the line-of-sight component and the other cases trace the plane-of-sky, then
the data obtained in this thesis cannot clearly discern between the two possible scenarios. This
research is performed toward an inhomogeneous sample of four distinct objects that belong to
four molecular clouds at different distances. Besides that not only the evolutionary stages of the
selected molecular clouds are different, we cannot discard that the initial conditions of each one
could have been different. It makes more difficult to determine an evolutionary track for those
molecular clouds based on the magnetic field structures uniquely.
143
Open questions and future prospects
Form the observational point of view, there is some debate about how accurate are the standard methods used to derive the magnetic field strength. In addition, some physical parameters
like volume density and velocity dispersion were obtained from extrapolations of their determinations from core molecular spectroscopy observations to the optical/near-infrared zones. A way to
improve the analysis would be to directly compare the results from simulations of magnetized and
turbulent cloud with the obtained data.
This work reinforces the importance of the magnetic field in molecular cloud environments by
providing comparative views in a multi-scale scenario. However, it is still unclear how the magnetic field morphology evolves in molecular clouds from large (parcsec) scale structures down to
the circumstellar environments (tens of AU). A representative example can be found in the Pipe
nebula, where the mean global field is remarkably ordered, with highly magnetized material in
some portions (the bowl), but at core scales this is not so clear. The collapse of subcritical clouds
and envelopes into supercritical cores is still a matter of debate in modern star formation theories.
For example, there is the well known issue of the angular momentum excess in a collapsing rotating cloud. Magnetic fields are expected to be the main agent to remove the angular momentum in
a cloud through magnetic braking. However, observational evidences of this phenomenon are still
scarce.
The Pipe nebula is a textbook case of a magnetized object on a very primordial state. Therefore, this object could be an interesting science case to carry out a multi-scale study of the magnetic
fields properties through multi-wavelength polarimetry. Its proximity to the Sun and the privileged
position in the southern sky will motivate the extensive use of the new generation of submm telescopes (ALMA, APEX), which will reveal unprecedented views of the dust universe at high spatial
resolutions. Observations of the starless Pipe cores will provide constraints on the ambipolar diffusion and/or MHD turbulence models by deriving what fraction of mass is already accreted to
the core. It would be also interesting to carry out this multi-scale work toward a molecular cloud
forming massive stars, like Orion, in order to obtain comparative parameters.
Moving toward particular objects, in protostars like NGC 2024 FIR 5 or IRAS 16293-2422,
high resolution polarization maps will trace magnetic field at disk scales. The large database
acquired in this thesis is very suitable as inputs for simulations on magnetized objects. On the other
hand, the very powerful new radioastronomical facilities, such as ALMA and EVLA, will make
possible to follow-up the multi-wavelength/multi-scale approach done in this thesis for a unique
molecular cloud. This kind of investigation will allow a detailed diagnostic on the dynamics of a
molecular cloud from the diffuse gas to the very dense circumstellar regimes.
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