Mid-Infrared Polarimetry: Insights Into Magnetic Fields and Dust Grain Properties in Young Stellar Objects and Protoplanetary Disks

MID-INFRARED POLARIMETRY: INSIGHTS INTO MAGNETIC FIELDS AND DUST GRAIN PROPERTIES IN YOUNG STELLAR OBJECTS AND PROTOPLANETARY DISKS

By HAN ZHANG

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

2018 ⃝c 2018 Han Zhang When I look at your heavens, the work of your fingers, the moon and the stars, which you have set in place, what is mankind that you are mindful of them, human beings that you care for them? – Psalm 8:3-4 ACKNOWLEDGMENTS Firstly, I would like to thank my advisor, Charles M. Telesco, for his patience, guidance, and generous financial supports for the past five years. It is a great privilege for me to work with Charlie and be part of the CanariCam science team.

I want to thank all my collaborators, without your contributions, I can not ﬁnish the work presented in this thesis. I am particularly thankful to Dan Li, Eric Pantin, Aigen Li, Christopher

M. Wright, Peter Barnes, and Naib´ıMari˜nas.Thank you for your insightful discussions and comments.

I thank my fellow graduate students here at University of Florida. My great classmates

Rebecca, Nolan, Chen and Pekki, I remember the days we worked on the homework and projects together. I want to thank Jingzhe, my ﬁrst-year roommate at UF, and Xiao, my driving coach. I want to thank Emily, Wenli, Chutipong, Shuo, Nahathai, Hanna, Tahlia,

Yinan, Amanda, Rachel, Alan, Krittapas, Ben Wu, and Billy. Thank you all for your company and love. Go Gators! Finally, a special thanks to my parents for always believing in me and supporting me. I am grateful for all my church friends both in Gainesville and China. Thank you for your prayers, comfort and encouragement. We love because He ﬁrst loved.

4 TABLE OF CONTENTS page

ACKNOWLEDGMENTS ...... 4

LIST OF TABLES ...... 7

LIST OF FIGURES ...... 8 ABSTRACT ...... 10

CHAPTER

1 INTRODUCTION ...... 12

1.1 Magnetic Fields in Star Formation ...... 12 1.2 Protoplaneatry Disks ...... 13 1.3 Polarimetry: An Important Technique to Study Magnetic Fields ...... 15 1.4 Challenges: Scattering, Radiative Grain Alignment ...... 17 1.5 Thesis Outline ...... 19

2 OBSERVATIONS AND DATA REDUCTION ...... 23

2.1 CanariCam ...... 23 2.2 Stokes Parameters ...... 23 2.3 Data Reduction ...... 24 2.3.1 Polarimetric Imaging Data Reduction ...... 25 2.3.2 Spectropolarimetry Data Reduction ...... 27

3 THE MID-INFRARED POLARIZATION OF THE HERBIG AE STAR WL 16: AN INTERSTELLAR ORIGIN? ...... 30

3.1 Introduction ...... 30 3.2 Observation ...... 32 3.3 Orign of the Polarization ...... 34 3.3.1 Extinction toward WL 16 ...... 34 3.3.2 Decomposition of Absorptive and Emissive Polarization ...... 40 3.3.3 Relationship of WL 16 and Regional Magnetic Fields ...... 43 3.3.4 Intrinsic Polarization ...... 44 3.4 Discussions ...... 45 3.4.1 PAHs in WL 16 ...... 45 3.4.2 Disk Morphology ...... 46 3.5 Summary ...... 48

4 DETECTION OF POLARIZED INFRARED EMISSION BY POLYCYCLIC AROMATIC HYDROCARBONS IN THE MWC 1080 NEBULA ...... 50

4.1 Introduction ...... 50 4.2 Observation and Data Reduction ...... 51

5 4.3 Results ...... 53 4.4 Discussion ...... 54 4.4.1 Numerical Calculations using SD09 ...... 55 4.4.2 Alignment with Magnetic Fields ...... 56 4.4.3 Relationship between Polarization Angles and the Ambient Magnetic Field ...... 58 4.4.4 Marginally Detected 10.3 µm Polarization Feature ...... 59 4.5 Summary ...... 60 5 MODELING POLARIZATION OF YOUNG STELLAR OBJECTS AND PROTOPLANETARY DISKS AT MID-IR ...... 64

5.1 Introduction ...... 64 5.2 Theoretical Understanding of Dust Polarization ...... 65 5.2.1 Polarization from Dichnoic Emission and Absorption ...... 66 5.2.2 Dust Scattering ...... 68 5.3 Model Description ...... 69 5.3.1 Magnetic Fields Setup ...... 69 5.3.2 Fiducial Model: Spherical Power-law Envelope ...... 70 5.3.3 Radiation Transfer with RADMC-3D ...... 70 5.3.4 Disk Model ...... 72 5.3.5 Results ...... 73 5.3.6 Example: AB Aur ...... 75 5.3.7 Discussion ...... 76 5.4 Summary ...... 77

6 UNDERSTANDING THE MAGNETIC FIELDS IN W51 IRS2 USING MID-IR POLARIMETRY 90 6.1 Introduction ...... 90 6.2 Observation and Data Reduction ...... 92 6.3 Discussion ...... 93 6.3.1 Polarization Components – The Aitken Method ...... 93 6.3.2 Polarization Results of W51 IRS2 ...... 94 6.3.3 Magnetic Field Structure ...... 96 6.3.4 Gas Emission from VLA ...... 97 6.3.5 Magnetically Driven Gas Flow? ...... 98 6.4 Summary ...... 99

7 CONCLUSIONS ...... 106

7.1 Future Directions ...... 108 APPENDIX: AITKEN’S METHOD ...... 109

REFERENCES ...... 111

BIOGRAPHICAL SKETCH ...... 119

6 LIST OF TABLES Table page

3-1 Basic Properties of WL 16 ...... 32

3-2 Observing Log ...... 34

3-3 Polarization Measurements of WL 16 ...... 43 3-4 Extinction and Polarization of WL 16 and Elias 29 ...... 44

4-1 Observing Log ...... 60

4-2 Diﬀerent models and polarization at 11.3 µm ...... 61

5-1 Model Parameters ...... 78 6-1 Observation Log ...... 100

6-2 Polarization and Flux Measurements ...... 100

7 LIST OF FIGURES Figure page

1-1 The formation of a low mass star...... 20

1-2 Illustration of the structures and physical processes in a protoplanetary disk. .... 21

1-3 Illustration of absorptive and emissive polarization in magnetically dust alignment theory...... 22

2-1 The frame of the object with o and e ray images...... 28

2-2 CanariCam wave-plate eﬃciency and Instrumental Correction...... 29 3-1 Total intensity maps of WL 16 at 8.7, 10.3, and 12.5 µm...... 35

3-2 The 8.7- µm linear polarization map of WL 16 superimposed on (total intensity) contours...... 36

3-3 The low-resolution (R≈50) spectrum of the brightest central 1′′.6 (21 pixels) region of WL 16...... 37

3-4 Polarization and emission/absorption decomposition results of WL 16...... 38

3-5 Polarization and emission/absorption decomposition results of Elias 29...... 39

3-6 The JHK color-color diagram...... 41 3-7 Comparison of the polarization proﬁles of WL 16 (black) and Elias 29 (blue). .... 42

3-8 Intensity and charge state of PAHs at two sides of the disk...... 47

4-1 Intensity map (contours) of MWC 1080 system at 11.2 µm...... 61

4-2 Intensity and polarization spectra of NW nebula...... 62 4-3 Signal-to-noise (S/N) ratio of polarized intensity, Stokes u(U/I ), and Stokes q(Q/I ) of the NW nebula...... 63

5-1 Ratio of the absorptive eﬃciency perpendicular and parallel to the shorter axis of the spheroid Qabs,⊥/Qabs,∥ covering wavelengths λ from 1.0 to 1000.0 µm...... 79

5-2 Ratio of the absorptive eﬃciency along two directions Q⊥/Q∥ vs changing grain radius a...... 80

5-3 Emissive polarization profiles vs wavelength...... 81 5-4 The product of the degree of polarization at 90◦ due to single scattering (P) and the dust albedo (ω) for dust size distributions with different values of amax (the value of amin is fixed at 0.01 µm)...... 82

8 5-5 Simulated linear polarization maps in a poloidal B-ﬁeld conﬁguration for a spherical envelope at λ=10.0 µm...... 83

5-6 Simulated linear polarization map in a toroidal B-ﬁeld conﬁguration for a spherical envelop at λ=10.0 µm...... 84

5-7 Dust scattering induced polarization map at λ=10.0 µm...... 84

5-8 Linear polarization map of a poloidal shape B-ﬁeld conﬁguration...... 85

5-9 Linear polarization map of a toroidal shape B-ﬁeld conﬁguration...... 86

5-10 Linear polarization map of an hour-glass shape B-field configuration...... 86 5-11 Linear polarization map of Aitken model IVa B-field configuration...... 87

5-12 Linear polarization map of Aitken model V B-ﬁeld conﬁguration...... 87

5-13 Linear polarization map of Aitken model VI B-ﬁeld conﬁguration...... 88

5-14 Linear polarization map of a dipole shape B-ﬁeld conﬁguration...... 88

5-15 Observation and modeling of AB Aur...... 89 6-1 Composite image of W51 IRS2...... 101

6-2 Polarization maps of W51 IRS2 at 8.7, 10.3, and 12.5 µm ﬁlters from top to the bottom...... 102 6-3 Decomposition results of each source in W51 IRS2 region...... 103

6-4 Maps of magnetic ﬁeld orientations...... 104

6-5 Magnetic ﬁelds overlaid with 14GHz continuum emission from VLA...... 105

A-1 Polarization proﬁles...... 110

9 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulﬁllment of the Requirements for the Degree of Doctor of Philosophy MID-INFRARED POLARIMETRY: INSIGHTS INTO MAGNETIC FIELDS AND DUST GRAIN PROPERTIES IN YOUNG STELLAR OBJECTS AND PROTOPLANETARY DISKS

Han Zhang August 2018

Chair: Charles M. Telesco Major: Astronomy

Polarization observations in star formation regions have been made covering different wavelengths, different scales, and different stellar evolution stages, from embedded cores to disks. One of the important goals of polarimetry observations is to explore the role of magnetic

ﬁelds in star formation regions, which are believed to be important in regulating star formation.

However, recent theoretical work and observations challenge the ability of polarimetry as an important technique to trace the magnetic ﬁeld morphology, as other non-magnetic mechanisms, e.g., dust scattering, can also produce signiﬁcant polarization signals.

This dissertation work focuses on two fundamental questions concerning polarimetry observations in star formation regions, (i) polarization mechanisms at mid-infrared wavelengths, and (ii) interpretation of the inferred magnetic ﬁeld structure. We address these two questions using simulations and observations from the mid-infrared facility camera CanariCam on Gran

Telescopio Canarias (GTC), a 10.4-meter telescope in La Palma, Spain. To explore the origins of the polarization: 1) we study WL16, a Herbig star with an extended disk, and we ﬁnd that the contamination from foreground extinction accounts for our detected polarization; 2) we model dust-scattering-induced polarization in the disk, reproducing the observations of AB Aur, a Herbig Ae star, and thereby constrains the size of dust grains to be micron-sized; 3) we discover ∼2% polarization from interstellar polycyclic aromatic hydrocarbon molecules, in the nebulous structure surrounding MWC 1080.

10 To be able to infer the magnetic field structure in protoplanetary disk from polarimetry observations, we conduct simulations of polarized disks expected for a variety of magnetic field structures, e.g, poloidal or toroidal. In the case of W51 IRS2, a star cluster formation region, by comparing the inferred magnetic fields with the ionized gas flow, we find that the gas flow is likely to be driven by the magnetic fields.

11 CHAPTER 1 INTRODUCTION

With eﬀorts and studies over centuries, we have gradually come to know our place in

the Universe, one with billions upon billions of stars. How was our Sun formed? How did the Earth come to be? Motivated by answering these questions, we look at an abundant sample of

star-planet systems at the early phases of their lifetime in the Universe.

1.1 Magnetic Fields in Star Formation

Star formation is expected to start from the dense regions in giant molecular clouds, by

gravitationally contraction (Shu et al., 1987; McKee & Ostriker, 2007). Most stars are born in groups or clusters, and very few are born alone (Lada & Lada, 2003). When the stable

dense core is suﬃciently disturbed or the mass of the core exceeds the Jeans mass, it tends to

collapse to form a star (Lada, 2005). Magnetic ﬁelds, together with turbulence and gravity, are

key forces in controlling star formation (McKee & Ostriker, 2007).

The ratio of gravitational energy to magnetic energy (the mass-to-ﬂux ratio), M/Mϕ √ (where Mϕ≡ϕ/2π G, ϕ is the magnetic ﬂux), determines whether the cloud is magnetically

supercritical or subcritical. In a magnetically subcritical cloud (M

when the core mass M reaches and exceeds the Mϕ, the core becomes supercritical and the collapse can happen. The ratio M/Mϕ may vary from place to place within the cloud complexes, and ambipolar diﬀusion may convert a subcritical cloud to a supercritical state.

The relative importance of turbulent energy to magnetic energy, which parameterizes whether the gas is sub-Alfvénicor super-Alfvénic.It can be studied by analyzing the linear polarization dispersion in the molecular clouds (detailed discussion of the technique is in Section 1.3). The magnetic fields inferred from the linear polarimetry appear to be fairly uniform and tend to preserve their orientations at different scales (Li et al., 2014b), suggesting that magnetic fields

are relatively stronger than the turbulence, in other words, the turbulence is sub-Alfv´enic.In

12 summary, magnetic ﬁelds are important in the evolution of molecular clouds, and possible observational probes have been discussed in Li et al. (2014b).

In the canonical star formation theory (Shu et al., 1987), the original ordered magnetic

fields lines in the cloud will be pinched to form an hourglass morphology along the major axis of the dense core (Galli & Shu, 1993). The strength of the pinch is expected to be larger in weak magnetic fields than strong magnetic fields (Crutcher, 2012). Girart et al. (2006) report a clear hour-glass shaped B-field morphology in a binary protostellar system NGC 1333

IRAS 4A. The hour-glass morphology is expected particularly for contracting clouds with

ﬂux-frozen magnetic ﬁelds (Galli & Shu, 1993). Simulations suggest that a toroidal magnetic

ﬁeld dominates during the accretion phase after the protostar forms (Safarzadeh et al., 2017; Cho & Lazarian, 2007; Tomisaka, 2011). Determining magnetic ﬁeld morphology is therefore an important observational test of star formation theory (Shu et al., 1987; Crutcher, 2012).

Both analytic arguments and ideal magnetohydrodynamic (MHD) simulations (Machida et al., 2011) imply that, in the gravitationally collapsed cloud, disk formation, once thought to be the natural consequence of the conservation of angular momentum, is suppressed in the presence of magnetic fields, if the magnetic fields are aligned with the infalling envelope’s rotation axis (Li et al., 2014c). Possible solutions include non-ideal MHD effects (ambipolar diffusion, Ohmic dissipation and Hall effect), turbulence, misalignment between the magnetic

ﬁeld and rotation axis in weakly magnetized cores (Li et al., 2013, 2014c). The last mechanism has been investigated observationally by Chapman et al. (2013) on the ∼10,000 AU scale,

Hull et al. (2013) on the ∼1000AU scale and Davidson et al. (2011), but with different conclusions, perhaps because of the different observation scales. The role of magnetic fields in star formation and planetary formation is an on-going topic of study (Crutcher, 2012; Reissl et al., 2016a). 1.2 Protoplaneatry Disks

Star formation starts with the collapse of dense regions in molecular clouds. An accretion disk is developed during the collapse phase, as a consequence of removal of high angular

13 momentum material. The existence of circumstellar disks has been confirmed by, for example, Hubble Space Telescope observations, where the disks are seen as shadows against the bright nebular background. Conventionally, Young Stellar Objects (YSOs) have been classified into four different stages, Class 0, Class I, Class II, and Class III, depending on the appearance of their spectral energy distribution (SED) (Fig.1-1)(Lada & Wilking, 1984; Andre et al., 1993). This classification scheme is an empirical classification based on the spectral index in the near-infrared (NIR) and mid-infrared (mid-IR). It has been found to quantitatively fit into the theoretical scenario of star formation (Adams et al., 1987) consisted with four evolutionary stages that young stars go through.

During the first stage of star formation, the Class 0 YSOs are deeply embedded within the optically thick gas and dust, and Class 0 sources are almost invisible in the optical and NIR wavelengths but have significant sub-millimeter emissions (Andre et al., 1993). At this stage, a rotationally supported disk may not be formed, and the fattened inner envelope is called a pesudodisk, extending to a few thousand AU (Chapman et al., 2013). A rotational signature of a disk is clearly detected in the Class I YSO, and it is still embedded in an envelope of infalling material, which is usually associated with strong outflows or jets. The SED of a Class I YSO shows rising infrared continuum that peaks at mid-to-far infrared wavelengths (Lada, 1987). In the third stage (Class II; (Williams & Cieza, 2011)), as the accretion proceeds, the envelope is eventually lost and the disk and central star become optically visible. The individual star and disk systems evolve differently depending on the mass of the stars and environment. The disk mass now is only a few percent of the central stellar mass and can be called a protoplanetary disk. The life time of the disk is of order several million years (Ribas et al., 2015). Once the gas disk has dissipated, and the central star reaches the main-sequence, it is the Class III phase, in which the disk evolves to a debris disk that is optically thin and gas poor, with larger dust grains, planetesimals and/or planets.

Protoplanetary disks undergo a variety of processes, including dust aggregation, dust settling, dynamical interaction with (sub)stellar companion and photo-evaporation (Williams &

14 Cieza, 2011). Thanks to the multi-wavelength high-resolution and high-sensitivity observations of circumstellar disks, we are able to see the subtle features in these disks, especially through the polarimetric imaging in NIR and (sub-)millimeter continuum and gas observations.

Multi-wavelength observations of protoplanetray disks reveal emission from diﬀerent regions of the disk, illustrated in Fig.1-2. Disks are usually optically thick in the NIR and mid-IR, and the emission is mainly from dust grains at the surface layer and near the surface layer, respectively

(Mari˜naset al., 2006), while the (sub-)millimeter observations trace larger and cooler dust grains at the disk mid-plane.

Intriguing asymmetric features in protoplanetary disks, such as spiral arms, gaps and warps, have been modeled as a result from the perturbation of the embedded planet(s) (Zhu, 2015; Dong et al., 2015a), e.g., MWC 758 (Benisty et al., 2015) and HD 142527 (Fukagawa et al., 2006). Observations by Atacama Large Millimeter/submillimeter Array (ALMA) are beginning to reveal the structure of protoplanetary disks at their midplanes. With the revolution starting with the fabulous ring structures seen in HL Tau (ALMA Partnership et al., 2015), a structure that can be reproduced by the simulation including perturbation by multiple planets in the disk. Observations of, e.g., TW Hydrae (Andrews et al., 2016) also show ring structures, and in Elias 2-27, spiral arms are detected (P´erezet al., 2016; Meru et al., 2017).

Magnetic fields must play a crucial role in the evolution of protoplanetary disks and the formation of planets. Magnetic fields influence the transport of dust and gas and even the migration of planetesimals and planets (Bertrang et al., 2017). In magnetized protoplanetary disks, MHD turbulence driven by the magnetorotational instabiliy (MRI) provides the source of viscosity, determining accretion rates and lifetime of the disks (Wardle, 2007). However, the observational constraints on magnetic fields remain a difficult task, as we discussed in the following. 1.3 Polarimetry: An Important Technique to Study Magnetic Fields

Even though magnetic ﬁelds are important, it is very diﬃcult to directly quantify magnetic

ﬁelds observationally (Robishaw, 2008). There are several observational techniques that are

15 available for observing magnetic ﬁelds. Zeeman splitting of spectral lines is used to measure the strengths and directions of magnetic ﬁelds along our line of sight. Spectral lines will be

split in a region that is embedded in magnetic ﬁelds and the splitting is proportional to the

strength of magnetic ﬁelds along the line of sight. However, the interstellar magnetic ﬁelds are

usually very weak, which cannot produce strong enough magnetic momentum for the detection of line splitting. Faraday rotation (Akahori & Ryu, 2010), eﬀects the light as it propagates

through the interstellar medium, with the plane of linear polarized background radiation

being rotated in the magnetic ﬁelds by an angle β, which is proportional to the strengths of magnetic ﬁelds along our line of sight, the electron density, and the wavelength of the radiation

(Crutcher, 2012). The ﬁngerprint of magnetic ﬁelds is also embedded in the polarization of the received

interstellar radiation. Dust-induced polarization is widely used as a tracer of magnetic ﬁelds

in star formation regions and is linked to the strengths and orientations of magnetic ﬁelds

(Matthews et al., 2009). Optical interstellar polarization was ﬁrst reported independently by Hall (1949) and Hiltner (1949), and recognized as due to the preferential dichroic extinction

of the background starlight. The reason why interstellar dust grains can produce polarized

light is because of their alignment. The details of the alignment mechanism for dust grains are

still unclear. The classical dust alignment theory suggests that non-spherical dust grains tend

to spin, perhaps as a result of radiative alignment torques from an anisotropic radiation ﬁeld (Lazarian, 2007; Cho & Lazarian, 2007). In the radiative alignment theory, when light shines

on a irregular dust grain it starts to rotate. The grains will precess around the local magnetic

ﬁeld. The process has been explained in a series of papers, e.g., Hoang & Lazarian (2014) and

Cho & Lazarian (2007), is the most favored and widely accepted mechanism.

Consequently, as shown in Fig. 1-3, in the presence of an external magnetic ﬁeld, these spinning non-spherical grains tend to align with their longer axis perpendicular to the magnetic ﬁeld lines. In this way, at optical and NIR, aligned elongated dust grains polarize the background starlight and the resultant polarization is along the direction of interstellar

16 magnetic fields (Left panel in Fig. 1-3), e.g., Goodman et al. (1990) and Cashman & Clemens (2014). At far-infrared and (sub)-millimeter, aligned dust grains emit polarized emission with the direction perpendicular to the magnetic fields (Right panel in Fig. 1-3). In the latter case, to infer the magnetic field directions, we need to rotated the detected polarization vectors by

90◦, e.g., Stephens et al. (2014). Mid-IR polarimetry is an incisive probe of B-field morphologies. At mid-IR wavelengths, the situation becomes more complicated, since the observed polarization can be a combination of dichroic absorption, emission, and/or scattering (Aitken et al., 2004). Scattering polarization is discussed in Section 1.4. Using template absorption and derived emission polarization profiles, Aitken et al. (2004) proposes a method to separate the relative contributions from dichroic absorption and emission (Appendix A). Separating these two components offers an opportunity to probe directly the line-of-sight magnetic fields structure, unique to mid-IR, and we call it ‘polarimetric tomograpy’. Barnes et al. (2015) has demonstrated the potential of this method by probing the line-of-sight magnetic fields structure of the massive star formation region K3-50.

We also emphasize that beside being a tracer of magnetic ﬁeld, the degree of polarization depends on the geometry and composition of dust grains, and can therefore provide information about dust properties (Cho & Lazarian, 2007) (see Chapter 5).

1.4 Challenges: Scattering, Radiative Grain Alignment

The origin of the polarization signal is still not fully understood. Besides the classical dust grain alignment in magnetic ﬁelds, there have been two other mechanisms proposed that can produce polarized emission, but are irrelevant to the study of magnetic ﬁelds. These are dust scattering (Kataoka et al., 2015), and radiative grain alignment (Tazaki et al., 2017).

Even though scattering was regarded as negligible at wavelengths longer than NIR, both observations and theoretical studies indicate that scattering can not be ignored if there are dust grains with sizes comparable with observation wavelengths. Polarization observations towards the circumstellar disks around HD 142527 (Kataoka et al., 2016b), HL Tau (Stephens

17 et al., 2017; Kataoka et al., 2017, 2016a) and IM Lup (Hull et al., 2018) by ALMA show evidence of polarization due to scattering instead of magnetical dust alignment. Kataoka et al.

(2016b) ﬁnds a sharp change in the directions of polarization vectors from the inner disk to outer disk in HD 142527, which is hard to explain in the context of magnetically aligned dust, but is consistent with the dust scattering. Stephens et al. (2017) shows that the polarization morphologies of HL Tau at three ALMA bands (band 3, band 6 and band 7) are diﬀerent, which indicates a change in the dominated polarization mechanism(s) with wavelengths.

And note that scattering polarization is very dependent on the wavelengths. Dust scattering produces polarization vectors along the azimuthal direction of the disk for a face-on disk (Yang et al., 2016). However, scattering depends on the dust properties, the geometry of the disks, inclinations, and anisotropy of the radiation, the scattering morphology can be complex. In the case of IM Lup, polarization vectors are roughly along the minor axis, which is indicative of polarization produced by dust scattering (Hull et al., 2018). If the observed polarization patterns are indeed from scattering-induced polarization, instead of providing information about the orientations of magnetic ﬁelds, it provides diagnostic constraints on the size of dust grains in protoplanetary disk, and evidence for dust growth (Kataoka et al., 2016a).

Tazaki et al. (2017) revisits the radiative torque alignment theory in protoplanetary disks and finds that larger dust grains are expected to be aligned by the radiation flux at mid-plane, which would correspond to the polarization vectors tracing the direction of radiation fields instead of the magnetic fields. For a face-on disk, the polarization pattern can be in the azimuthal direction if the dust is aligned by the radiation fields, even in the presence of magnetic fields. Kataoka et al. (2017) finds that polarization vectors of HL Tau are along azimuthal direction at ALMA band 3, which supports the radiative torque alignment.

Of course, the discussion of the dust alignment is not limited to these two. For instance, if grains are mechanically aligned by outﬂows (Lazarian & Hoang, 2007), then the polarization is expected to be parallel to the B-ﬁeld (Hull et al., 2013).

18 There are various physical eﬀects that can produce polarized radiation at infrared and millimeter wavelengths, and interpreting the polarization data is complicated. Multi-wavelength

polarimetric observations are essential and signiﬁcant to improve our understanding of the

polarization signal, such as the multi-band polarimetry observations of HL Tau by ALMA

(Stephens et al., 2017). We expect future polarimetry observations to solve the problem with observations of more protoplanetary disks systems.

1.5 Thesis Outline

My dissertation is organized as follows. In Chapter 2, we give a brief introduction to

the mid-IR facility Canaricam on GTC, and then describe the data reduction. In Chapter 3, we show the polarimetric imaging and spectra of a well-resolved protoplanetary disk, WL 16. In Chapter 4, we report the detection of the PAH polarization in the nebula around the stellar cluster MWC 1080. Chapter 5 displays a library of maps of linear polarization of a

protoplanetary disk at 10 µm. In Chapter 6, we show the polarimetry imaging of a protocluster

W51 IRS2 and introduce the method of “polarimetric tomography” to infer the magnetic ﬁeld structures in the region. We summarize this thesis work in Chaper 7.

19 Figure 1-1. The formation of a low mass star. The plot is adapted from Dauphas & Chaussidon (2011). Left: SED signatures of five different phases, from prestellar core to Class 0-III YSOs. Right: Illustration of different stages. From top to bottom: star formation starts from the collapse of a dense molecular core. A protostar is formed (Class 0 YSO). Rotation disk and the star is embedded in an envelope (Class I YSO). The envelope dissipates and the disk is visible (Class II YSO). The disk continues to evolve and becomes a debris disk (Class III YSO).

20 MIR

Scattered Light

(sub-)mm

1 2 3

4 a b

d c

Distance in AU

1 10 100 1 Turbulent Mixing (radial or vertical) 2 Vertical Settling 0.35 mm 3.0 mm ALMA

3 Radial Drift 10 µm VLTI/MATISSE 4 a) Sticking b) Bouncing 2 µm 10 µm EELT c) Fragmentation with mass transfer d) Fragmentation JWST/MIRI

Figure 1-2. Illustration of the structures and physical processes in a protoplanetary disk from Testi et al. (2014). The right side shows the regions of the disk that can be probed at various wavelengths. Near-infrared, mid-IR and sub-mm emission are from dust grains at the very surface layer, below surface-layer, and mid-plane of the disk, respectively. The left side shows the dust transportation and collision mechanisms.

21 Figure 1-3. Illustration of absorptive and emissive polarization in magnetically dust alignment theory, adapted from Lazarian (2007). (a)Left panel – Polarization of starlight passing through a cloud of aligned dust grains. The direction of polarization is parallel to the plane of the sky direction of magnetic ﬁeld. (b)Right panel– Polarization of radiation from a optically thin cloud of aligned dust grains. The direction of polarization is perpendicular to the plane of the sky direction of magnetic ﬁeld.

22 CHAPTER 2 OBSERVATIONS AND DATA REDUCTION

2.1 CanariCam

CanariCam is a multi-mode mid-IR (8-25 µm) facility camera developed at UF (Telesco

et al., 2003), which started science operation in 2012 at the 10.4-meter Gran Telescopio Canarias (GTC), on La Palma, Spain. GTC is a partnership of Spain, Mexico, and the

University of Florida, and located at the Spanish Observatorio del Roque de los Muchachos of

the Instituto de Astrofs´ıcade Canarias, on the island of La Palma. CanariCam was mounted at

the GTC Nasmyth-A platform. It has a 320×240 Raytheon array, corresponding to a pixel scale of 0′′.08 and a ﬁeld of view of 25′′.6×19′′.2. It allows Nyquist sampling at 8 µm. The theoretical

angular resolution of the camera at 10 µm is 0′′.25 (1.22λ/D), but the seeing at the GTC degrades this somewhat, often being 0′′.3–0′′.4, depending on observing conditions. CanariCam is equipped with a suite of narrow-band and broad-band 10 and 20 µm filters and provides the low and moderate-resolution (R=100 –1300) slit spectroscopy in the 10 and 20 µm regions. It permits a convenient switch between different modes, imaging, spectrospopy, polarimetry and coronagraphy. It uses the standard chop-nod techniques to account for the thermal background radiation and the offset in the thermal background by the telescope.

In this thesis work, observations are mainly conducted using the polarimetry mode provided by CanariCam (both imaging and spectropolarimetry). We will discuss in detail the polarimetric observations and polarimetric data reduction with CanariCam in Section 2.3.

2.2 Stokes Parameters

The stokes parameters quantify the polarization properties of the radiation ﬁeld and can

fully describe the characteristics of a partially polarized light. Single electromagnetic waves

traveling in the z direction can be describe by

i(kz−ωt+ϕx ) Ex (z, t) = E0x e (2–1)

i(kz−ωt+ϕy ) Ey (z, t) = E0y e (2–2)

23 Stokes parameters are deﬁned as: ⟨ ⟩ ⟨ ⟩ ∗ ∗ I = Ex Ex + Ey Ey (2–3) ⟨ ⟩ ⟨ ⟩ ∗ − ∗ Q = Ex Ex Ey Ey (2–4) ⟨ ⟩ ⟨ ⟩ ∗ ∗ U = Ex Ey + Ey Ex (2–5) ⟨ ⟩ ⟨ ⟩ ∗ − ∗ V = i( Ex Ey Ey Ex ) (2–6)

Or can be written as

◦ ◦ ◦ ◦ I = I0 + I90 = I45 + I135 = IRHC + ILHC (2–7)

◦ − ◦ Q = I0 I90 (2–8)

◦ − ◦ U = I45 I135 (2–9)

V = IRHC − ILHC (2–10)

where I denotes the total intensity, Q and U describe the two-dimensional state of linear polarization, V describes circular polarization, RHC is right-hand circular light, and LHC is √ left-hand circular light. The degree of polarization is then: p = Q2 + U2 + V 2/I .

When a unpolarized light is incident on a briefringent material, it will split into two polarized components, one with its vibration direction along the fast axis, called the ordinary ray, and the other in the direction of the slow axis, and called the extraordinary ray. The directions of the oscillations of o ray and e ray are orthogonal to each other, their intensities are often written as Iα and Iα+90. The sum of the o and e ray intensities equals to the total intensity, i.e., the Stokes parameter I.

2.3 Data Reduction

For polarimetric observations, the incident beam propagates within CanariCam as follows (see CanariCam user manual). First the light passes through the focal plane mask. The focal

plane mask is used to eliminate overlapping of the orthogonally polarized beams on the array.

It blocks 50% of the ﬁeld of view, and the ﬁeld of view in the polarimetry mode is therefore

24 reduced to 26′′× 9′′.6 made up of several smaller pieces, each of which is 26′′× 3′′.2. Then the light passes through the half-wave-plate. The half-wave-plate is used to modulate the position

angle of polarization by the Wollaston prism rather than rotating the instrument. A mechanical

rotation of θ results in an optical rotation of 2θ, i.e., rotating the half-wave plate by 22.5◦ is equivalent to rotating the analyzer by 45◦. With the half wave plate at 0◦ and 22.5◦, both Stokes Q and U can be derived based on Eqs.7-10, but two independent confirmation at angles of 45◦ and 67.5◦ are recommended to correct for the sensitivity difference in the two channels of the polarimeter. The light beam finally passes through the Wollaston prism, which is made of the birefringent crystal calcite, where the light is split into the two orthogonally polarized beams, o and e rays. These two rays are displayed on the detector plane simultaneously, as shown in Fig.2-1. In the field of view, two perpendicular polarized images are present and the

mask is used to prevent the overlapping of the images.

I adapt the data reduction procedures presented in Li (2014) and Berry et al. (2005), and

describe how we reduce the imaging and spectropolarimetry data in detail below. The data reduction package can be found at github.

2.3.1 Polarimetric Imaging Data Reduction

1. Read in the FITS file image A FITS file generated by CanariCam has multiple extensions. The first extension (i.e., Ext. 0) only contains a ASCII header, which stores the complete information, such as the object coordinates, observation time, filters, and the history of data. For the other extensions (Ext. 1, 2, 3 etc), each contains a 3-dimensional array of 320×240×2, where 320×240 is the size of the field of view in pixels and 2 corresponds to a nod pair, one is with source and the other is off-source. To get the emission from the target, we need to subtract the off-source frame from the frame with source. In the polarimetry mode, half-wave-plate is rotated to four orientations 0, 22.5, 45, and 67.5 degrees and that is stored in the parameter nsave. After reading in the FITS file, we obtain four images, corresponding to four wave plate orientations, and each image contains a 320×240 array.

2. Extraction of the o and e ray images The entire ﬁeld of view of a polarimetry image is divided into six slots (i.e., three o and e ray pairs) by the polo-mask, shown in Fig. 2-1 (we use the data of W51 IRS2 as an illustration). The next step is to separate and extract o and e ray images. o ray and e ray images need to be identical and save into two separate arrays for further processing. The o and e ray images have a 35 pixels (2′′.8) separation because of the position of the

25 mask. We divide the image into two sub images, so o and e ray images are separated. Then we use the centroid function to ﬁnd the center of o and e ray images and crop the image into sizes that we want. The cropped o and e ray images are displayed in the right panel in Fig. 2-1.

3. Image alignment Now we have eight images, corresponding to o and e ray images at four different wave-plate angles. The precise alignment between these different image is important to derive the accurate polarization measurements. To register the images, we used the cross-correlation algorithm, which outputs the offsets between images depending on the location of the peak in the cross-correlation matrix. We select a frame as the reference, by default the o ray image at wave-plate angle 0◦. A pair of o and e ray images before and after registration is plotted in the right panel in Fig. 2-1.

4. Stokes parameters The Stokes parameters I, Q, and U provide a full description of the linear polarization. The mathematical connection between the Stokes parameters and the intensities are described in the following equation.

I0 − I90 = Ipcos(2θ) = Q, I0 + I90 = I (2–11)

I45 − I135 = Ipsin(2θ) = U, I45 + I135 = I (2–12)

Where Iα represents the intensity of the o ray image, and Iα+90 is the intensity of the e ray image. Normalized Stokes parameters q and u are deﬁned as q=Q/I and u=U/I . By subtraction and addition between o and e ray images at diﬀerent wave-plate angles, we are able to derive the normalized stokes parameter, q and u.

5. Correction for instrumental effects The tertiary mirror of the telescope introduces significant instrumental polarization (IP). To characterize the degree of instrumental polarization, we select a sample of intrinsically unpolarized stars from Cohen standard (Cohen et al. 1999)and measure their polarization, which should come totally from the instrument. We find that the amplitude of the instrumental polarization is between 0.6% and 0.7%. The position angle of the instrumental polarization is given by the empirical equation θIP =ZD-RMA-31.9, where ZD (zenith distance) and RMA (rotator mechanical angle) are recorded in the FITS header.

u = uobs − pIP cos(2θIP ) (2–13)

q = qobs − pIP sin(2θIP ) (2–14)

We subtract the instrumental effects from the observed Stokes uobs and qobs . Wave-plate efficiency also needs to be corrected to account for the loss in transmission, and the polarimetric efficiency profile is plotted in the right panel in Fig.2-2.

6. Calculation of the polarization percentage and polarization angle

26 With instrumental eﬀect corrected Stokes parameter u and q, the polarization degree and orientation with corresponding uncertainties are given √ √ 2 2 − 2 2 2 p = q + u σp, σp = (udu) + (qdq) /p

θ = 0.5atan(u, q), σθ = σp/2p

The uncertainties σq and σu associated with the normalized Stokes parameters are derived using a 3-sigma clipping algorithm (Robinson, 1987), and they are then propagated through the analysis to obtain the polarization uncertainty σp and polarization PA uncertainty σθ = σp/2. The obtained polarization position angle needs to be calibrated to the North. There are two approaches, one is to use the polarization calibration star, with known polarization position angles, given in Smith et al. (2000). The other way to use the empirical relationship displayed in the left panel in Fig. 2-2. We examine a large sample of calibrations stars and find a constant offset value between the observed polarization position angles and the true position angle, relative to the North. For the imaging flux calibration, we use the flux-calibrated standard stars in Cohen et al. (1999). Aperture photometry of the standard star is performed in ADUs and then we compute the ratio between a number of counts (ADUs) per second and the real flux of the star. We apply the ratio to the target images and derive the flux of the science object. The accuracy of photometry is ∼10% using this method. The final polarization parameters are usually presented graphically in the form of a polarization map. Each measurement is represented as a vector, in which the length of the vector is proportional to the degree of polarization, and the orientation of the vector is the polarization position angles. The vectors are usually binned to reduce the number of vectors and better show the results.

2.3.2 Spectropolarimetry Data Reduction

The first steps of spectropolarimetry data reduction are similar to the polarimetric imaging reduction. After correctly stacking the o and e ray 2 dimensional spectra, which are rectangular regions containing all source flux, we only need to do extraction and calibration, following the procedures in González-Mart´ınet al. (2013).

1. Extract the one-dimensional spectra from the two-dimensional spectra We extracted one-dimensional spectra by integrating the central region that we are interested along the slit direction. The width of the extraction region depends on whether it is a point-like or extended sources. Usually we integrate across the whole region to get the maximum signal.

2. Wavelengths and ﬂux calibration We use sky emission features in the reference stacked raw spectra to do the wavelength calibration. There are about 8 sky lines (refer to GTC/CanariCam website) with known

27 200

150

Pixels 100

0 0 50 100 150 200 250 300 Pixels

Figure 2-1. Left: The field of view of CanariCam in the case of W51 IRS2 in polarimetry mode. It has 320×240 pixels. The o and e ray images have a 35 pixel separation with a mask. Right: Comparison of reference image and off-set images before and after the alignment. Each panel contains the reference image, offset image, and the cross-correlation.

peak wavelengths in N bands. After identifying at least three lines, we fit a second-order (or higher) polynomial function for the wavelength calibration. For the flux calibration, we use the ratio between the observed associated standard and its corresponding flux calibrated template given by Cohen et al. (1999). The final flux-calibrated spectrum is obtained by dividing the spectrum (in counts; ADUs) by this ratio.

28 1.00

Error-weighted mean = 120.3 +/- 0.8 0.95 150

0.90

100 0.85 Efficency 0.80 50

0.75 Calibration offset (degree)

0.70 0 7 8 9 10 11 12 13 Wavelength (μm) 0 5 10 15 20 25 30 File #

Figure 2-2. CanariCam wave-plate efficiency and instrumental correction. Left panel: The wave-plate efficiency shows the trend through the N-band as window. Polarization measurements should be corrected for that. For imaging polarization at Si2 (8.7 µm), Si4 (10.3 µm), and Si6 (12.5 µm), we use 0.9, 0.99, and 0.88 to calibrate the efficiency. Right panel: The constant polarization position angle calibration value in the sample.

29 CHAPTER 3 THE MID-INFRARED POLARIZATION OF THE HERBIG AE STAR WL 16: AN INTERSTELLAR ORIGIN? 3.1 Introduction

Magnetic ﬁelds (B-ﬁelds) play an important role in almost all stages of star formation as

discussed in the comprehensive star formation review by McKee & Ostriker (2007). However,

there are still many uncertainties about how B-ﬁelds regulate the protoplanetary disk formation

and evolution. For example, magnetically driven core-collapse models (Shu et al., 1987; Galli &

Shu, 1993) predict an hourglass-shaped B-ﬁeld geometry at early stages in the disk evolution, a scenario challenged by recent observations (e.g. Chapman et al., 2013; Davidson et al.,

2011; Hull et al., 2013). The only way to address these issues is with high angular resolution

observations of the B-ﬁeld morphologies in a variety of young disks and their environments.

Polarimetry is a potentially incisive observational probe of B-ﬁeld morphology (Barnes et al., 2015; Crutcher, 2012; Matthews et al., 2009; Hull et al., 2014). Dust grains can

polarize light by scattering, dichroic absorption, or dichroic emission, the latter two processes

attributed to non-spherical dust grains with their long axes aligned perpendicular to the B-ﬁeld

lines, perhaps as a result of radiative torque (Lazarian, 2007; Hoang & Lazarian, 2014).

Dichroic absorption by aligned non-spherical dust grains can partially polarize background starlight with the transmitted E-ﬁeld direction parallel to the aligning B-ﬁeld lines (Cashman

& Clemens, 2014). Light scattering by spherical and non-spherical dust grains can produce high fractional polarization prominently in the optical and near-IR. At far-IR and sub-mm wavelengths, aligned non-spherical dust grains emit polarized light with the emitted E-ﬁeld direction being perpendicular to the B-ﬁeld lines. In the mid-infrared (mid-IR, 8–30 µm), the

situation becomes more complicated, since the observed polarization can be a combination

of dichroic absorption, emission, and/or scattering (Aitken, 2005). Nevertheless, mid-IR

polarimetry has some distinct advantages compared to other wavelength regions: the predicted

emissive polarization is much larger than that at longer wavelengths (Cho & Lazarian, 2007), and we can potentially disentangle both the absorptive and emissive polarization components

30 simultaneously along the line of sight and thereby infer the three-dimensional structure of the B-ﬁelds (Barnes et al., 2015; Smith et al., 2000).

Herbig Ae/Be stars (1.5

(Herbig, 1960; Hillenbrand et al., 1992). WL 16 was discovered by Wilking & Lada (1983) and identiﬁed as a late-stage Herbig Ae star embedded in the ρ Ophiuchus molecular cloud L1688

(Ressler & Barsony (2003), herafter RB03). Key physical properties of WL 16 are given in

Table 3-1. No outﬂow and only weak 1.3 mm emission are observed for this object (RB03).

Because of its high extinction (AV ≈ 25–30 mag), WL 16 is undetectable in the optical but displays extended, resolved emission in the mid-IR. The most plausible interpretation of the extended emission is that it is a disk with a diameter of nearly 900 AU. Kinematic modeling of near-IR CO vibrational overtone emission arising from the innermost region suggests that there is indeed a ﬂat Keplerian gas disk (Carr et al., 1993; Najita et al., 1996).

Nevertheless, whether the entire structure is an unusually large protoplanetary disk or a smaller disk associated with a remnant of the collapsing envelope is still unclear. The very extended emission is generally ascribed to a population of very small grains (VSGs) and polycyclic aromatic hydrocarbons (PAHs). The latter population is indicated by the IR spectra of WL 16 rich in PAH emission features (DeVito & Hayward, 1998; Geers et al., 2007). Because of their

small size (several dozens to hundreds of carbon atoms), PAHs are dynamically well coupled to the gas and less aﬀected by dust settling. The PAHs observable in the mid-IR likely reside in

the disk surface layers. PAHs can also be easily ionized by stellar UV radiation due to their low

ionization potentials, and ionized PAHs can be the tracer of low density optically thin regions

(Maaskant et al., 2014).

In this paper, we present high-resolution (∼0′′.4) mid-IR polarimetric imaging and spectropolarimetry of WL 16. In addition, we ﬁnd it illuminating to consider complementary observations of Elias 29 (our calibration star), which is a low-mass luminous Class I protostar

(36 L⊙) and a neighbor of WL 16 in the ρ Ophiuchus molecular cloud (Boogert et al., 2002).

31 Table 3-1. Basic Properties of WL 16 Properties Values References Distance 125 pc RB03 Stellar mass 4 M⊙ RB03 Luminosity 250 L⊙ RB03 Disk inclinationa 62.2◦ 0.4◦ RB03 Disk PAb 60◦ 2◦ RB03 −6.8 −1 Accretion rate 10 M⊙ yr Natta et al. (2006) Disk mass ¡0.001 M⊙ Andrews & Williams (2007) Disk diameter 900 AU RB03 a 0◦for face-on b Position angle of the major axis of the disk

The paper is organized as follows. In Section 3.2 we describe our observations. In Section 3.3,

we discuss the origin of the observed polarization from polarimetric imaging and spectroscopy, with detailed consideration given to the contribution associated with the foreground extinction

and B-ﬁeld. In Section 3.4 we examine the spatial distribution of the ionized and neutral PAHs

along the major axis of the disk and draw attention to morphological features that may provide

clues to WL 16’s dynamical evolution. Finally, in Section 3.5, we summarize this work.

3.2 Observation

CanariCam is the mid-IR (8–25 µm) multi-mode facility camera of the 10.4-meter Gran

Telescopio Canarias (GTC) on La Palma, Spain (Telesco et al., 2003). It has a ﬁeld of view

of 26′′ × 19′′ with a pixel scale of 0′′.079, which provides Nyquist sampling at 8.7 µm. In the

polarimetry mode, the actual ﬁeld of view is reduced to 26′′ × 2.′′6 after a focal mask (to avoid overlapping between o and e beams) is used. We obtained polarimetric images of WL 16 in three ﬁlters near 10 µm on 6 August 2013 and a low-resolution (R≈50) polarimetric spectrum of WL 16 from 7.5 to 13 µm on 4 and 5 July 2015 (Table 3-2), as part of the CanariCam

Science Team guaranteed time program (PI: C. M. Telesco) at the GTC. The imaging and

spectroscopic observations of WL 16 were interlaced with observations of standard star HD 145897 (Cohen et al., 1999) for ﬂux and point-spread-function (PSF) calibration, and the

standard star Elias 29, selected from Smith et al. (2000) to calibrate the polarization position

angle (PA). The achieved angular resolution (full-width at half maximum intensity) for the

32 polarimetric images was 0′′.4–0′′.6 (Table 3-2). CanariCam was rotated so that the polarimetry ﬁeld mask and the detector array’s long axis were along the major axis of the disk at PA=60◦.

The standard chop-nod technique was applied with a 15′′ chop throw in the North-South

direction. For spectropolarimetry, we positioned the 1′′.04×2′′.08 slit with the slit’s longer axis

oriented at 72◦ from the North to cover the brightest part of the disk. The chop throw was set at 8′′ in the North-South direction.

The data were reduced using custom IDL software, as described in Berry & Gledhill

(2014); Li (2014). We computed normalized Stokes parameters q and u, where q=Q/I and √ 2 2 − 2 u=U/I. The degree of polarization p = q + u σp, where the last term (the “debias” term) was introduced to remove the positive oﬀset in the signal ﬂoor resulting from noise.

The polarization PA is computed as θ = 0.5arctan(u/q). The uncertainties σq and σu associated with the normalized Stokes parameters were derived using a 3-sigma clipping algorithm (Robinson, 1987), and they were then propagated through the analysis to obtain the

polarization uncertainty σp and polarization PA uncertainty σθ = σp/2. The total intensity (Stokes I ) images of WL 16 in the three passbands are presented in Fig. 3-1. The polarization

image at 8.7 µm, where the highest signal-to-noise ratio is achieved, is shown in Fig. 3-2.

Polarizations in the Si2 (8.7 µm) and Si4 (10.3 µm) ﬁlters measured with an aperture of 1′′

in radius centered on the star are given in Table 3-3. The Si6 (12.5 µm) data are too noisy to

provide meaningful polarization information. Note that in the polarimetric images, the upper and lower edges of the WL 16 disk are

truncated by the focal mask, and the polarization vectors near the edges are unreliable and

thus not displayed in Fig. 3-2. The data presented in Fig. 3-2 have been smoothed by 5×5

′′ ′′ pixel (0.4 × 0.4) binning. Vectors are only plotted where p/σp ⩾ 2.0 and p ⩽ 6%. For spectropolarimetry, we extracted one-dimensional spectra by integrating the central 21 pixels (1′′.6) along the slit. We ﬁtted a second-order polynomial of identiﬁed skylines to

calibrate the wavelength. We rebinned the raw polarization data (o and e ray spectra) into 0.1

µm wavelength (5 pixels) bins, i.e., downsampling, and then applied an additional 5-pixel (0.1

33 Table 3-2. Observing Log Imaging Filters ∆λ Date Integration Sensitivity FWHM (PSF) (µm) (µm) (UT) Time (s) (mJy/10 σ/1 h) (′′) Si2(8.7) 1.1 2013 Aug 6 946 8.3 0.50 Si4(10.3) 0.9 2013 Aug 6 873 10.8 0.60 Si6(12.5) 0.7 2013 Aug 6 952 20.7 0.40 Spectropolarimetry Source(s) Date Integration (UT) Time (s) WL 16 2015 Jul 4&5 2648 Elias 29 2015 Jul 4&5 530

µm) boxcar-smoothing to the data to further increase the signal-to-noise ratio resulting in the

equivalent spectral resolution R≈25. We masked out the region between 9.4–10.0 µm, which

was dominated by the atmospheric ozone features. For the total intensity spectrum presented in Fig. 3-3 , we smoothed the raw data with a 3-pixel (0.06 µm) boxcar and the resultant

spectral resolution R≈50. Polarimetric spectra of WL 16 and Elias 29 are shown in Figs. 3-4

and 3-5.

3.3 Orign of the Polarization

Our observations (Fig. 3-1) conﬁrm that WL 16 is well-resolved and extended in the mid-IR, which was previously ascribed to the emission from PAHs and VSGs (RB03). Our

spectrum (Stokes I ) of WL 16 indeed shows PAH emission features at 8.6, 11.2, 12.0, and 12.7

µm (Fig. 3-3) that dominate the spectrum. Most pertinent to our primary focus on B-ﬁelds in

disks is our finding that the 8.7 µm polarization vectors in WL 16 are roughly uniform in both magnitude and orientation across most of the field of view. This rough uniformity implies that the observed polarization results from grain alignment in a correspondingly uniform B-field.

3.3.1 Extinction toward WL 16

The interstellar extinction toward WL 16 is relatively high, and our ﬁrst task before

characterizing the B-ﬁeld giving rise to the polarization is to determine the relative roles of

the polarization arising in the immediate disk environment and in the general intervening

interstellar medium. The 2MASS stellar extinction map implies AV = 26.40.6 mag at the location of WL 16 (Lombardi et al., 2008). It is not trivial to deduce the interstellar extinction

34 Figure 3-1. Total intensity maps of WL 16 at 8.7, 10.3, and 12.5 µm from top to bottom. Contours are surface brightness and logarithmically spaced. Parts of the disk structure are truncated by the CanariCam mask. Some peculiar features of the disk, including a spiral-arm-like structure (green dots) and a dark lane in the SW disk, which may indicate a disk warp, are highlighted.

35 Figure 3-2. The 8.7- µm linear polarization map of WL 16 superimposed on (total intensity) contours. The polarization vectors are plotted at the center of each 5 × 5 binned ′′ ′′ pixels, corresponding to 0.4 × 0.4 (50 × 50 AU), and are only plotted where p/σp ⩾ 2.0 and p ⩽ 6%. The lengths of polarization vectors are scaled to the polarization percentage and orientations correspond to the polarization PA. The green vector at the center, which is oriented at 30◦from North, is the polarization PA observed in the optical (Goodman et al., 1990) and near-IR (Sato et al., 1988) bands. for young stars, since they can also exhibit optical and near-IR excess emissions from their accreting disks. To help disentangle the interstellar extinction from the properties intrinsic to

WL 16, we consider the two-color diagram as a tool to estimate the foreground interstellar extinction. Meyer et al. (1997) combined the observed near-IR properties of T Tauri stars and accretion disk models, and found that the dereddened colors of T Tauri stars occupy a narrow band, called the locus of classical T Tauri stars (CTTS locus), in the two-color (JHKL) diagram. While recognizing that the CTTS locus is derived from T Tauri stars, and Herbig stars may have diﬀerent properties, we nevertheless apply this method to WL 16 and Elias 29, taking their near-IR photometry (Table 3-4) from Cutri et al. (2003) and plot them on the

JHK two-color diagram in Fig. 3-6. We decompose the total reddening into a component of interstellar extinction and a component of intrinsic reddening. We use the following relation to derive the corrected J-band interstellar extinction for objects with excess in the near-IR

(Gorlova et al., 2010):

36 Figure 3-3. The low-resolution (R≈50) spectrum of the brightest central 1′′.6 (21 pixels) region of WL 16. The slit (white rectangle) is shown on the inset image of WL 16 at 8.7 µm. The raw data were smoothed with a boxcar of 3 pixels (0.06 µm) in width. PAH emission features are seen at 8.6, 11.2, 12.0, and 12.7 µm. The 8.6 µm feature originates from C-H in-plane bending. The 11.2, 12.0, and 12.7 µm features originate from C-H out-of-plane bending.

A /E(J − H) A = J J,corr k −1 − E(H − K) E(J − H) {CTTS / } (J − H) − (J − H)0 − [(H − K) − (H − K)0] (3–1) kCTTS

where AJ is the total extinction, E(J-H) and E(H-K) are the color excesses, H-K and J-H are the observed colors, (H-K)0 and (J-H)0 are the intrinsic colors depending on the spectral

37 Figure 3-4. Polarization and emission/absorption decomposition results of WL 16. Black dots with 1 σ error bars are measurements from spectropolarimetry. The atmospheric ozone band is masked out. The data are integrated across the central 1′′.6 (21 pixels) region. We downsample the original data over 0.1 µm wavelength (5 pixels) bins and then apply a 5-pixel boxcar smoothing to increase the signal-to-noise ratio. The resultant spectral resolution is about 25. Overlayed red points with 1 σ-error are measurements from polarimetric imaging at 8.7 and 10.3 µm. The dashed and the dotted lines are the best ﬁtting absorptive and emissive components, and the solid lines are the combination. From upper left to the bottom right: a) Normalized Stokes parameter q (Q/I). (b) Stokes u (U/I). (c) Polarization degree p. (d) Position Angle (PA) θ. θ is approximately 33◦ regardless of the wavelength. The decomposition ﬁtting indicates that it is absorptive-polarization dominant.

38 Figure 3-5. Polarization and emission/absorption decomposition results of Elias 29. Black dots with 1 σ error bars are measurements from spectropolarimetry. The atmospheric ozone band is masked out. The data are integrated across the central 1′′.6 (21 pixels) region. We apply a 5-pixel boxcar smoothing to increase the signal-to-noise ratio. The resultant spectral resolution is about 48. Overlayed red points with 1 σ-error are measurements from polarimetric imaging at 8.7,10.3, and 12.5 µm. The dashed and the dotted lines are the best ﬁtting absorptive and emissive components, and the solid lines are the combination. From upper left to the bottom right: a) Normalized Stokes parameter q (Q/I). (b) Stokes u (U/I). (c) Polarization degree p. (d) Position Angle (PA) θ. θ is approximately 20◦ regardless of the wavelength. The decomposition ﬁtting indicates that it is absorptive-polarization dominant.

39 type of stars (Kenyon & Hartmann, 1995), and kCTTS = 0.58 0.11 is the slope of CTTS

locus for JHK. Adopting the near-IR extinction relations AJ /AK =2.840.46, E(J-H)/E(H- K)=1.770.13 (Wang & Jiang, 2014) and the Ophiuchus extinction law (Chapman et al.,

2009) to convert near-IR extinction to visual and mid-IR extinction, we derive a value for the

interstellar extinction (AV =28 mag) toward the central star. Thus, the interstellar material accounts for most of the extinction along our line of sight. We derive the extinction toward

WL 16 at 10.3 µm, A10.3, to be 1.970.30 mag. The interstellar visual extinction of Elias 29 is about 43 mag and A10.3 is 3.00.37 mag using the same approach (Table 3-4). 3.3.2 Decomposition of Absorptive and Emissive Polarization

We have shown that the extinction due to the foreground interstellar medium is signiﬁcant, and therefore it may also account for much of the observed mid-IR polarization.

However, the dust inside the disk can potentially emit polarized thermal emission that

contributes to the net polarization as we see toward WL 16. To evaluation the contribution

from emissive polarization, we adopted the method present in Aitken et al. (2004), which

showed that, in the mid-IR, the emissive and absorptive polarization components can be identiﬁed, and separated from each other, using spectral polarimetry. Aitken’s method is

based on their finding that the emissive and absorptive polarization profiles (pem(λ) and pabs(λ)) across the 10- µm silicate feature correlate with each other through the extinction, i.e., pem(λ) = pabs(λ)/τ(λ), where τ(λ) is the extinction (due to silicate) near 10 µm. In practice, the absorptive profile, pabs(λ), is taken as that of the Becklin-Neugebauer (BN) object, which contains absorptive polarization alone, and the extinction curve, τ(λ), is derived from the observations of the Trapezium region of Orion. Aitken’s method has been successfully used by a number of studies to separate emissive and absorptive polarization components from the observed total polarization when spectral polarimetry, or imaging polarimetry at multiple wavelengths, is available (e.g., Smith et al. 2000; Barnes et al. 2015).

We apply this method to the polarization data of WL 16 and Elias 29, with the results

shown in Figs. 3-4 and 3-5, respectively. Normalized Stokes parameters q and u, polarization

40 Figure 3-6. The JHK color-color diagram. The green dots are the loci of dwarfs (Kenyon & Hartmann, 1995), which represent the intrinsic color of stars of diﬀerent spectral types. The black dashed line is the interstellar reddening vector (Kenyon et al., 1998), with plus symbols indicating AV =10 mag intervals along the vector. The magenta dot-dashed line is the CTTS locus (Meyer et al., 1997). The black dot and blue triangle with 1 σ errorbars are the near-IR photometry measurements of WL 16 and Elias 29 (Cutri et al., 2003). We decompose the total extinction to the sum of an interstellar extinction vector and an intrinsic reddening vector, as shown by the dotted lines.

41 Figure 3-7. Comparison of the polarization proﬁles of WL 16 (black) and Elias 29 (blue). Both stars are located in/behind the same molecular cloud. At 10.3 µm, where the polarization peaks, we ﬁnd their fractional polarizations are proportional to their interstellar extinctions.

fraction p, and polarization position angle for WL 16 and Elias 29 are shown in each plot. The position angles θ for both WL 16 and Elias 29 are almost constant with wavelength from 8.0

to 13.0 µm, indicating that a single mechanism probably produces the polarization (Efstathiou

et al., 1997). Should there be multiple components, we would usually expect θ to change with wavelengths (i.e., unless the absorbing and emitting ﬁelds are at 90◦). In addition, the value of the polarization p peaks around 10.3 µm, which is expected from the absorptive polarization of astronomical-silicate feature in this spectral region. The decomposition

indicates that an absorptive-dominant polarization proﬁle provides an excellent ﬁt for both

42 Table 3-3. Polarization Measurements of WL 16 λ Flux Density p θ ( µm) (Jy) (%) (◦) 8.7 5.32(0.50) 0.91(0.12) 27.09(3.71) 10.3 1.68(0.17) 2.05(0.48) 29.02(6.70) 12.5 3.30(0.30) .. .. Values in parentheses are 1 σ uncertainties of measurements. All position angles are calibrated East from North.

stars, with negligible emissive components (less than 0.25% for both cases). This result strengthens our conclusion that the mid-IR polarization of WL 16 is primarily due to absorption

by interstellar silicate dust. Since absorption by elongated interstellar particles produces

polarization parallel to the projected B-ﬁeld, the direction of projected foreground magnetic

ﬁeld is about 33◦4◦(measured from spectral polarimetry and averaged over the entire 10- µm band).

The observed polarizations at 10.3 µm for both WL 16 and Elias 29 are proportional to their respective values of interstellar extinctions as shown in Fig. 3-7. From this ratio, we derive

a value for the polarization eﬃciency, which is deﬁned as the ratio of polarization percentage

−1 to the extinction (Cashman & Clemens, 2014), (p10.3/A10.3) ≃ 1% mag in Table 3-4. The parameter can be useful for interpreting the polarization properties of other sources and

understanding the dust alignment eﬃciency, B-ﬁeld strength, and alignment mechanisms in

dense molecular clouds. This value is within the 0–3% range derived in Smith et al. (2000).

We note however that the observed polarization corresponds only to the B-ﬁeld component projected on the sky (integrated along the line of sight), whereas the extinction depends on the total dust column density along the line of sight. Since there is no reason to assume that the projected B-ﬁeld is the same everywhere, we recognize that the diagnostic power of this value of the ratio (p10.3/A10.3) beyond the immediate environment of WL 16 may be limited. 3.3.3 Relationship of WL 16 and Regional Magnetic Fields

Goodman et al. (1990) probed the large-scale B-ﬁeld morphology of the Ophiuchus dark cloud complex at optical wavelengths. The distribution of polarization of background starlight

43 Table 3-4. Extinction and Polarization of WL 16 and Elias 29 WL 16 Elias 29 Ja 14.164 (0.029) 16.788 (0.178) Ha 10.478 (0.023) 11.049 (0.044) K a 8.064 (0.016) 7.140 (0.021) A10.3 1.97 (0.30) mag 3.00 (0.37) mag p10.3 2.00 (0.24)% 3.21 (0.07)% −1 −1 p10.3/A10.3 1.02 (0.20) % mag 1.07(0.13) % mag a(Cutri et al., 2003), in units of magnitude Values in parentheses are 1 σ uncertainties of measurements. across this region is fairly smooth, and our polarization measurements agree well with this trend of the large-scale field (Fig. 3-2). In addition, the K-band polarimetry of WL 16 by Sato et al. (1988) and Beckford et al. (2008), indicates a fractional polarization p=4.870.23% with θ=27.01.4◦ and p=5.100.05% with θ=33.900.03◦, respectively. These values of θ are consistent with our measurements across 8–13 µm, thus strengthening our conclusion that our polarization measurements do not constrain the B-field inside the disk, but instead, trace the foreground B-field.

3.3.4 Intrinsic Polarization

While the observed polarization of WL 16 is mainly from the foreground, and the spectropolarimetry decomposition suggests a very low emissive polarization value (less than

0.25%), can we still place a limit on the intrinsic polarization from the disk? The emissive polarization percentage detected in the case of AB Aur, an archetypal Herbig Ae star (Li et al., 2016), is 0.5%. Assuming the foreground polarization is 2% with a ﬁxed position angle, a 0.5% emissive polarization component could result in, at most, 7◦deviation from the assumed foreground polarization orientation. The uncertainties of our measurements (Table

3-3 and Fig. 3-4) prevent us extracting from the total observed polarization any intrinsic emissive polarization component if it is less than 0.5%. Reiterating the limitation that we are only sensitive to the projected B-ﬁeld, we place an upper limit of 0.5% on the intrinsic polarization in WL 16. The intrinsic emissive mid-IR polarization in WL 16 is therefore likely to be much lower than a few percent predicted by Cho & Lazarian (2007). Polarization

44 from protoplanetary disks depends on the dust properties, e.g., dust sizes, oblateness, and composition, and also the entanglement of magnetic ﬁelds with dust grains, e.g., dust

alignment and the strength of magnetic ﬁelds (Hughes et al., 2013). In the case of WL 16, it

may result from a combination of these factors.

3.4 Discussions

3.4.1 PAHs in WL 16

WL 16 is rich in PAH emission features, making it useful for studying PAH properties in

the environments of Herbig stars (Geers et al., 2007; DeVito & Hayward, 1998). ISO/SWS and

Spitzer/IRS spectra of WL 16 show emission features at 6.2, 7.7, 8.6, 11.2, 12.7, 16.4, and

17.0 µm identiﬁed with de-excitation via C–C or C–H vibrational transitions of the UV-excited

PAHs (Leger & Puget, 1984; Draine & Li, 2001). The 3.3 µm PAH feature is not detected (Geers et al., 2007). Because a PAH molecule can be excited by a single UV photon, PAHs can trace the disk emission up to large distances from the star. The intensities of the C–C stretching and C–H in-plane bending modes, which fall in the 6–9 µm range, are generally

stronger for ionized PAHs than PAH neutrals. We use the total intensity spectrum (Stokes

I ) from spectropolarimetry observations to derive the ratio of the 8.6 to 11.2 µm surface

brightness proﬁles, I8.6 and I11.2 (band-width 0.33 µm), in order to trace the charge state of PAHs along the disk major axis (Joblin et al., 1996). The PAH features are often blended with

neighboring PAH features (e.g., the 8.6 µm feature is on the wing of 7.7 µm feature). To

correct the blended PAH emission features and subtract the continuum, we adopt the package PAHFIT by Smith et al. (2007) to derive the power emitted in each PAH features. There is

as much as a 10% brightness diﬀerence in the PAH features and continuum emission between

the integrated NE and SW side disk ﬂux. Figure 3-8a shows the derived spatial distribution of

PAHs at 8.6 and 11.2 µm in the central 2′′.0 region along the major axis of the disk. Although

the spatial behaviors of 8.6 and 11.2 µm are slightly diﬀerent, the SW disk intensity is much

lower than that of the NE disk. Moreover, I8.6/I11.2 reaches the maximum (about 2.0) at the central region and decreases farther from the star (Fig. 3-8b), which means there are more

45 ionized PAHs near the star, with neutral PAHs dominating the external region, as expected (Weingartner & Draine, 2001).

Interestingly, we also notice (Fig. 3-8b) that, while the values of I8.6/I11.2 on the two sides of the disk are roughly comparable within 0′′.3 (38 AU) of the star, they are markedly

′′ diﬀerent between the two sides of the disk beyond about 0.5 (63 AU), with I8.6/I11.2 being higher on the SW side than that of the NE side in these outer regions as shown in Fig. 8c.

If the disk at this large radius is optical thin in the mid-IR, the asymmetry can be explained by the neutralization of PAHs through electron recombination: PAH cations recombine more eﬀectively with electrons in the NE than they do in the SW (Li & Lunine, 2003). However,

WL 16, like most young Herbig-star disks (e.g., AB Aur, Mari˜naset al. (2006)), probably has an optically thick disk, the mid-IR emission that we see most likely arises in a thin layer near

the disk surface (the disk ‘atmosphere’) (Testi et al., 2014). Thus, the interpretation of the

anti-correlation is not obvious. Complicated disk structures, such as an asymmetric puﬀed-up

disk inner rim and disk warps, combined with the inclined viewing angle of disk, may provide explanations. To solve the puzzle, multi-wavelengths observations are necessary.

We do not see any polarization features at PAH emission bands (e.g., 8.6 and 11.2 µm) in the case of WL 16 (Fig. 3-4). Analytical modeling does predict detectable PAH polarization

in astrophysical environments (Sironi & Draine, 2009). Though the astrophysical conditions

they considered may be diﬀerent from the condition in protoplanetary disks, PAH polarization is too small (0.1–0.5%) to be distinguished from the contribution of linear dichroism by aligned

foreground dust.

3.4.2 Disk Morphology

The total intensity maps (Fig. 3-1) of WL 16 reveal intriguing asymmetric features in the disk, including: (1) an S-shaped, spiral-arm-like structure extending to both sides of the disk (green dots in Fig. 3-1); (2) a dark lane immediately outside the spiral-arm-like structure

in the SW disk, at 1′′.3 (163 AU) from the star; (3) twisted surface brightness contours, i.e.,

position angles of the contours’ major axes are changing from 95◦ (at smaller radii) to 50◦

46 3.0 2.0 NE SW 1.8 NE SW

2.5 11.2 /F

1.6 8.6 R=F 2.0 1.4 (b) 1.2 1.5 1.0 0.5 0.0 -0.5 -1.0 offset (arsec) 1.2 Flux density (Jy) 1.0 1.1 NE /R

0.5 SW 8.6 µm 1.0 R (a) 11.2 µm (c) 0.0 0.9 1.0 0.5 0.0 -0.5 -1.0 0.0 0.2 0.4 0.6 0.8 1.0 offset (arsec) offset (arsec) Figure 3-8. (a): The inner 2′′.0 spatial distribution of intensity at 8.6 and 11.2 µm along the major axis of the disk. There is a clear brightness asymmetry of SW (blue) and NE (red) sides of the disk at both wavelengths. (b): R=I8.6/I11.2 along the major axis of the disk as a tracer of the charge state of PAHs. The larger the value, the more ionized are the PAHs. The ratio is decreasing farther from the central star as the decreasing UV radiation. (c): The relative RSW and RNE . There are more ionized PAHs at the SW side of the disk than the NE.

(at larger radii); and (4) an asymmetric brightness distribution, the NE side being signiﬁcantly brighter than the SW side of the disk. Though especially obvious in the PAH bands, some of these features are also seen in the continuum. In general, they appear to be qualitatively consistent with the scenario of an warped inner disk with respect to the outer disk as the result of precession induced by an unseen planet or stellar companions (Dong et al., 2015b). In this scenario, the dark lane in the SW could be a shadow cast by the disk warp. The illumination of a warped inner disk can mimic spiral features (Quillen, 2006). Although the twisted contours could be a result of a stellar companion of WL 16, a search for such a companion turned out

47 to be unsuccessful (Barsony et al., 2003). At 40′′ away, Elias 29 is the nearest (in projection) star of WL 16, but there is no obvious evidence that these two objects are dynamically related.

We expect high-resolution and high-sensitivity radio telescopes, such as ALMA and IRAM, could lead to our new understanding of the dynamic and structure of the object.

3.5 Summary

We present mid-IR polarimetric imaging and spectral observations of WL 16 obtained with GTC/CanariCam. WL 16 has a well resolved, extended disk (diameter ∼ 900 AU) in the mid-IR with ∼ 2% polarization. Our main conclusions are as follows:

1. Spectropolarimetry of WL 16 firmly supports the hypothesis that the observed mid-IR polarization is dominated by absorptive polarization arising from aligned non-spherical dust grains in the foreground. Polarized emission from dust inside the disk is non-measurable with an upper limit 0.5%. Because, in the most widely accepted dust alignment mechanisms, the absorptive polarization is parallel to the direction of B-field, we interpret the observed polarization map as indicating that the B-field in the molecular cloud is fairly uniform with projected orientation of about 33◦ from North. The direction is consistent with the near-IR polarization at WL 16 and the large-scale optical ρ Ophiuchus star formation region polarimetry. Though our original goal was to probe the B-field inside the protoplanetary disk, our study shows the importance of characterizing the foreground polarization as well.

2. The maximum values of the polarization of WL 16 and the nearby-polarized standard Elias 29 are proportional to their interstellar extinction. Using this ratio, we are able to characterize the polarization efficiency of dust grains in the dense molecular cloud, −1 (p10.3/A10.3) ≃1% mag . Keeping in mind that the observed polarization is associated with the projected B-field component, the parameter may be useful for constraining the dust alignment efficiency and properties in this region and for interpreting the observed polarization to other sources.

3. WL 16 is rich in PAH emission features and we have detected the 8.6, 11.2, 12.0, and 12.7 µm features in its disk. We see an asymmetry in the ratio I8.6/I11.2 between the two sides of the disk, with the NE (SW) side being brighter (fainter) at both 8.6 and 11.2 µm but with a lower (higher) value of I8.6/I11.2. This anti-correlation may be explained by complicated disk structures, e.g., warps and asymmetric disk inner rim.

4. The total intensity maps of WL 16 reveal asymmetric features, such as the S-shaped spiral-arm-like structure, twisted contours, asymmetric brightness distributions, and a dark lane on the SW side of the disk. These may indicate a disk warp, with future observations, especially with ALMA and IRAM, likely to fully clarify this picture.

48 This chapter, with minor diﬀerences, was published in its entirety under the same title in Monthly Notices of the Royal Astronomical Society, Volume 465, Issue 3, p.2983-2990

49 CHAPTER 4 DETECTION OF POLARIZED INFRARED EMISSION BY POLYCYCLIC AROMATIC HYDROCARBONS IN THE MWC 1080 NEBULA 4.1 Introduction

A distinctive series of infrared (IR) emission features generally attributed to the stretching

and bending vibrational modes of planar polycyclic aromatic hydrocarbon (PAH) molecules are

observed in most dusty astronomical objects at 3.3, 6.2, 7.7, 8.6, 11.3, and 12.7 µm (Leger

& Puget, 1984; Allamandola et al., 1985). Leger (1988, hereafter L88) ﬁrst noted that these

IR emission features, if due to PAHs, are expected to be polarized as a result of anisotropic illumination by a source of ultraviolet (UV) photons (e.g., stars). UV absorption is favored

when the molecular plane faces the illuminating source. If the spinning of IR-emitting PAHs

do not deviate signiﬁcantly from their initial orientations at UV absorption, the IR emission

will preferentially come from those PAHs that are facing the illuminating source at the time of UV absorption. Therefore, PAHs will emit polarized light, with the polarization direction

of out-of-plane modes (11.3, 12.7 µm) being along the source-molecule direction and that of in-plane modes (3.3, 6.2, 7.7, 8.6 µm) being perpendicular to it. Sironi & Draine (2009,

hereafter SD09) revisited the L88 scheme by considering realistic rotational dynamics of PAHs

as well as an arbitrary degree of internal alignment between the grain symmetry axis and its angular momentum. Using realistic estimates of rotational temperatures for a typical PAH

molecule of 200 carbon atoms, SD09 derived a value for the polarization fraction of 0.53%

for the 11.3 µm feature in the case of the Orion Bar. Sellgren et al. (1988) performed the ﬁrst

systematic search for the polarization of the 3.3 and 11.3 µm PAH features in a number of astronomical sources, obtaining upper limits of 1% and 3% for the 3.3 and 11.3 µm features,

respectively, in the Orion Bar.

To test the PAH identiﬁcation of these IR features and gain insight into the alignment

of PAHs, we searched for linearly polarized PAH emission in the nebula associated with MWC

1080, a stellar cluster located at a distance of 2.2 kpc (Wang et al., 2008). The primary

4 star, MWC 1080A, is classiﬁed as a B0e star and has a luminosity of L/L⊙ ≈ 10 , which,

50 together with its stellar companions, illuminates the surrounding gas and dust in the adjacent molecular cloud. The mid-IR image of MWC 1080 at 11.2 µm resembles a pinwheel, with

opposing arms curving oﬀ to the northwest and southeast (Fig. 4-1). The extended mid-IR

emission resembling spiral arms or wings around MWC 1080 actually traces the internal

surfaces of a biconical cavity created by the outﬂow from MWC 1080A (Li et al., 2014a; Sakon et al., 2007). The brightest part of the nebula (green rectangle in Fig. 4-1) lies 0.03 pc in

projection to the northwest (hereafter NW nebula) of MWC1080A and extends ∼0.1 pc from

the northeast to the southwest. That may well provide an optimal, Orion-Bar-like viewing

geometry, i.e., a long column density along the line of sight through the photodissociation

region and at an angle between the line of sight and illumination direction (α≈90◦) that is almost ideal for observing maximum polarization (SD09).

Anomalous microwave emission (AME) is often ascribed to the rotational emission from

rapidly-rotating nanoparticles (Draine & Lazarian, 1998a,b). PAHs are often considered to be

associated with the AME due to their abundances and small sizes (Kogut et al., 1996; Leitch et al., 1997), although there now appears to be some doubt about the hypothesis (Hensley

et al., 2016). Nitrogen-substituted PAHs (i.e., nitrogen in place of carbon), with greater dipole

moments, may also be important components of the carriers of the AME (Hudgins et al., 2005;

Mattioda et al., 2008). Therefore, our observations have broader implications for determining

the alignment and polarization of rapidly spinning PAHs, which bears on the quest for the cosmic microwave background (CMB) B-mode (Hoang et al., 2013).

4.2 Observation and Data Reduction

CanariCam is the mid-IR (8-25 µm) multi-mode facility spectrometer and camera on

the 10.4 m Gran Telescopio CANARIAS (GTC) in La Palma, Spain (Telesco et al., 2003). It

employs a 320×240-pixel Raytheon detector array with a pixel scale of 0′′.079, which provides a ﬁeld of view of 26′′×19′′with Nyquist sampling (two pixels per λ/D) of the diﬀraction-limited point-spread function at 8 µm. Polarimetry is accomplished through the use of a Wollaston prism and a half-wave plate rotated to angles of 0◦, 22.5◦, 45◦, and 67.5◦. A Wollaston prism

51 in the optical path divides incoming light into two beams (ordinary and extraordinary), which are recorded by the detector simultaneously.

We obtained low-resolution (R≡λ/∆λ≈50) spectropolarimetry observations of the NW

nebula of MWC 1080 on 2015 July 31, August 5, and August 7 spanning the wavelength

range 7.5–13.0 µm. We made four separate measurements, as indicated in the observation log presented in Table 4-1. The spectroscopic observations of the NW nebula were interlaced

with observations of the Cohen standard star HD 21330 (Cohen et al., 1999) for ﬂux and

point-spread-function (PSF) calibration, and the standard star AFGL 2591, selected from

Smith et al. (2000) to calibrate the polarization position angle. The standard mid-IR chop-nod technique was applied with an 11′′ chop throw in the northwest-southeast direction. We positioned the 1′′.04×2′′.08 slit with the slit’s longer axis oriented at 45◦ from the North to intersect the brightest part of the nebula, enclosed by the green rectangle in Fig. 4-1. The

11.2 µm image of MWC 1080 is adopted from Li et al. (2014a), and the data were taken using

Michelle, the facility mid-IR camera at Gemini North. The data were reduced using custom IDL software, as described in Berry & Gledhill

(2014) and Li (2014). We extracted one-dimensional spectra by integrating the central 21

pixels (1′′.6) along the slit direction. Wavelength calibration was done using several sky lines

identiﬁed in the raw images. We computed normalized Stokes parameters q (q=Q/I ) and u

(u=U/I ) using both the diﬀerence and ratio methods, with each providing consistent results (Tinbergen, 2005). The data were calibrated for instrumental eﬃciency and polarization.

The estimated instrumental polarization was 0.6% as measured with HD 21330 and was

subtracted from the observations of the NW nebula in the Q − U plane. The degree of √ polarization p = q2 + u2 − σ2, where the last term (the ‘debias’ term) was introduced to

remove a positive offset in the signal floor resulting from squared background noise. Debiasing may introduce negative values if the noise fluctuations are stronger than the signal. The

polarization position angle was computed as θ = 0.5arctan(u/q). The uncertainties σq and

σu associated with the normalized Stokes parameters were derived using a standard 3-sigma

52 clipping algorithm (Robinson, 1987), and were then propagated through the analysis to

obtain the polarization uncertainty σp and position angle uncertainty σθ = σp/2p (Patat & Romaniello, 2006). All the polarization position angles were calibrated east from north. We

masked out the region between 9.2–10.0 µm, which is dominated by the atmospheric ozone

feature. The three-pixel (0.06 µm) boxcar-smoothed intensity spectrum of the nebula (Stokes I) is presented in Fig. 4-2a.

To further increase the signal-to-noise ratio (S/N) of the polarization measurements,

we rebinned the ordinary and extraordinary ray spectra into 0.12 µm wavelength (6 pixels)

bins (downsampling) and then applied an additional three-pixel (0.36 µm) boxcar-smoothing

to the data. That results in an equivalent spectral resolution of the polarization spectrum of R≈32 (Fig. 4-2b). Stokes u and q are plotted in Figs. 4-3b and c, respectively. To emphasize

the statistical signiﬁcance of the measurements, we plot the S/N of the polarized intensity in

Fig. 4-3a.

4.3 Results

We present in Fig. 4-2 mid-IR intensity and polarization spectra of the NW nebula covering the 8.0–13.0 µm wavelength range. The PAH emission features are clearly seen in

Fig. 4-2a, including the in-plane C–H bending feature at 8.6 µm and the out-of-plane C–H

bending features at 11.3 (solo-CH), 12.0 (duet-CH), and 12.7 µm (trio-CH) (Allamandola

et al., 1989). The relative strengths of the PAH features depend on the size, structure, and

charging of PAHs (Allamandola et al., 1999; Draine & Li, 2007), and the physical conditions of the region where they are found (Bakes & Tielens 1994; Weingartner & Draine 2001). By

ﬁtting the spectrum of MWC 1080 obtained with the Infrared Space Observatory (ISO), which

exhibits a more complete set of PAH emission features but mixed emission from both stars

and the nebula, Seok & Li (2017) determine that the best ﬁt of PAHs in this environment are mostly neutral and large. Exposed to the energetic photons from a B0e star with an eﬀective

temperature of ∼30,000 K (Wang et al., 2008), small PAHs are probably unstable, and the only PAHs that survive are ones that are large and cata-condensed in structure.

53 The polarization spectrum shown together with 1σ error bars of the NW nebula is presented in Fig. 4-2b. Two spectral regions show signiﬁcant polarization. One is in the range

◦ ◦ of 10.9–11.7 µm, with p11.3=1.90.2% and position angle of 77.2 3.2 , the latter indicated by the solid red lines superimposed on the intensity map of MWC 1080 in Fig. 4-1. There

is good consistency among the four separate measurements listed in Table 4-1. The other

signiﬁcant polarization is at 10.0–10.7 µm, peaking around 10.3 µm, and with p10.3=5.41.6% and position angle of 46.7◦8.2◦. While the 10.3 µm polarization feature is seemingly higher

than that at 11.3 µm, the statistical signiﬁcance of the results needs to be considered. We

note here that the detection of polarization near 10.3 µm is only marginally signiﬁcant, being

barely 3σ, whereas the 11.3 µm detection is robust, being around 9σ (Fig. 4-3a). The 3σ upper limits for the polarization at 8.6, 12.0 and 12.7 µm are 1.9%, 2.0%, and 2.8%, respectively

(Fig. 4-2b). While, theoretically, the emission at longer wavelengths is expected to have higher

polarization (SD09), the 8.6, 12.0 and 12.7 µm PAH emission features are much weaker

than the 11.3 µm feature and the lack of detection of the polarization in these regions is not surprising.

Examining Stokes u and q explicitly (Fig. 4-3) demonstrates that the 10.3 µm polarization

is apparent mainly in Stokes u, while the 11.3 µm polarization is mainly in Stokes q. This

diﬀerence implies a diﬀerent origin for the 10.3 µm if real and 11.3 µm features, almost

certainly indicating that they originate in diﬀerent dust populations. 4.4 Discussion

The polarization feature between 10.9 and 11.7 µm is well correlated in wavelength

position with the 11.3 µm PAH emission feature (Fig. 4-3), and we conclude that the polarized

emission is indeed due to PAH molecules. The peak value p11.3 ≃ 2% is consistent with the previous PAH polarization search by Sellgren et al. (1988) who established an upper limit of 3% on its polarization in the Orion Bar. The polarization position angle of the feature has an

oﬀset angle of ∼60◦from the position angle of the projected illumination direction from the

star to the nebula (∼315◦), as shown in Fig.4-1.

54 4.4.1 Numerical Calculations using SD09

We adopt the up-to-date SD09 models to model the degree of polarization in the

environment of a reﬂection nebula. SD09 calculated the polarization for randomly oriented

PAHs. They considered the intramolecular vibrational-rotation energy transfer (IVRET)

process, which allows the eﬃcient energy exchange between rotation and vibration. SD09

model the polarization of PAH emission by introducing two parameters, γ0 = Trot/T0 and

γir = Trot/Tir, where Trot is the rotational temperature determined by gas-grain interactions,

photon absorption and IR emission, T0 is the vibrational grain temperature that determines internal alignment prior to UV absorption, and Tir is the temperature during IR emission. Alignment by an external magnetic ﬁeld is ignored in their model, and the polarization degree

of PAH emission features is essentially determined by two parameters, γir and γ0. Since

the internal alignment temperature Tia ≡ Tir is ﬁxed for the diﬀerent PAHs, and T0 is

determined by the radiation ﬁeld, the polarization degree is determined by Trot. Consequently,

the knowledge of Trot is critical for achieving realistic predictions for the polarization of PAH emission. Collisions with gas neutrals and ions, UV absorption and subsequent IR emission, and

electric dipole emission contribute to the rotation of PAHs (see Draine & Lazarian 1998b;

Hoang et al. 2010). We assume in a reﬂection nebula that the gas temperature Tgas=100

3 −3 3 K, gas density nH = 10 cm , and the radiation ﬁeld parameter U = 10 . We consider the PAH geometry as in Draine & Lazarian (1998b) and a typical grain size of a=7.5 A˚ (200 carbon atoms) in which most of the PAH mass is concentrated as in the ISM (SD09). We

then carry out simulations of PAH dynamics using the Langevin code (Hoang et al., 2010) and

calculate the degree of polarization. However, the values of polarization obtained using the

SD09 model with the consideration of diﬀerent hydrogen ionization fractions xH, i.e., nH+ /nH

(nH+ is the number density of ionized hydrogen), are less than 0.5% (Table 4.2), much smaller than our measured value of ∼2%. It appears that other mechanisms that can enhance the

PAH alignment need to be considered.

55 4.4.2 Alignment with Magnetic Fields

SD09 discussed two possibilities that can signiﬁcantly enhance the polarization of PAH

emission, including suprathermal rotation (i.e., the PAH rotational temperature Trot is much

higher than the gas temperature Tgas) and perfect internal alignment (i.e., the molecule principal axis is aligned with the angular momentum during both UV absorption and IR

emission). The former is unlikely, since there are no obvious physical processes that can spin-up nanoparticles to suprathermal rotation rates (Draine & Lazarian 1998b; Hoang et al.

2010). On the other hand, perfect internal alignment can only be achieved at very low dust

temperatures (T0 of a few K) during the UV photon absorption, which requires very eﬃcient energy exchange among the vibrational-rotational modes. This is also very unlikely due to quantum suppression that may occur in nanoparticles (Draine & Hensley 2016).

Alternatively, we recognize that the enhanced polarization may arise from external alignment, i.e., the partial alignment of the angular momentum with an ambient magnetic

ﬁeld. Therefore, we have repeated the modeling incorporating the mechanism of resonance paramagnetic relaxation to align nanoparticles (Lazarian & Draine, 2000). Subject to an external magnetic ﬁeld, protons in aromatic hydrocarbons in the laboratory are known to

experience stronger shielding (or deshielding) eﬀects than regular hydrocarbons, because the

π-electrons are delocalized and are free to circulate. Astronomical magnetic ﬁelds can induce

diamagnetic ring currents and polarizabilities in the π-electron clouds, resulting in coupling

between the magnetic ﬁelds and two-dimensional PAHs, thereby forcing some alignment. In our models, the magnetic ﬁeld strength is assumed to be B=100 µG(Crutcher, 2012). The

calculation is described here brieﬂy, with more details presented in Hoang (2017).

∥,⊥ We define uˆ-vˆ to be the plane of the sky (see Hoang 2017). We define Fu,v to be the in-plane (∥) and out-of-plane (⊥) emission by a PAH molecule with the electric field E in the

∥,⊥ ∥,⊥ uˆ-vˆ plane. Then Iu,v is the emission intensity from the PAH. The ﬂux Fu,v depends on: 1)

fLTE(θ, J), the probability distribution of the principal axis of the PAH plane being aligned with

the grain angular momentum J (LTE stands for local thermal equilibrium); and 2) fJ (J), the

56 probability distribution of the angular momentum J being aligned with the direction of the magnetic ﬁeld. The grain angular momentum J has spherical angles θ and ϕ. β is the nutation

angle between J and the principal axis of the grain. The emission Iw, with w = (u, v), is obtained by integrating over the distribution functions ∫ ∫ π ∥,⊥ Iw (α) = fJ (J)dJ fLTE,0(θ0, J)dθ0 J∫ 0 π × ∥,⊥ fLTE,ir(θ, J)dθA⋆(β, θ0)Fw (β, ϕ, θ, α), (4–1) 0

where A⋆ is the cross-section of UV absorption as given in SD09. fLTE,0 and fLTE,ir describe the thermal ﬂuctuations of the principal axis of PAHs before UV absorption and during IR emission. fLTE(θ, J) can be described by the Boltzmann distribution (Lazarian & Roberge, ∫ π 1997) with 0 fLTE(θ, J)sinθdθ = 1. To simplify the calculation and derive the maximum value of polarization, we assume that the magnetic ﬁeld is parallel to the stellar incident

radiation direction. We simulate the distribution of angular momentum from the Langevin

equation assuming the ergodic system approximation and compute numerically the intensity of

radiation using Equation (4–1). The resulting degree of polarization with the viewing angle α for in-plane and out-of-plane modes is

∥ ⊥ ∥ ⊥ I , (α) − I , (α) p∥,⊥( ) = u v , α ∥,⊥ ∥,⊥ (4–2) Iu (α) + Iv (α)

We show the modeling results in Table 4.2 for the reﬂection nebula, which includes the ratio of the rotational temperature Trot and the gas temperature Tgas, the degree of alignment of the angular momentum with the magnetic ﬁeld QJ, and the estimated polarization for the

◦ diﬀerent hydrogen ionization fractions xH with a viewing angle α=90 . The polarization varies from 0.14% to 0.34% in model a, increasing to 0.87%–2.1% when the external alignment is taken into account as in model b. In Table 4.2, the degrees of polarization p computed for both models increase with the increasing hydrogen ionization fraction xH. The results suggest that the polarization of PAH emission is dominated by PAHs in regions with a higher fraction of hydrogen in ionic form. In regions with a higher xH (i.e., higher nH+ /nH), there will be more

57 electrons available to neutralize the PAH ions created by photoionization (Tielens, 2005). Indeed, as shown in Seok & Li (2017), the aromatic hydrocarbon emission features observed

in MWC 1080 are best modeled in terms of a mixture of PAHs with ∼ 80% being neutral and

∼ 20% being ionized. As mentioned earlier, the delocalized π-electrons in neutral PAHs may

play a crucial role in coupling neutral PAHs with the magnetic ﬁeld.

Partial alignment of PAHs with the magnetic ﬁeld at a level of QJ ≃ 0.08–0.1 (the averaged degree of alignment of angular momentum J with B) is required to reproduce the observed ∼2% polarization fraction at 11.3 µm. This scenario also accounts for the

observation that the polarization angle is oﬀset from the illumination direction. When PAHs

are aligned with the magnetic ﬁeld, even though only partially, the polarization direction of the out-of-plane mode emission is expected to be along the magnetic ﬁeld (Hoang 2017).

4.4.3 Relationship between Polarization Angles and the Ambient Magnetic Field

Both L88 and SD09 predict that the polarization associated with emission arising from the

out-of-plane vibration mode should be along the illumination direction, which contrasts with

our observed polarization angle having a ∼60◦ offset. We explore one possible explanation, namely, PAH alignment by an external magnetic field (Table 4.2). If magnetic alignment is important, we expect the polarization direction to match that of the ambient magnetic field lines. Indeed, we find that the optical polarimetry observations of background stars within a few degrees on the sky from MWC1080 (serveral hundred parsecs in distance), indicates a fairly uniform optical polarization position angle of ∼80◦, which suggests a smooth interstellar magnetic field threads the whole region (Manset & Bastien 2001; Maheswar et al. 2002; Heiles

2000). The value of the position angle agrees well with our measured polarization position

angle of 77.23.2◦ at 11.3 µm, which supports the hypothesis that PAHs are at least partially

aligned with the ambient interstellar magnetic ﬁeld threading the nebula and its neighborhood. Nevertheless, the emission and alignment of PAHs depend on local astrophysical

conditions and the detailed properties of PAHs, especially their sizes. Nanoparticles with

radii ≲10 A˚ are thought to be negligibly polarized with the greatest quantum suppression

58 of alignment (Draine & Hensley, 2016). Based on our results, it seems that other physical processes such as Faraday rotation braking that facilitate the alignment of nanoparticles need

to be considered (Papoular, 2016), since it is evident that the starlight anisotropy scheme alone

in L88 is not suﬃcient to explain the measured high level of polarization.

It is also worth noting that, given their abundances and small sizes, emission by rapidly spinning PAHs is widely believed to be the origin of AME in the 10–60 GHz frequency range

(Draine & Lazarian, 1998b,a). If true, the considerable alignment of PAHs as suggested by our

detection, naturally produces polarized spinning dust emission for which the polarization level is

proportional to the degree of alignment of the PAH angular momentum with the magnetic ﬁeld

at ∼GHz frequencies (Hoang et al., 2013). It implies that polarized emission from spinning Galactic-foreground PAHs can indeed constitute an obstacle to the detection of the CMB

B-mode signal.

4.4.4 Marginally Detected 10.3 µm Polarization Feature

As shown in Fig. 4-3a, we have a barely signiﬁcant polarization detection at 10.3 µm (3σ).

If real, the different behaviors of the 10.3 and 11.3 µm features in Stokes u and q (Fig. 4-3) suggest that they originate in different dust populations. Therefore, it does not affect our interpretation of the high S/N (9σ) polarization detection at 11.3 µm, our main focus of this

work. We do note, however, that there is no distinct Stokes I spectral ﬁngerprint coinciding

with the 10.3 µm polarization. It is unlikely that the well-known silicate feature or one of its

variants can account for this polarization, since the silicate absorptive polarization proﬁles are broad, spanning the entire 8–13 µm region (e.g., Henning & Stognienko 1993; Smith

et al. 2000; Zhang et al. 2017) rather than relatively narrow and sharp as the feature we see

here. Other possibilities, including nanoparticles with silicate (Tielens, 2013) or metallic Fe

compositions, e.g., hygrogenated iron nanoparticles (Bilalbegovi´cet al., 2017), might be worth investigating (Hoang & Lazarian, 2016) if further observations conﬁrm and gain insight into the feature.

59 Table 4-1. Observing Log a a UT Date Target RA DEC Integration Airmass p11.3 θ11.3 J2000 J2000 seconds % ◦ 2015 Jul 31 NW nebula 23 17 25.18 60 50 44.56 993 1.18–1.23 2.46(0.42) 80.2(4.8) 2015 Aug 5 NW nebula 23 17 25.18 60 50 44.56 993 1.18–1.20 1.48(0.44) 88.7(8.2) 2015 Aug 5 NW nebula 23 17 25.18 60 50 44.56 993 1.21–1.28 1.37(0.38) 72.0(7.7) 2015 Aug 7 NW bebula 23 17 25.18 60 50 44.56 993 1.20-1.27 1.95(0.35) 70.2(5.1)

Table 4-2. Diﬀerent models and polarization at 11.3 µm a b xH Trot/Tgas γir γ0 p(%) QJ p(%) 0.001 0.62 1.54 0.31 0.14 0.058 0.87 0.003 0.707 1.76 0.35 0.19 0.069 1.1 0.005 0.76 1.90 0.38 0.22 0.076 1.6 0.010 0.94 2.35 0.47 0.34 0.088 2.1

4.5 Summary

We report the unambiguous detection of polarized PAH emission at 11.3 µm with a position angle of 77.23.2◦ and polarization degree of 1.90.2%, which confirms the PAH hypothesis that PAH molecules can indeed emit polarized light. The detection of polarization indicates that the alignment of PAHs is considerable. We find that the starlight anisotropy scheme alone is not sufficient to account for this polarization. The PAHs are at least partially aligned by the ambient magnetic field threading this young stellar region and its neighborhood, a conclusion strongly supported by the fact that the measured polarization angle is identical to the large-scale interstellar magnetic field spanning this region. This observation could have important consequences for the accurate estimate of Galactic foreground polarization, a consideration relevant to current goals to detect the CMB B-mode signal. We expect future polarimetry observations, e.g., with SOFIA/HAWC+ and GTC/CanariCam, covering the complete suite of PAH emission features (e.g., the 6.2 µm band dominated by PAH cations and 3.3 µm band by small PAHs) and various astrophysical environments, will deepen our understanding of the properties and alignment of PAHs, e.g., the effects of their sizes and charge states

This chapter, with minor diﬀerences, was published in its entirety under the same title in The Astrophysical Journal, Volume 844, Issue 1, article id. 6, 7 pp. (2017).

60 N E

46'' DEC (J2000) DEC

41''

60 ◦ 50'36'' 27.5s 26.5s 23h 17m 25.5s 24s RA (J2000)

Figure 4-1. Intensity map (contours) of MWC 1080 system at 11.2 µm adopted from Li et al. (2014a). The slit (dashed rectangle) is positioned to enclose the brightest part of the reﬂection nebula in CanariCam/GTC spectropolarimetry observations. We integrate the polarization signal from the region enclosed by the dashed rectangle at 11.3 µm. The thicker segment, together with the two thinner segments, shows the derived polarization position angle with 1σ uncertainties of the 11.3 µm PAH emission feature. The position angle of the projected illumination direction from the star to the nebula is ∼315◦.

61 µ

µ µ 0µ

p 0 0 µ

Figure 4-2. (a): Canaricam/GTC low-resolution (R≈50) spectrum of the brightest central 1′′.6 (21 pixels) region of the NW nebula. The raw data were smoothed with a boxcar of width 3 pixels (0.06 µm). PAH emission features are seen at 8.6, 11.3, 12.0, and 12.7 µm, in which the 8.6 µm feature originates from C-H in-plane bending modes and the 11.3, 12.0, 12.7 µm features originate from C-H out-of-plane bending modes. (b): Polarization percentage p of the NW nebula. The polarization data were downsampled by 6 pixels (0.12 µm) and then smoothed with a boxcar of width 3 pixels (0.36 µm). The ﬁnal spectral resolution R≈32. We masked out the region between 9.2–10.0 µm which is dominated by the atmospheric ozone feature (the dashed box).

62 10 (a) 8

S/N of polarized intensity 0 6 (b) 4

u (%) 0

-2 -4 6 (c) 4

q (%) 0

-2

-4 8 9 10 11 12 13 Wavelength (µm) Figure 4-3. (a) Signal-to-noise (S/N) ratio of polarized intensity of the NW nebula in Fig. 4-2. The 11.3 µm feature has around 9σ detection. (b) Stokes u(U/I ). (c) Stokes q(Q/I ). The thick gray lines in (b) and (c) are the scaled intensity spectrum. The dashed line denotes the position 11.3 µm PAH emission feature. The 10.3 µm detected polarization feature mainly comes from in Stokes u, while the 11.3 µm polarization mainly from Stokes q. The diﬀerence implies that they originate in diﬀerent dust populations.

63 CHAPTER 5 MODELING POLARIZATION OF YOUNG STELLAR OBJECTS AND PROTOPLANETARY DISKS AT MID-IR 5.1 Introduction

There are still many unknowns about the role of magnetic (B) ﬁelds in the formation and evolution of young stars and disks (Shu et al., 1987; McKee & Ostriker, 2007; Crutcher,

2012; Li et al., 2014c), even though B fields have long been considered crucial in regulating star formation. Unfortunately, B fields are not well quantified because they are difficult to detect directly. Polarization is an important observation technique to obtain the morphology of projected B fields on the sky, and recent polarization observations have demonstrated its potential in mapping out the B field structures in star formation regions, e.g., Young Stellar

Objects (YSOs), protoplanetary disks and environments around T Tauri and Herbig Ae/Be stars (Barnes et al., 2015; Stephens et al., 2014; Chapman et al., 2013; Davidson et al., 2011; Hull et al., 2013).

Spinning elongated dust grains are expected to be coupled to the B ﬁelds, aligned with their longer-axes perpendicular to the B ﬁelds lines, producing dichroic absorption and/or emission (Lazarian, 2007). The dust alignment is likely made possible through radiative torques (Hoang & Lazarian, 2014; Andersson et al., 2015). Dichroic absorption by aligned non-spherical dust grains can partially polarize background starlight with the transmitted

E-field direction parallel to the aligning B-field lines (Goodman et al., 1990). At far-IR and sub-mm wavelengths, the direction of polarized emission is perpendicular to the B-field lines

(Girart et al., 2006). Magnetically aligned dust polarization traces the projected B field morphology, and it is not intuitive to infer the three-dimensional B field structures. To reconstruct the three dimensional configuration of B field lines from observed polarization vectors, we adopt the approach of modeling polarization with known B field properties then compare the modeling with observations. Pioneering work by Aitken et al. (2002) simulates polarization maps in infrared and sub-mm wavelengths and shows distinct polarization patterns in different B fields

64 structures. Following more sophisticated works, e.g., Cho & Lazarian (2007); Padovani et al. (2012); Reissl et al. (2016b), incorporate radiative torque alignment mechanism and simulate

polarized thermal emission at sub-mm wavelengths.

At mid-IR wavelengths (5-30 µm), which is the main focus of this work, besides absorptive

and emissive polarization, polarization due to scattering, can no longer be regarded as negligible according to recent theoretical and observational progresses (Kataoka et al.,

2015; Yang et al., 2016; Li et al., 2016). In the presence of micro-sized dust grains, dust

scattering can produce signiﬁcant polarization. With the most up-to-date consideration

of polarization mechanisms, including dichroic absorption, emission and scattering, we

perform a three dimensional radiation transfer computation using the package RADMC3D (Dullemond, 2012) to estimate the linear polarization of protoplanetary disks and present the

linear polarization maps for a set of B ﬁeld conﬁgurations. It will help the interpretation of the

forthcoming infrared polarization observations, e.g., GTC/CanariCam (Telesco et al., 2003) and

SOPHIA/HAWC (Dowell et al., 2013), This paper presents a gallery of polarization maps from protoplanetary disks at mid-IR

wavelengths. In Section 5.2, we investigate the dependence of polarization on the properties of

dust grains. In Section 5.3, we construct a spherical density model and a protoplanetary disks

model and perform radiation transfer calculations using diﬀerent B ﬁeld models to obtain the

linear polarization maps. We also discuss the results and limitations of the model. In Section 5.4 we summarize our work.

5.2 Theoretical Understanding of Dust Polarization

In this section, we estimate the degree of polarization because of dichroic absorption, emission and scattering by dust. Here we do not use a detailed disk model for the computation but only investigate the polarization dependence on the properties of dust grains, such as the dust composition and geometry.

65 5.2.1 Polarization from Dichnoic Emission and Absorption

Polarized emission and absorption arise from diﬀerential cross sections of elongated dust grains with directions parallel and perpendicular to the transmitted E direction. (Cho &

Lazarian, 2007; Hoang & Lazarian, 2014). Cross sections of dust grains inside protoplanetary disk depend on geometries and compositions of dust grains, which are not well constrained by observations (Min et al., 2016). We study here oblate dust grains composed of astronomical silicate and ice-coated silicate with longer-to-shorter axis ratio of 1.5:1.0 and 2.0:1.0. The fractional thickness of the water ice mantle, ∆a/a, is set to be 0.6, where a is the eﬀective radius. The refractive index of astronomical silicate is from Weingartner & Draine (2001) and optical constants of ice from Warren (1984). We adopt the package DDSCAT (Draine & Flatau, 2012), which implements the discrete dipole approximation method, to calculate

2 differential absorptive efficiency Qabs (Qabs ≡Cabs /πa , where Cabs is the absorption cross section) along and perpendicular to the symmetric axis of oblate dust grains. The ratio of Qabs along two directions is an indicator of the polarizing ability of dust grains, regardless of their alignment in B fields.

The plot of Qabs,⊥/Qabs,∥ is shown in Fig. 5-1. From the ratio profiles, silicate and ice-coated silicate dust grains behave differently. It is not surprising to see that more oblate dust grains are more likely to have larger ratios, hence higher polarizing ability, than rounded grains. Actually, at a certain wavelength, the value Qabs,⊥/Qabs,∥ is fairly constant only when the size parameter x, defined as 2πa/λ, is less than 1.0. As illustrated in Fig. 5-2, at wavelength λ=10.0 µm, with the increased size of dust grains (consequently increased size parameter x), the ratio of absorptive efficiency drops to close to unity. If the value of the ratio of efficiency for large grains is close to unity, it means large dust grains contribute little to the polarization even though they are aligned. Taking that into account, Fig. 5-1 in fact displays the highest expected polarizing ability of spheroid dust grains and the values can be lower if size parameter x is larger than 1.0.

We derive the polarization proﬁles following expressions described in Lazarian (2007),

66 e−τ,∥ − e−τ,⊥ p = ≈ −(τ∥ − τ⊥)/2 (5–1) abs e−τ,∥ + e−τ,⊥ −τ,∥ −τ,⊥ (1 − e ) − (1 − e ) τ∥ − τ⊥ ≈ pem = − ∥ − ⊥ (5–2) (1 − e τ, ) + (1 + e τ, ) τ∥ + τ⊥ where τ(λ) is optical depth and proportional to the absorption eﬃciency Qabs (Assuming

Kirchhoﬀ’s law, Qabs equals to grain emissivity Qem;Greﬀet et al. 2016). We derive the following equations to compute the degree of polarization, based on Eqs.5–1 and 5–2, which

requires the sum and diﬀerence of cross sections parallel and perpendicular to the magnetic ﬁelds.

∫ amax 2 pabs (λ) = f [Qext,⊥(a) − Qext,∥(a)]a N(a)da (5–3) ∫amin amax 2 [Qem,⊥(a) − Qem,∥(a)]a N(a)da p (λ) = amin ∫ (5–4) em amax 2 [Qext (a)]a N(a)da amin

where Qext is the extinction eﬃciency, N(a) is the number of dust grains with radius a and f is a dimensionless parameter converting absorptive eﬃciency to optical depth. We assume a

−3.5 MRN dust size distribution (Mathis et al., 1977), dN(a) ∝ a da, amin < a < amax . We use amin=0.01 µm and amax =1000.0 µm (Cho & Lazarian, 2007; Kataoka et al., 2016a) and then integrate the sum and diﬀerence of absorptive and emissive eﬃciency over the distribution of

dust grain radius. The emissive polarization proﬁles at mid-IR and sub-mm wavelengths, are

shown in Fig. 5-3.

The computed degree of polarization at sub-mm wavelengths is consistent with the results in Cho & Lazarian (2007), in which they predict a value of polarization ∼2-3% at sub-mm

wavelengths from protoplanetary disks. However, observations do not conﬁrm that value

but report a much lower fractional polarization in protoplanetary disks (Hughes et al., 2009,

2013). Multiple factors that can suppress the polarization have been discussed, e.g., reduce

eﬃciency of alignment, rounding of larger dust grains, and magnetic ﬁeld tangling. Similarly, the discrepancy between observations and theoretical predictions is also seen in the mid-IR

67 (Li et al., 2018). Around 10 µm, the estimated degree of polarization could be as high as 10% as shown in Fig. 5-3, much higher than the typical polarization values from observations

(∼1%), as reported in Li et al. (2018). The same suppression factors may apply here as well.

But generally, the estimated polarization at mid and far-infrared wavelengths is higher than that in the sub-mm, and it suggests that polarization is more likely to be detected at infrared wavelengths.

5.2.2 Dust Scattering

At optical and near-IR wavelengths, images of polarized scattered light from dust grains at the very surface layer of protoplanetary disks, are important to characterize disk structures

(Wang et al., 2015). Recent studies by Kataoka et al. (2015); Yang et al. (2016); Kataoka et al. (2016a); Stephens et al. (2017) extend the importance of dust scattering to longer wavelengths. If the size of dust grains is comparable to the wavelengths, dust scattering is expected to produce signiﬁcant polarization even at sub-mm region. Following the approach in Kataoka et al. (2015), we estimate the degree of mid-IR polarization produced by dust scattering (please refer to Kataoka et al. (2015) for details). There are two important curves,

◦ scattering phase function at 90 , which is P=-Z12/Z11, and the albedo ω=κsca/(κsca + κabs ). The scattering properties of dust grains are computed by DDSCAT, with the assumption that particles are homogeneous spherical silicate particles, and, as a comparison, DIANA opacity model, which approximates the coagulation process in disks (Woitke et al., 2016)

(available at http://www.diana-project.com/data-results-downloads). DIANA standard opacity uses a mixture of silicate and amorphous carbon that are complex aggregates of hollow spheres that are porous (25%) (Min et al., 2005). These may provide a more accurate interpretation of dust aggregates in protoplanetary disks (Min et al., 2016). We adopt the MRN dust size distribution and take amin to be 0.01 µm.

The polarization P times the albedo ω with amax is plotted in Fig. 5-4. The product Pω provides a diagnostic of dust grains that contribute most to the polarization at given wavelengths. It should be considered as an upper limit to the theoretical expectation for

68 scattering properties of dust grains since we take the polarization P at the scattering angle of 90◦. The curves computed using DDSCAT are in solid lines and DIANA model in dashed lines, and at three most used mid-IR ﬁlters(centered at 8.7 µm, 10.3 µm and 12.5 µm) in

GTC/CanariCam. Comparing these two models, discrepancies are more pronounced for larger values of amax since large aggregates display diﬀerent scattering phase functions as discussed in Min et al. (2016). Unlike the Pω plot at sub-mm wavelengths (Fig. 5-4 in Kataoka et al. 2015)

, which peaks at a certain amax , the value of Pω at mid-IR wavelengths generally gets larger with the increasing dust radius.

Therefore, if the dust grains are suﬃciently large at the surface layer of the disk, where the mid-IR emission comes from, there might be detectable polarization signal from scattering. Besides dichroic emission and absorption, we need to incorporate the dust scattering process for the mid-IR polarization modeling even though it further complicates the interpretation of polarization observations. In the next chapter, we show the polarization maps of a protoplanetary disk model at an exemplary wavelength of λ = 10.0 µm. 5.3 Model Description

In this section, we investigate the mid-IR polarization by using a protoplanetary disk model. Our aim is to build up a gallery of the polarization maps of disks in different B fields configurations and viewing angles, to compare with polarization observations. We consider two models: (1) a spherical density distribution, which serves as a fiducial model to show the maps of polarization for a simple density geometry with poloidal and toroidal B fields and dichroic emission and absorption; and (2) a disk model, with parameters from the protoplanetary disk around an archetype Herbig Ae star, AB Aur. We consider seven B fields configurations with analytical expressions given in Aitken et al. (2002).

5.3.1 Magnetic Fields Setup

For the simulated polarization maps, we consider seven B fields geometric configurations as described below, which have been analytically defined in Aitken et al. (2002). Compared with Aitken et al. (2002), this work is performed with higher spatial resolution and more

69 detailed consideration of dust grain properties. Poloidal, toroidal and the classical hour-glass shaped B-ﬁeld conﬁgurations are included among these models:

1) Pure axial Br =Bϕ=0, Bz =constant

2) Toroidal Br =Bz =0,Bϕ=constant

3) Hourglass Bϕ=0, Bz =constant,Br =γ(z/r)Bz , γ=2.0

4) Br =γ(z/r)Bz ,Bϕ=α(z/r)Bz ,Bz =constant,α=2.0

5) Br =0, Bϕ=α(z/r)Bz ,Bz =constant,α=2.0

6) Bϕ=αr, Br =0,Bz =constant

3zr 2z 2−r 2 7) Br = (r 2+z 2)5/2 ,Bz = (r 2+z 2)5/2 ,Bϕ=0. 5.3.2 Fiducial Model: Spherical Power-law Envelope

A spherical dusty envelope, a bipolar outﬂow, and possibly a circumstellar disk are

usually considered for a simple Class 0 YSO model (Chiang et al., 2012). We do not include

the outﬂow cavity or a disk here, and as a simple illustration, we only consider an envelop

geometry that applies to a rotating sphere in free-fall gravitational collapse (Whitney et al., 2013; Simpson et al., 2013). To start with, we build up a simple power-law density proﬁle,

−s ρ=ρ0r , where ρ0 is the density at radius r=1 AU and s is the density power-law index. We construct a three-dimensional density distribution in a Cartesian coordinate (x, y, z) with grids

containing 153×153×153 cells. The radius of the spherical envelope is 10,000 AU. The model

parameters are T∗=10,000 K, R∗=2.5R⊙, M=0.01M⊙, and s=1.5. For dust grains, we assume a MRN size distribution with amin=0.005 µm and amax =0.25 µm. We assume a distance to the source of 100 pc.

5.3.3 Radiation Transfer with RADMC-3D

We set up a thermal Monte Carlo run to calculate the dust temperature throughout

the spherical envelope using the 3D radiative transfer code RADMC-3D (Dullemond, 2012), developed by C. P. Dullemond. The code is frequently used to make observational predictions

(Pohl et al., 2016) and the benchmark tests of this code have been discussed in Kataoka

et al. (2015). We assume the temperature distribution to be independent of the shape of

70 dust. Hence, the particle opacities adopted here are calculated by using DDSCAT with the assumption that dust grains are homogeneous astronomical silicate spheres. Number of

photons for the radiation transfer to compute the dust temperature is 5×107.

After we have temperature distribution of the spherical envelope, we then use the ray tracing algorithm described in Davidson et al. (2014) to obtain Stokes parameters Q, U, and I, and the algorithm considers both the dust emission and absorption when light travels

through a volume of particles along our line of sight. Ray tracing equations in Davidson et al.

(2014) contain parameters characterizing polarization properties of dust grains, the alignment

efficiency and local B field configurations. In the computation, we assume oblate silicate dust

grains with longer-to-shorter axis ratio 1.5:1.0 and obtain opacities along two directions at 10.0

2 −1 2 −1 µm using DDSCAT, which are κ⊥=4080.5 cm g and κ∥=2833.75 cm g , respectively.

What makes interstellar dust grains aligned is still not fully understood. Radiative torque

is a promising mechanism for dust alignment (Lazarian, 2007; Hoang & Lazarian, 2014;

Andersson et al., 2015). The full calculation shall use the local energy density of radiation, number density, temperature and gas drag to constrain the size of dust grains that can be

aligned at that location (Cho & Lazarian, 2007). Instead, in a simpliﬁed approach, as a

statistically measure of the amount of alignment, we use the so-called Rayleigh reduction

factor R (Greenberg, 1968; Lazarian & Efroimsky, 1996; Aitken et al., 2002), that relates the

properties of the grain ensemble to the properties of the observed polarized radiation. R is related to the averaged angle between magnetic ﬁeld and the rotational symmetry axis of dust.

Grains completely aligned in the ﬁeld with their spin axes parallel to the ﬁeld lines have R=1, while randomly oriented grains have R=0. We adopt the R value of 0.25 in this study (Aitken

et al., 2002; Hoang & Lazarian, 2008). The choice of R values linearly changes the values of

polarization degree. We only consider the polarization from aligned dust grains in magnetic ﬁelds in this

model. After we get intensity maps of Stokes parameter Q, U, and I from the radiation

transfer equations, we then use the conventional equations to derive the degree of polarization

71 p and polarization position angle θ. The degree of linear polarization p is determined by √ p= U2 + Q2/I and its projected position angle θ=0.5arctan(U/Q). The ﬁnal output image

has 51× 51 pixels with the pixel scale 3.92′′(392 AU at distance of 100 pc). We bin the data

by 5×5 pixels in the images to better present the results. Maps of linear polarization in the poloidal and toroid B ﬁelds at diﬀerent viewing angles are shown in Fig. 5-5 and Fig. 5-6, respectively. The length of the segments is scaled to the polarization percentage and the

orientation of the segments represents polarization position angle. The direction of polarization

at outer radius is perpendicular to the direction of B ﬁelds and only in the central region

(r<2000AU), the orientation is long the B ﬁeld lines. It means that at the center region, the

optical depth is higher and it is therefore dominated by absorptive polarization. 5.3.4 Disk Model

Now we consider a disk model. We initialize our simulations using the star and disk

parameters of a well-studied and archetypal Herbig Ae star AB Aur (Tang et al., 2012; Perrin

et al., 2009; Tang et al., 2017), with a disk extending from 0.5 to 400 AU (Mari˜naset al.,

2006). We construct a three-dimensional density distribution in a spherical coordinate (r, θ, ϕ) with grids containing 100×120×40 cells. We assume a hydro-static smooth disk with no gaps and envelope. The disk surface density is described by

r −α Σ(r) = Σ0( ) (5–5) r0 The disk is ﬂared, i.e., with

r β h(r) = h0( ) (5–6) r0 where h is the scale height. We adopt the MRN distribution and set amin=0.01 µm and amax =1.0 µm. Considering the process of dust growth and dust settling (Dominik et al., 2007; Boehler et al., 2013), the distribution of dust grain sizes is not expected to be the same in

the disk. However, since the mid-IR emission mostly comes from the surface layer of the disk and the mid-plane is optically thick (Testi et al., 2014), we use the same dust size distribution

throughout the disk here. More sophisticated dust model should be considered in the future.

72 Star and Disk parameters are summarized in Table 5-1 and collected from literature (Robitaille et al., 2007; Perrin et al., 2009; Dullemond & Monnier, 2010).

We use the same radiation transfer approach as discussed in Section 5.3 to get the

temperature distribution throughout the disk. Number of photons for the radiation transfer

to compute temperature is 1×109. In the surface layer of the disk, where most of the mid-IR emission comes from, the temperature of the disk decreases from ∼900 K at 2 AU to ∼120 K

at 100 AU. As discussed in Section 5.2, the contribution of scattering in the polarization signal

should be incorporated in the modeling. We use DDSCAT to compute scattering properties of

spherical dust grains (0.01–1.0 µm), and generate a synthetic image of scattering polarization

with a set of inclinations, which are shown in Fig. 5-7. The polarization segments has the characteristic circular pattern with directions perpendicular to the illuminating directions.

Because of the complexity of the problem, scattering from elongated dust grains or scattering

from magnetically aligned dust grains are not considered in this work, and the complication

have been proposed and discussed in more sophisticated theoretical works (Whitney & Wolﬀ, 2002; Yang et al., 2016, 2017).

The right panel of Fig. 5-7 shows that the scattering-induced polarization map of the

disk at diﬀerent viewing angles at 10.0 µm. The output image has 51×51 pixels with the

spatial resolution 0′′.082 (12 AU at the distance of 144 pc). The polarization segments show circular patterns perpendicular to the illumination direction from the central star. Fractional polarization at the 1′′ distance from the star as a function with the inclination of the disk (0◦is

face-on) is plotted in the left panel in Fig. 5-7. Polarization degree p for a resolved disk is

larger when the disk is more inclined. We combine the polarization from both dichroism and

scattering in Stokes parameter space. The results are shown by the polarization maps from

Fig. 5-8 to Fig. 5-14 and will be discussed next. 5.3.5 Results

Maps of polarization in the seven B ﬁelds of protoplanetary disks are shown from Fig. 5-8

to Fig. 5-14. For each plot, we show the sketch of B-ﬁeld conﬁguration and polarization images

73 of the disk at four viewing angles, 0◦, 30◦, 60◦, and 80◦. Polarization in these plots is the net polarization from a combination of dichroic emission, absorption and scattering.

We now examine the characteristics of the composite polarization pattern. It is seen that

most of the B ﬁelds conﬁgurations deduce their distinguishable polarization patterns. Yet

some models have similar features, e.g., Fig. 5-9 and Fig. 5-13. The net polarization for almost edge-on disks can barely see any footprint of scattering polarization, compared with low or

intermediate inclinations, where the inclusion of scattering polarization makes more diﬀerence,

e.g., azimuthal ‘nulls’ appears in a toroidal magnetic ﬁeld conﬁguration, where the polarization

from dichroism cancels that from the scattering exactly.

As one of the most simple polarization conﬁgurations, poloidal B-ﬁeld model (Fig. 5-8) shows uniform polarization patterns at the inner disk and circular pattern at the outer disk.

The magnitude of fractional polarization increases with the increasing inclination of the disk.

The polarization direction is along the radial direction in the toroidal B-ﬁeld model (Fig. 5-9) and shows a preferential direction along the shorter axis of the disk for high inclinations, opposite to that of the poloidal B-ﬁeld model. There appear polarization nulls toward the outer radius for the low inclinations. It shares similarities with the polarization patterns of

Aitken model VI shown in Fig. 5-13. Since polarization traces the projected B ﬁeld on the

sky plane, when we try to infer the three-dimensional spatial structure, it is hard to break the

degeneracy unless combined with other observation methods, e.g., Faraday rotation, to get the information of B ﬁeld along our line of sight (Akahori & Ryu, 2010). Hour-glass shaped

B-ﬁeld (Fig. 5-10), was proposed in the classical star formation theory because of the pinched

ﬁeld lines of the rotation disk (Shu et al., 1987; Chapman et al., 2013). Polarization segments

are along azimuthal directions and show two nulls points at the inclination of 30◦. For highly

inclined disk, the direction tends to trace the major axis of the disk. Aitken model IVa and V in Fig. 5-11 and Fig. 5-12 exhibit asymmetric polarization patterns for disks viewed at intermediate

inclinations and the preferential direction is not relevant to the disk axes. Aitken model VII in

74 Fig. 5-14 resembles the polarization pattern in Fig. 5-10, and again, it is because the projections of these two B ﬁeld conﬁgurations are the same.

These polarization maps can be compared with the mid-IR imaging polarimetry

observation of Herbig Ae star, AB Aur (Li et al., 2016), to infer which B-ﬁeld model is favored.

The disk has an low inclination angle, ∼20◦. We ﬁnd that the observed polarization can be well reproduced when both polarized emission and polarization from scattering are included in

the model. For the inner disk, we infer a poloidal B-ﬁeld conﬁguration titled relative the disk

spin axis. For the outer disk, the centrosymmetric pattern can be explained by dust scattering.

It demonstrates the potential of the modeling, and we expect to use this method to explain

more polarimetry observations of disks in the future. 5.3.6 Example: AB Aur

We mapped out the mid-infrared polarization of the protoplantary disk around the Herbig

Ae star AB Aur using CanariCam at the 10.4 m telescope GTC. We detect about 0.44%

polarization at 10.3 µm with uniform orientations at inner radius less than 80 AU. While at the outer radius, the degree of polarization rise to ∼ 1.4% and display centrosymmetric pattern as shown by the black segments in Fig.5-15. The model that ﬁts the observation best

is shown by the red segments in Fig.5-15. The goodness of ﬁt was ﬁrstly evaluated visually

by superimposing the model with the data in order to narrow down the parameter space. The

best ﬁtting model supports that the mid-IR polarization from the disk of AB Aur contain both

dichroic emission and polarization due to dust scattering, which was regarded as negligible because of the lack of large dust grains. 1) For the inner disk, thermal emission at 10.3 µm

overwhelms the scattered light, and the observed polarization is dominated by the dichroic

thermal emission. The uniform polarization pattern can be ﬁtted well with a titled poloidal

magnetic ﬁelds morphology. 2) For the disk at larger radii, thermal emission drops faster than does the scattered light, and consequently, polarization arising from scattering can not be

ignored. We acknowledge the degeneracies of the geometry dust grain, size distribution of dust

grains and the dust alignment eﬃciency, i.e., a high degree of polarization can be a result of

75 highly elongated dust gains with low alignment eﬃciency, or well-aligned particles of axis ration close to unity. We set the longer-to-short axis ratio of elongated dust grains to be 1.5:1.0 with alignment eﬃciency R = 0.05.

A quantitative comparison of the best ﬁtting model we found with the observation was conducted and shown in Fig.5-15. We conclude that the model could reproduce well the observation data and prove the robustness of this modeling method.

5.3.7 Discussion

There are several factors that affect the degree of polarization, including the dust properties, disk structure and B-field structures. In terms of the effect of B-field configurations, even with the same disk and dust setting, the magnitude of polarization can be substantially different, for example, the degree of polarization in Aitken model VI (Fig. 5-13) is 75% higher than that in Aitken model V (Fig. 5-12). In addition, the choice of Rayleigh reduction factor

R values linearly changes the resultant values of polarization. We note the degeneracy of the choice of R and dust properties, which means a high degree of polarization can be a result of highly elongated dust gains with low alignment eﬃciency, or well-aligned particles of axis ratio close to unity. It is not easy to disentangle these factors, and we might be able to constrain these parameters only through multi-wavelengths polarization observations (Hughes et al.,

2009).

It is a simple model and we do not include complex disk features, e.g., a gap. For the future reﬁnement of the model, the disk should be treated with more features. Another complication is the dust scattering. We do not consider scattering from non-spherical dust grains, as discussed in Yang et al. (2016). For a future investigation, we also want to extend the modeling work to longer wavelengths, e.g., far-infrared for polarimetry observations from

SOPHIA and sub-mm observations from ALMA. Then we need to consider the dust growth and settling process.

76 5.4 Summary

It is not intuitive to infer the spatial structure of B ﬁelds directly from the polarization observations, so it is useful to have a gallery of polarization maps with well-understood B

ﬁeld conﬁgurations that can be compared with observations. We present a comprehensive mid-IR polarimetry model to understand resolved polarimetry observations of protoplanetary disks. Dust absorption, emission and scattering, as possible mechanisms to contribute to mid-IR polarimetry, are all included in the modeling. The model successfully explains the protoplaneatry disk around the Herbig Ae star AB Aur and demonstrates its capabilities to interpret the polarimetry observations. Our main conclusions are summarized as follows:

1. Polarizing ability of dust grains depend on dust composition and geometry. More oblate dust grains are expected to have higher polarizing ability. Theoretical calculations of mid-IR polarization can be as high as 10%, and the suppression of polarization is seen compared with observation data.

2. Scattering-induced polarization is expected to be signiﬁcant with the existence of larger dust grains. If the disk is resolved, the existence of micro-sized dust grains can produce ∼1% polarization at outer radius of the disk, which is detectable by mid-IR facilities.

3. A library of polarization maps in a set of B ﬁeld conﬁgurations are presented. Incorporation of scattering polarization is more seen for disks more with low inclinations than high inclinations. Application of the modeling to the case of AB Aur reproduces the main features in the real data, and it demonstrates the capability of this model.

77 Table 5-1. Model Parameters Parameter Value Stellar mass M∗ 2.4 M⊙ Stellar radius R∗ 2.5 R⊙ Stellar eﬀective temperature T∗ 10000 K Disk Rinner 0.5 AU Disk Router 400 AU Surface density power index α 1.2 Flaring angle β 1.125 Scale Height (h100AU ) 8.5 AU Disk Mass(gas+dust) 0.012 M⊙ Dust 0.01-1.0 µm Distance 144 pc Disk Inclination 0, 30, 60, 80◦

78 4 1.0:1.5 Silicate 1.0:2.0 Silicate 1.0:1.5 Ice-Silicate 3 1.0:2.0 Ice Silicate para,abs

/Q 2 perp,abs

Q 1

0 1 10 100 1000 Wavelength (µm)

Figure 5-1. Ratio of the absorptive eﬃciency perpendicular and parallel to the shorter axis of the spheroid Qabs,⊥/Qabs,∥ covering wavelengths λ from 1.0 to 1000.0 µm. It is computed by using the package DDSCAT for silicate and ice-coated silicate (∆a/a=0.6) dust grains with diﬀerent oblateness. Radius of particles a are chosen to be 0.1 µm to satisfy that the size parameter 2πa/λ less than 1. The ratio represents the polarizing ability of elongated dust grains. The higher the ratio, the larger polarization we expect.

79 2.5 Qperp,abs/Qpara,abs

2.0 para

/Q 1.5 perp Q 1.0

0.5 0.01 0.10 1.00 10.00 100.00 2 π a/λ

Figure 5-2. Ratio of the absorptive eﬃciency along two directions Q⊥/Q∥ vs changing grain radius a (i.e., 2πa/λ) at wavelength λ=10µm for a silicate spheroid. For 2πa/λ is less than 1, the ratio can be as high as 1.4 and then drops to below 1.0 when 2πa/λ is greater than 1.

80 20 12 1.0:2.0 Silicate 1.0:1.5 Silicate 1.0:1.5 Silicate 1.0:1.5 Ice Silicate 1.0:2.0 Ice Silicate 10 15 1.0:1.5 Ice Silicate 8 10 6

p (%) 5 p (%) 4 2 0 0 -5 -2 6 8 10 12 14 16 1 10 100 1000 Wavelength (µm) Wavelength (µm)

Figure 5-3. Emissive polarization profiles vs wavelength. Left: Expected emissive polarization profiles for silicate and ice-coated silicate with longer-to-shorter axis ratio 2.0:1.0 and 1.5:1.0 from 7–13 µm. Right: Expected emissive polarization profiles for silicate and ice-silicate with longer-to-shorter axis ratio 1.5:1.0 from 1-1000 µm. The computation of fractional polarization p is based on Eq. 5-4. Theoretically, the degree of polarization at mid-IR wavelengths is higher than that at sub-mm wavelengths.

81 0.25 Si6 (12.5) µm Si4 (10.3) µm 0.20 Si2 (8.7) µm

0.15 ω P 0.10

0.05

0.00 0.1 1.0 10.0 100.0 amax (µm)

Figure 5-4. The product of the degree of polarization at 90◦ due to single scattering (P) and the dust albedo (ω) for dust size distributions with different values of amax (the value of amin is fixed at 0.01 µm). Each line corresponds to the wavelengths of 8.7, 10.3, and 12.5 µm, which are the center wavelengths of three most used filters for GTC/CanariCam. Solid lines are calculated using the DDSCAT package and dashed lines are from DIANA standard opacities.

82 10000.0 incl 0 3% incl 30 3%

5000.0

0.0 R (AU) R

Aitken Model I, Bz=constant -5000.0

-10000.010000.0 incl 60 3% incl 80 3%

− 5000.0

0.0 R (AU) R -5000.0

-10000.0 -10000.0-5000.0 0.0 5000.0 10000.0-10000.0-5000.0 0.0 5000.0 10000.0 R (AU) R (AU)

Figure 5-5. Simulated linear polarization maps in a poloidal B-field configuration for a spherical envelope at λ=10.0 µm. Left: Sketch of the poloidal B-field configuration. Right: Maps with pattern of linear polarization overlaid with log-scaled total intensity Stokes I (Blue shade). Four panels are polarization images for disk inclinations: 0◦(face-on disk), 30◦, 60◦, 80◦.

83 10000.0 incl 0 3% incl 30 3%

5000.0

0.0 R (AU) R

Aitken Model II, Bφ=constant -5000.0

-10000.010000.0 incl 60 3% incl 80 3%

− 5000.0

0.0 R (AU) R -5000.0

-10000.0 -10000.0-5000.0 0.0 5000.0 10000.0-10000.0-5000.0 0.0 5000.0 10000.0 R (AU) R (AU)

Figure 5-6. Simulated linear polarization map in a toroidal B-ﬁeld conﬁguration for a spherical envelop at λ=10.0 µm. Same as Fig.5-5.

300.0 5% incl 0 5% incl 30

150.0

0.0

R (AU) R 5

-150.0 4

3 -300.0 300.0 incl 60 5% incl 80 5% p (%) 2

150.0 − 1 0.0 0

R (AU) R 0 20 40 60 80 Inclination (deg) -150.0 -300.0 -300.0 -150.0 0.0 150.0 300.0 -300.0 -150.0 0.0 150.0 300.0 R (AU) R (AU)

Figure 5-7. Dust scattering induced polarization map at λ=10.0 µm. Left: Maps with pattern of linear polarization overlaid with log-scaled total intensity Stokes I at four diﬀerent viewing angles, 0◦, 30◦, 60◦, and 80◦. Right: Fractional polarization p at a distance of 1′′.0 from the central star vs. inclination.

84 300.0 5% incl 0 5% incl 30

150.0

0.0 R (AU) R

Aitken Model I, B =constant z -150.0

-300.0 300.0 5% 5% incl 60 incl 80

150.0 − 0.0

R (AU) R -150.0 -300.0 -300.0 -150.0 0.0 150.0 300.0 -300.0 -150.0 0.0 150.0 300.0 R (AU) R (AU)

Figure 5-8. Left: Sketch of the poloidal shape B-field configuration. Right: Maps with pattern of linear polarization at wavelength λ = 10.0 µm for disks with embedded, poloidal shape B-field. Four panels show predicted polarization images for different disk inclination: 0◦(face-on disk), 30◦, 60◦, 80◦. The length of the segments is scaled to the polarization degree and the orientation is polarization position angle. Data have been rebinned 5×5 pixels and the polarization segments are plotted at the center of the 5×5 pixels. Blue shading is log-scaled total intensity (Stokes I).

85 300.0 5% incl 0 5% incl 30

150.0

0.0 R (AU) R

Aitken Model II, Bφ=constant -150.0

-300.0 300.0 5% 5% incl 60 incl 80

150.0 − 0.0

R (AU) R -150.0 -300.0 -300.0 -150.0 0.0 150.0 300.0 -300.0 -150.0 0.0 150.0 300.0 R (AU) R (AU)

Figure 5-9. Toroidal B-ﬁeld conﬁguration.

300.0 5% incl 0 5% incl 30

150.0

0.0 R (AU) R

Aitken Model III, B =constant, γ=2.0 z -150.0

-300.0 300.0 5% 5% incl 60 incl 80

150.0 − 0.0

R (AU) R -150.0 -300.0 -300.0 -150.0 0.0 150.0 300.0 -300.0 -150.0 0.0 150.0 300.0 R (AU) R (AU)

Figure 5-10. Hour-glass shape B-ﬁeld conﬁguration.

86 300.0 5% incl 0 5% incl 30

150.0

0.0 R (AU) R

Aitken Model IVa, B =constant, α=2.0 z -150.0

-300.0 300.0 5% 5% incl 60 incl 80

150.0 − 0.0

R (AU) R -150.0 -300.0 -300.0 -150.0 0.0 150.0 300.0 -300.0 -150.0 0.0 150.0 300.0 R (AU) R (AU)

Figure 5-11. Aitken model IVa B-ﬁeld conﬁguration.

300.0 5% incl 0 5% incl 30

150.0

0.0 R (AU) R

Aitken Model Va, B =constant, α=2.0 z -150.0

-300.0 300.0 5% 5% incl 60 incl 80

150.0 − 0.0

R (AU) R -150.0 -300.0 -300.0 -150.0 0.0 150.0 300.0 -300.0 -150.0 0.0 150.0 300.0 R (AU) R (AU)

Figure 5-12. Aitken model V B-ﬁeld conﬁguration.

87 300.0 5% incl 0 5% incl 30

150.0

0.0 R (AU) R

Aitken Model VI, B =constant, α=2.0 z -150.0

-300.0 300.0 5% 5% incl 60 incl 80

150.0 − 0.0

R (AU) R -150.0 -300.0 -300.0 -150.0 0.0 150.0 300.0 -300.0 -150.0 0.0 150.0 300.0 R (AU) R (AU)

Figure 5-13. Aitken model VI B-ﬁeld conﬁguration.

300.0 5% incl 0 5% incl 30

150.0

0.0 R (AU) R

Aitken Model VII, a dipole field -150.0

-300.0 300.0 5% 5% incl 60 incl 80

150.0 − 0.0

R (AU) R -150.0 -300.0 -300.0 -150.0 0.0 150.0 300.0 -300.0 -150.0 0.0 150.0 300.0 R (AU) R (AU)

Figure 5-14. Dipole shape B-ﬁeld conﬁguration.

88 2 Surface brightness (log[Jy/arcsec ]) Radius (AU) -0.5 0.0 0.5 1.0 1.5 2.0 0 50 100 150 200 3.0 Offset (AU) Data a -200 -100 0 100 200 2.5 Model (total) Model (scattering) 1.5 2.0 Model (polarized emission) 200 1.5 3001.0 1.0

100 Polarization (%) 0.5 0.5 0.0

200 0.0 0 Data b Model

Offset (AU) 20 Difference Offset (arcsec) -0.5 -100 100 0 -1.0 PA (degree) -20 -200 -1.5 3% 0 0 -1.5 -1.0100 -0.5 0.0200 0.5 1.0300 1.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Offset (arcsec) Radius (arcsec)

Figure 5-15. Left: The best-fit model (red vectors) superimposed on the observation (black vectors). Displayed in the background is the surface brightness of the model disk, superimposed by model polarized intensity contours. In this model, the disk is threaded by a tilted poloidal B-field, the projected orientation of which is shown in the upper-left sketch (green line). Credit: Li et al. (2016) Right: Illustration of the goodness of fit. Azimuthally averaged degree of polarization (a) and polarization P.A. (b) of the model (blue lines) and the observation (black lines with 1σerror bars) are compared at a range of deprojected distances from the star. In the outer disk (r ≥ 0′′.5), most polarization is contributed by scattering (green dotted line). Toward the inner disk (r ≤ 0′′.5), scattered polarization becomes negligible and polarized emission (red dashed line) from aligned dust grains dominates. Credit: Li et al. (2016)

89 CHAPTER 6 UNDERSTANDING THE MAGNETIC FIELDS IN W51 IRS2 USING MID-IR POLARIMETRY

6.1 Introduction

W51 giant molecular cloud is one of the most active and massive star formation regions in

the Galaxy. It is located at a distance of 5-8 kpc and contains an aggregation of H II regions, which are produced from the ionizing radiation by massive stars, and major sources A, B and C (Ginsburg et al., 2015). There is little foreground and background contamination of

the complex, which makes it particularly unique for our polarimetric study. W51 A complex

contains two protoclusters regions, W51 main and IRS2. W51 IRS2 consists of many H II regions and young stellar objects (YSOs), some of them are massive YSOs candidates. W51

IRS2 is located at a distance of 5.41 kpc, based on parallax measurements (Xu et al., 2009).

This region has been studied at multiple wavelengths, covering near-Infrared (NIR) to radio

wavelengths (Tang et al., 2013; Zapata et al., 2009). Some objects only show emission at radio wavelengths, such as the well-studied massive young stellar object W51 North. The most prominent sources in this region at mid-infrared (mid-IR) wavelengths are IRS

2E and IRS 2W (Barbosa et al., 2016; Okamoto et al., 2001). Detection of the CO overtone

in IRS 2E at NIR suggests the presence of an accretion disk. IRS 2W is an ultra compact H II region (UC H II) with an O3 ionizing star (Barbosa et al., 2008). UC H II regions (r∼0.1pc) form when massive stars ignite dense molecular clouds and high energy UV photons ionize the surrounding neutral material. It has a relatively small size and high electron density. UC

H II regions expand until they reach the equilibrium with the surrounding material, eventually evolving into H II (∼10 pc) regions (Zhu et al., 2005).

W51 IRS2 region has abundant identified outflows and jets (Fig.6-1). A high velocity, blueshifted jet was first discovered by Lacy et al. (2007) in W51 IRS2 region from [Ne II] and

[S IV] line emission . It is shown that the underlying jet of gas interacts with the ambient gas

and is coincident with the lower extinction region (Barbosa et al., 2016). The same feature is

detected in H77α line (Ginsburg et al., 2016) and the molecular CO counter part of the jet is

90 subsequently discovered, which indicates that a molecule outflow is being ionized as it emerges into the H II region (Ginsburg et al., 2017). The massive star W51 North is also reported to derive a bipolar outflow (Ginsburg et al., 2017; Zapata et al., 2009). The mid-IR emission of W51 IRS2 is confined well with the Very Large Array (VLA) 14GHz and 5Hz continuum emissions which traces the ionized gas (Ginsburg et al., 2016). W51 IRS2 therefore provides an ideal target to study the possible links between B fields and gas flows.

Dust polarization is commonly used to trace B fields in star formation regions. Non-spherical dust grains tend to spin, perhaps as a result of radiative alignment torques from an anisotropic radiation field (Lazarian, 2007; Cho & Lazarian, 2007). In the presence of an external B field, these spinning grains will align, producing polarized dust extinction from background starlight that is parallel to the B field or polarized thermal dust emission that is perpendicular to the

field lines. Therefore, polarimetry can be used to infer the projected B field directions on the plane of the sky. However, the ability of polarimetry to study B fields has been challenged recently since other non-magnetic effects can also produce significant polarization. The mechanisms include scattering from dust grains in an isotropic radiation field (Kataoka et al.,

2015; Yang et al., 2016) and dust alignment along the direction of the radiation ﬁeld (Tazaki et al., 2017). These theoretical studies and observations (Stephens et al., 2017; Kataoka et al., 2016b) indicate that the observed polarization signal may be a combination of several mechanisms, yet we still have a relatively small sample of sources to identify the origins of polarization. Tang et al. (2013) and Koch et al. (2018) present polarization observations of the

W51 IRS2 region at 870 µm. Sub-millimeter (sub-mm) emission traces different sources than does the mid-IR emission. They compare B field morphologies at different scales and study the correlation of the B field in the large scale envelope to the small core.

In this paper, we present high-resolution mid-IR polarimetric imaging observations of W51 IRS2 with an angular resolution ∼0′′.4 (∼2200AU at the distance of 5.41 kpc). We use the method of polarimetry tomography to infer the spatial structure of the B ﬁeld, and we discuss the relationship of the B ﬁelds with the ionized gas (Barnes et al., 2015). The paper

91 is organized as follows: Section2 describes the mid-IR observations and data reduction of W51 IRS2. Section 3 we analyze the polarization results of each source in the region and discuss the

correlation of B ﬁelds with the ionized gas. In Section 4, we summarize our work.

6.2 Observation and Data Reduction

We obtained the polarimetric images of W51 IRS2 using three mid-IR ﬁlters (Si2, Si4 and Si6) with CanariCam in June 2014 and Aug 2013 as part of the CanariCam Science Team guaranteed time program. CanariCam is the mid-IR multi-mode facility camera on the

10.4-meter Gran Telescopio Canarias (GTC) in La Palma, Spain (Telesco et al., 2003). It has a

ﬁeld of view of 26′′ × 19′′ with a pixel scale of 0′′.079. Polarimetry is accomplised through the use of a Wollaston prism, which produces a separation between the beams of o ray and e ray (i.e., ordinary ray and extraordinary ray), and a half-wave plate, rotating sequentially to four orientations (0, 22.5, 45, and 67.5 degrees) during observations.

The imaging observations of W51 IRS2 were interlaced with observations of standard star Vega for ﬂux and point-spread-function (PSF) calibration (Cohen et al., 1999) and the

standard star AFGL 2591 from Smith et al. (2000) to calibrate the polarization position angle (PA). Standard chop-nod sequences were used, with a chop-throw of 15′′ at the position angle

20◦ East of North to minimize contamination from emission for background measurement.

CanariCam was rotated so that the polarimetry ﬁeld mask and the detector array’s long axis were along the direction of the Lacy jet (Lacy et al., 2007), which was 20◦ from the North. In

the polarimetry mode, the actual ﬁeld of view is reduced to 26′′ × 2.6′′ after a focal mask to avoid overlapping between o and e beams is used. Since the W51 IRS2 emission region extends

over the ﬁeld of view in the polarization mode, we split our observations of the target into two

parts by centering the polarization mask slots on the source IRS2E and W51 d1 (Table 6-1).

Observations at diﬀerent telescope point time provided overlapping by a few pixels, for the registration and to avoid edge eﬀects. The achieved angular resolution (full-width at half

maximum intensity) for the polarimetric imaging was 0′′.35-0′′.4 (Table 6-1), slightly higher

compared to the diﬀraction limit of 0′′.3. The acquisition image taken with CanariCam through

92 10.3 µm ﬁlter is shown in Fig. 6-1, which serves as a guide to construct the ﬁnal mosaic of the polarization map from two polarization mask slots. The relative positions of W51d1 and

IRS 2E are used to register and build the mosaic of the region. The outﬂows superimposed

on the color-scaled mid-IR emission in Fig. 6-1 are from radio observations. The heavy purple

contour is the H77α radio recombination line from VLA observation Ginsburg et al. (2016). The red and blue contours are the redshift and blueshift of CO molecular outﬂows from ALMA

(Ginsburg et al., 2017).

The data were reduced with custom IDL software, as described in Li (2014). We

computed normalized Stokes parameters q and u, where q=Q/I and u=U/I . The degree √ of polarization is p = q2 + u2 and the polarization PA is computed as θ = 0.5arctan(u/q).

The uncertainties σq and σu associated with the normalized Stokes parameters were derived using a 3-sigma clipping algorithm (Robinson, 1987), and they were then propagated through

the analysis to obtain the polarization uncertainty σp and polarization PA uncertainty

σθ = σp/2. Instrumental polarization has been determined during the commissioning of CanariCam, and its behaviour is well known. We corrected the instrumental polarization in the

Q-U plane. Aperture polarization measurements of individual sources in this region are given in

Table 6-2, and the size of the aperture is determined by the full-width half maximum of each

source.

The polarization maps obtained in three bands are presented in Fig. 6-2. The data presented in Fig. 6-2 have been smoothed by 3×3 pixels (0′′.24×0′′.24) binning. Vectors are only plotted where I /σI ≥ 8 and p ≤ 12%. We also show the contours of polarized intensity in pink √ 2 2 color, Ip, deﬁned as Q + U . 6.3 Discussion

6.3.1 Polarization Components – The Aitken Method

The observed mid-IR polarization can be explained as arising from thermal emission and/or absorption from aligned dust grains. Aitken et al. (2004) proposed a method to

disentangle the emissive and absorptive polarization components using the spectral signature of

93 silicates through a multiwavelength study (refer to the Appendix). Polarization measurements for at least two wavelengths is needed with this approach. This method is optimized to minimize χ2 of the ﬁt to the normalized Stokes parameters q and u, independently. The method has limitations, e.g., it does not take into account other polarization process such as dust scattering, and it only works under the assumption that the signiﬁcant dust grains are silicate. However, it appears to work well in a variety of astronomical objects (Li et al., 2018;

Lopez-Rodriguez et al., 2017) and can be veriﬁed by the goodness of ﬁt of the decomposition to the polarization data. This technique can be a powerful diagnostic tool to probe the complex polarimetric nature of an astronomical environment.

We apply this approach to both the aperture and imaging polarimetry data of W51 IRS2 to disentangle the polarization mechanisms and consequently derive the spatial B ﬁeld geometry in the region.

6.3.2 Polarization Results of W51 IRS2

Previous mid-IR spectro-polarimetric observations of W51 IRS2 in Smith et al. (2000) determined the position angles of absorptive polarization and emissive polarization to be 1381◦and 391◦, respectively, using the developed Bayesian approach of Aitken’s method (Lopez-Rodriguez, 2016). W51 IRS2 contains multiple H II regions and OB stars. Our observations resolve individual sources in this region: W51d1, OKYM2, IRS 2E, the Lacy Jet, and IRS 2W, with their locations denoted in Fig. 6-1 and aperture polarization measurements in Table. 6-2. Spectral decompositions of polarimetric measurements at three wavelengths of each source are shown in Fig. 6-3, using Aitken’s method. We present a detailed discussion of each object here.

W51 d1: W51d1 (OKYM5) is seen as a NIR, mid-IR and radio source. It is a UC H II region and contains a compact cluster of stars (Figuerdo et al., 2008). The spectrum of W51d1 shows very little silicate absorption, with the ﬂux increasing towards longer wavelengths

(Barbosa et al., 2016). It is seen in the polarimetry observations since the polarization is

94 dominated by thermal emission. If emissive polarization, we infer the B ﬁeld direction by rotating the polarization vectors by 90◦, and the derived B ﬁeld direction is ∼60◦.

OKYM2: A source identiﬁed in Okamoto et al. (2001). The radio source has an oﬀset

from the mid-IR emission peak. It is located in the relatively low extinction region (Barbosa

et al., 2016). In terms of polarization, it seems to be at an intermediate phase between W51d1 and IRS 2E, since it is best ﬁt with a combination of absorptive and emissive polarization with

polarization PA ∼ 130◦.

IRS 2E: The spectrum of IRS 2E (OKYM1) shows a deep silicate absorption feature

(Okamoto et al., 2001) with the estimated Av ≃ 63 mag towards IRS2E, much higher than the average extinction in this region (Barbosa et al., 2016, 2008). IRS 2E shows the CO overtone feature from NIR spectroscopy, indicating the presence of accretion in the inner disk (Barbosa

et al., 2008). It is not known to be associated with any UCH II region and lacks sub-millimeter emissions. These characteristics are expected for very young massive stars, probably still in the hot core phase, transitioning to an UC H II region (Zapata et al., 2010). IRS 2E is the most embedded source in the region, and the analysis by Okamoto et al. (2001) suggests

that it is located behind the ionized gas of the cluster and the extinction is partly intrinsic to

the embedded source. The picture is consistent with our polarimetry measurements, which

are ﬁtted well with the absorptive component (panel 3 in Fig. 6-3), with the polarization PA

∼140◦. Lacy Jet: Lacy jet was ﬁrstly reported in Lacy et al. (2007) using the mid-IR [Ne II]

emission line and later conﬁrmed with the H77α radio recombination line (Ginsburg et al.,

2016). The molecular (CO) counterpart of the jet is subsequently reported in Ginsburg

et al. (2017), indicating a scenario that a molecular outﬂow becomes ionized when moving

−1 through a H II region. The velocity of the ambient gas is ∼60 km s and the velocity of the blueshifted jet is ∼-50 km s−1 from the position-velocity map (Ginsburg et al., 2016). Is the

polarization orientation related with the ionized jet? Unfortunately, the polarization direction

is neither parallel nor perpendicular to the direction of highly collimated ionized jet (Fig. 6-2

95 and Fig. 6-3). Instead, it preserves the polarization direction with W51d1 and IRS2E. The polarization percentage is relatively low in the Lacy jet area, and, as especially evident at

12.5µm, the polarization vectors do not have a preferred orientation, becoming chaotic, which

suggests that the ionized jet might be disturbing the B ﬁelds.

IRS 2W: Okamoto et al. (2001) relates the mid-IR source to the NIR source IRS2W. IRS 2W is the NIR counter part of the radio source W51d. Later Figuerdo et al. (2008) ﬁnd that

the mid-IR peak has an oﬀset from the NIR and the radio emission through the composite

image. The peak of mid-IR emission seems to coincide with the second peak of the radio

emission from W51d Okamoto et al. (2001). There might be multiple massive stars forming

in this region. IRS 2W is identiﬁed as a cometary UC H II region. It is probably the most evolved star in this region, still ionizing its surrounding region, but with the surrounding region

being dissipated enough for the photospheric features of the central star to become observable

(Barbosa et al., 2016). IRS 2W is spectroscopically classﬁed as a O3 star (Barbosa et al.,

2008). The observed polarization of the source is the net signal resulting from a combination of the emissive and absorptive polarization (panel 5 in Fig. 6-3). More discussion about the IRS

2W is in Section 3.4.

As a summary, we see a clear transition of dominant polarization mechanism from W51d1

to IRS2E, which might be explained by the relatively diﬀerent locations of these young stars

in the parenting cloud and therefore diﬀerent extinctions along our line of sight. We do not see an obvious correlation between the polarization PA and the direction of Lacy jet, and a

property also seen in other star formation regions, e.g., Hull et al. (2017). The narrow jet

might not have a detectable eﬀect in shaping the B ﬁeld morphology.

6.3.3 Magnetic Field Structure

We apply Aitken’s approach to polarimetry imaging data at three wavelengths, and the decomposition is computed for each 5×5 pixels (0′′.4×0′′.4) binned pixel to match the

observation resolution and further increase the signal-to-noise ratio. We derive absorptive and

emissive polarization pabs and pem with their corresponding PAabs and PAem.

96 Taking the classical dust alignment theory (Lazarian, 2007), in the presence of B ﬁelds, elongated dust grains tend to spin with their angular momentum and grain minor axis aligned

with the ﬁeld direction. Therefore the polarization from the diﬀerential extinction by dust

grains is believed to polarize the background starlight with directions parallel to the B

fields (θB =PAabs ), while emissive polarization, on the other hand, has polarized emission with a direction perpendicular to the B fields. From emissive polarization, the B field

morphology can be inferred by rotating the detected polarization of the thermal emission

◦ ◦ by 90 (θB =PAem+90 ). In Fig. 6-4, we display the θB,abs map in panel (a), and θB,em in panel (b), with the emissive vectors rotated by 90◦. Examples of the decomposition at two locations, denoted in Fig. 6-4 by 1 and 2 are shown in the Appendix.

The histograms of angles θB,abs and θB,em are plotted in Fig. 6-4 (c). The distribution

◦ of θB,abs , well approximated by a Gaussian, peaking ∼140 , is consistent with the previous

spectropolarimetry results from Smith et al. (2000). For comparison, the distribution of θB,em

is non-Gaussian due to a structure evident in the θB,em map.

We overlay the θB,abs and θB,em in Fig. 6-5, and we notice that in some regions, e.g., W51d, the B ﬁelds orientations of both components are well aligned with each other, which

means the B ﬁelds are uniform across the absorption and emission region along our line of

◦ sight. We select the vectors where the diﬀerence between θB,abs and θB,em are less than 20 and these vectors are plotted in Fig. 6-5 (b). 6.3.4 Gas Emission from VLA

The mid-IR emission region coincides well with the ionized gas emission mapped at radio

wavelengths. In Fig. 6-5 (b), we superimpose the 14 GHz continuum from VLA (Ginsburg

et al., 2016) on the θB map. Such long wavelength emission cannot be from dust, but rather it traces the ionized gas emission. VLA observations show the full image of a limb-brightened

cometary-shaped H II region of W51d. The ionized gas from the W51d region is expanding, and gas is escaping into the low density region. Cometary H II regions are mostly observed at the edges of molecular clouds (Steggles et al., 2017). The B ﬁeld seems to follow the gas

97 ﬂow direction quite closely. The radio emission has a cometary morphology with a bright head pointing towards the Lacy jet and a tail-like structure that extends away into the low density

region. The radio emission is correlated spatially with the mid-IR emission in Fig. 6-5

6.3.5 Magnetically Driven Gas Flow?

We focus on the B ﬁeld structure in the cometary-shaped H II region, W51d. UC H II

regions are coincide with massive OB stars, because massive stars emit extreme high-energy UV radiation that ionize the surrounding neutral gas (Steggles et al., 2017). There are two

major proposed models to explain the formation of the cometary shape of the H II region: the

champagne ﬂow and the bow shock model, or a combination of these(Steggles et al., 2017).

In the champagne flow model, the ionizing star is located at the edge of the cloud, and the ionized gas flows down the density gradient to the diffuse medium. In the bow shock model, an

ionizing star moves supersonically with respect to the cloud.

As seen in Fig. 6-5 (b), B field lines are parallel to the direction of ionized gas flow and follow the curvature of the ‘comet’ head. In W51d, the B field orientations from both

◦ components are well-aligned (∆B ≤20 ), which means that the ﬁeld is uniform across the absorption and emission region along our line of sight. The B ﬁeld lines are along the ambient

B ﬁeld of the whole cloud inferred from dichroic absorption (PA ∼140◦), shown by the yellow

vector at the center of the image. Whether the B ﬁeld lines shaped by the dynamics of the

gas, or is the gas ﬂow shaped by the B ﬁeld?

The MHD simulation of the champagne ﬂow by Gendelev & Krumholz (2012) ﬁnd

that when the B ﬁeld is perpendicular to the edge of the H II region, it ejects energy most

efficiently compared to no B field condition or B field along other directions (see Fig. 5 in their

paper). It is consistent with what we see in W51d, where the B ﬁeld is along the gas ﬂow and

perpendicular to the edge of this region. Similar relationships between B ﬁelds and gas ﬂows

have been observed in other H II region, e.g., Eswaraiah et al. (2017). The clear correlation

between the B field lines and ionized gas flow in W51d suggests that B fields play an important

role in regulating gas ﬂow in star formation region.

98 6.4 Summary

W51 IRS2 is an active star formation region with massive stars at different evolutionary stages and provides one of the best laboratories to study massive star formation. We have presented ∼0′′.4 imaging polarimetry observations of W51 IRS2 at three mid-IR filters. We apply the classical Aitken’s method to decompose the polarization data into absorption and emission components. With this approach we have determined the B field morphology in this region, and we compare this with the ionized gas flow determined using VLA. Our main results are as follows.

1. We measured the polarization degree and position angle of each mid-IR source in W51 IRS2 region, which contains W51d1, OKYM2, IRS 2E, Lacy jet, and IRS 2W. Among these sources, W51d1’s polarization is primarily emissive, whereas W51 IRS 2E’s polarization is primarily absorptive. The other sources show a combination of absorption and emission polarization. That might be explained by their diﬀerent locations in the cloud. The absorptive polarization is relatively uniform, with the PA value ∼140◦, consistent with previous spectropolarimetry measurements at larger scale.

2. The CO outflows and the well-collimated Lacy jet do not show an obvious correlation with the B field structure. We do see a drop in polarization around Lacy jet, which suggests that the narrow jet might perturb the B field lines.

3. Comparison of the B field map with the 14 GHz continuum from the VLA shows that ionized gas flows along the B field lines, consistent with the large scale B field of the envelope, which indicates that the gas flow is likely to be magnetically driven.

99 Table 6-1. Observation Log Imaging Filters ∆λ Date Integration FWHM (PSF) (µm) (µm) (UT) Time (s) (′′) Si2(8.7) 1.1 2014 June 18 509 0.40 Si4(10.3) 0.9 2014 June 18 509 0.35 Si6(12.5) 0.7 2014 June 9 761 0.40 Si2(8.7) 1.1 2013 Aug 20 582 0.40 Si4(10.3) 0.9 2013 Aug 20 582 0.38 Si6(12.5) 0.7 2013 Sep 1 761 0.36

Table 6-2. Polarization and Flux Measurements Object λ Flux Density p θ (µm) (Jy) (%) (◦) W51d1 8.7 1.46 (0.15) 6.91 (0.05) 149.30 (0.22) 10.3 1.89 (0.20) 12.32 (0.05) 150.05 (0.11) 12.5 3.95 (0.40) 10.66 (0.08) 148.80 (0.20 OKYM2 8.7 0.80 (0.20) 2.55 (0.04) 126.42 (0.46) 10.3 3.70 (0.42) 4.31 (0.02) 130.21 (0.13) 12.5 1.66 (0.40) 2.80 (0.06) 133.00 (0.70) IRS 2E 8.7 2.02 (0.20) 2.30 (0.02) 139.27 (0.23) 10.3 0.80 (0.08) 5.37 (0.15) 139.01 (0.80) 12.5 7.45 (0.80) 2.43 (0.02) 142.39 (0.20) Lacy Jet 8.7 0.97 (0.10) 1.48 (0.04) 151.42 (0.73) 10.3 3.71 (0.40) 3.58 (0.02) 140.98 (0.18) 12.5 3.67 (0.40) 0.86 (0.05) 154.16 (1.79) IRS 2W 8.7 1.76 (0.20) 3.10 (0.03) 209.62 (0.26) 10.3 2.35 (0.20) 4.39 (0.03) 190.39 (0.21) 12.5 7.37 (0.80) 4.48 (0.04) 212.80 (0.24) Values in parentheses are 1 σ uncertainties of measurements. All position angles are calibrated East from North.

100 12.0"

10.0" IRS 2W

W51 d1

08.0" Dec (J2000)Dec

06.0"

OKYM2 Lacy Jet

CO2-1 blue0-45 IRS 2E +14°31'04.0" CO2-1 red73-130 H77α

40.40s 40.20s 40.00s 39.80s 19h23m39.60s RA (J2000)

Figure 6-1. The W51 IRS2 region with the 10.3 µm CanariCam acquisition image as the background. CO outﬂows are in red and blue contours, adapted from Ginsburg et al. (2016, 2017). Radio recombination line H77 α is in heavy purple contours from Ginsburg et al. (2016). The mid-IR sources are labeled.

101 9

4 ) −

1 arcsec (Jy 5% SurfaceBrightness

5 )

2 − 1 (Jyarcsec 5% BrightnessSurface

2.08 41

1.04 20 ) − 0.0 (Jy arcsec (Jy δ SurfaceBrightness -1.04 5% 1

-2.08 -5.4 -2.7 0.0 2.7 5.4 δ

Figure 6-2. Polarization maps of W51 IRS2 at 8.7, 10.3, and 12.5 µm ﬁlters from top to the bottom. In each panel, the bluescale image is for the total intensity Stokes I, and the pink contours depict the polarized intensity Ip. Contours are (3, 4.2, 6, 9, 13.0) × σ, where 1σ is 0.01 Jy arcsec−2 (top panel), 0.02 Jy arcsec−2 (middle panel) and 0.04 Jy arcsec−2 (bottom panel). The polarization orientations are displayed with segments and plotted at the center of each 3×3 binned pixels, corresponding to 0′′.24×0′′.24 (1296 × 1296 AU at a distance of 5.4 kpc). We only show polarization measurements at locations where the total intensity Stokes I is greater than 8-σI . The dark red vector shows the direction of North.

102 0 0 0 0 p( ( 0

( p

0 0 0 0 0

( 0

0 (

0 0 0 0 0

Figure 6-3. Decomposition results of each source in W51 IRS2 region. From left to right, it shows W51d1, OKYM2, IRS2E, Lacy Jet, and IRS2W. The positions of these objects are noted in Fig. 6-1. For each object, ﬁtting results are given in polarization percentage p and PA θ. Errors are marginal compared to the values of measurements (Table 2). In each panel, the red dashed line is the absorptive component, the blue dotted line is emissive component and the black solid line is the ﬁtting result.

103 (a)

2.08 (b)

1.04 1

0.0

δ 2

-1.04 5%

-2.08 -5.4 -2.7 0.0 2.7 5.4 δ

Absorptive Component Emissive Component 80 (c)

60 N 40

0 50 100 150 200 Θ∘

Figure 6-4. (a) θB,abs map. The vectors show the B ﬁeld lines inferred from the absorptive components for each 5×5 pixels. The color scale is the 10.3µm image taken from CanariCam. (b) θB,em map. The vectors show the B ﬁeld lines inferred from the emissive components for each 5×5 pixels, which have rotated the emissive polarization vectors by 90◦. The two black dotted circles in the bottom panel show the locations of the two sample decompositions in Fig. 6-4. (c) Histogram of θB,abs in panel (a). It is peaking at ∼140◦. 104 2.08 (a)

1.04

0.0 δ

-1.04 5%

-2.08 -5.4 -2.7 0.0 2.7 5.4 δ

4.0

(b)

2.0

0.0 δ

-2.0 5%

14GHz continuum -4.0 -5.4 -2.7 0.0 2.7 5.4 δ

Figure 6-5. (a) Overlay of θB,abs and θB,em from Fig. 6-4. The underlaying bluescale image is the same as the 10.3µm emission image in Fig. 6-2. (b) Maps of B fields orientation where the B fields that give rise to the absorptive and emissive ◦ polarization are aligned, i.e., ∆B ≤20 . The radio emission at 14GHz is plotted at 0.015, 0.022, 0.032, and 0.048 Jy from Ginsburg et al. (2016). The yellow vector plotted at the center of the image is orientated at 140◦, corresponding to the inferred ambient B field from absorptive105 polarization component. CHAPTER 7 CONCLUSIONS

Magnetic ﬁelds play an important role in the formation and evolution of young stars.

Among all the observation techniques, mid-IR polarimetry provides an opportunity to make breakthroughs in understanding magnetic ﬁelds and dust properties in star formation regions.

The goal of this thesis is to advance our understanding of polarization in young stars, using

mid-IR polarimetry observations from CanariCam/GTC.

The works of this thesis are summarized as following:

In Chapter 3, I present high-resolution (0′′.4) mid-IR polarimetric images and spectra of WL 16, a Herbig Ae star at a distance of 125 pc. In a sample of disks we observed with

GTC/CanariCam, WL 16 is at one end of the spectrum, that the observed polarization is from foreground extinction. Mid-IR polarization of WL 16, mainly arises from aligned elongated dust grains present along the line of sight, suggesting a uniform morphology of polarization vectors with an orientation of 33◦(East from North) and a polarization fraction of ∼ 2.0%.

Using polarizations of WL 16 and Elias 29, a nearby polarization standard star, we constrain

the polarization eﬃciency, p10.3/A10.3, for the dust grains in the ρ Ophiuchus molecular cloud to be ≃ 1.0% mag−1.

In Chapter 4, I dig into the dust alignment theory and explore the possibility of alignment of a peculiar interstellar molecule, polycyclic aromatic hydrocarbons (PAHs). PAH are

ubiquitous in astrophysical environments, as revealed by their pronounced emission features

at 3.3, 6.2, 7.7, 8.6, 11.3, and 12.7 µm commonly ascribed to the C–H and C–C vibrational

modes. Although these features have long been predicted to be polarized, previous searches for

PAH polarization led to null or, at best, tentative detections. We report the deﬁnite detection of polarized PAH emission at 11.3 µm in the nebula associated with the Herbig Be star MWC

1080. We measure a polarization degree of 1.90.2%, which is unexpectedly high compared to

models. This poses a challenge on the current understanding of the alignment of PAHs, which

is required to polarize the PAH emission but thought to be substantially suppressed. PAH

106 alignment with a magnetic ﬁeld via a resonance paramagnetic relaxation process may account for such a high level of polarization.

In Chapter 5, I present the modeling work of mid-IR polarization of protoplanetary disks to

better interpret the observations. Polarization observations of protostars at mid-IR wavelengths

have revealed complex structures. Fully understanding of all the possible mechanisms to produce the detected polarization signal is important to subsequently infer the structures

of magnetic ﬁelds. Magnetically aligned non-spherical dust grains can partially polarize

background starlight or emit polarized emission at mid-IR wavelengths. Dust scattering has

been discussed recently to contribute signiﬁcant polarization if there exist dust grains with sizes

comparable to the observation wavelengths. We implement the dichroism and dust scattering to model mid-IR polarization under a set of magnetic ﬁelds conﬁgurations. The obtained linear

polarization maps of protoplanetary disks show distinguishable patterns, and can be compared

with the forthcoming mid-IR angular resolved polarization observations of young stars to derive

magnetic ﬁeld structures in disks. In Chapter 6, I present the high-resolution mid-IR polarimetric imaging of W51 IRS2, an

active massive star formation region. We examine the possible links among magnetic ﬁelds,

detected outﬂows, jets, and the gas ﬂow in the cometary Ultra Compact H II region, W51d.

Polarization vectors are neither parallel nor perpendicular to molecular outflows and jets. But in the region of W51d, we find the ionized gas flow direction follows the magnetic field lines, is consistent with the uniform magnetic field orientation of the cloud, suggesting that gas flow in the Ultra Compact H II region are likely to be magnetically driven.

The works of this thesis show that mid-IR polarimetry can be a signiﬁcant tool to understand the magnetic ﬁelds in star formation region, if the polarization mechanisms can be fully understood. On the other hand, if polarization shows the sign of dust scattering, it provides a unique insight into the properties of dust grains, e.g., size and composition.

107 7.1 Future Directions

Opportunities with ALMA. Mid-IR polarized emission is from (sub-)µm dust grains near the surface layer of the disk, because the disk is optically thick at mid-IR. Theoretical studies of dust alignment (Tazaki et al., 2017) suggest that (sub-)µm dust grains at the surface layer, where the gas density is lower and less affected by the gaseous damping, are more likely to be aligned in B fields. Conversely the larger dust grains in the mid-plane of the disk are less aligned by B fields but instead aligned by the radiation. On the other hand, polarized emission at (sub-)mm wavelengths is from dust grains at mid-plane, and combined with the mid-IR polarization data, one can map the polarization morphology from the surface to the mid-plane of the disk. (Sub)millimeter polarimetry can provide essential and complimentary information of B field to the mid-plane of the disk.

108 APPENDIX AITKEN’S METHOD

Polarization at the mid-IR wavelength, is generally regarded to be the result of a

combination of dichroic absorption and emission by aligned non-spherical dust grains. Since absorption and emission result in a 90◦diﬀerence in the polarization PA for the same grain

alignment, we want to separate them in order to derive the morphology of the B ﬁeld. In

Aitken et al. (2004), they propose an observing strategy to address this issue.

Silicate dust is an acceptable approximation for the mid-IR polarization, as used in Aitken

et al. (2004). This method needs to input the normalized pure absorptive polarization proﬁle and emissive polarization proﬁle. Eqs. A1 and A2 are the expressions of absorptive polarization

pabs and emissive polarization pem as a function of τ∥, optical depth in the direction of the dust

alignment and τ⊥, optical depth perpendicular to the direction of the dust alignment.

e−τ,∥ − e−τ,⊥ p = ≈ −(τ∥ − τ⊥)/2 (A–1) abs e−τ,∥ + e−τ,⊥ −τ,∥ −τ,⊥ (1 − e ) − (1 − e ) τ∥ − τ⊥ ≈ pem = − ∥ − ⊥ (A–2) (1 − e τ, ) + (1 + e τ, ) τ∥ + τ⊥

Thus we have pem ≈ pabs /τ. Aitken et al. (2004) assume that the observed spectropolarimetry of BN object in Orion is typical pure absorptive, and then they use τ from the observation of

Trapezium region of Orion to derive pure emissive polarization proﬁle as displayed in Fig. A-1.

The observed normalized Stokes parameters, q, u, are assumed to be the linear combination of Stokes parameters arising from dichroic absorption and emission as shown in the following relations.

q(λ) = qabs (λ) + qem(λ) = Apabs + Bpem (A–3)

u(λ) = uabs (λ) + uem(λ) = Cpabs + Dpem (A–4)

Once we have the polarization measurements for at least two wavelengths, it is feasible to separate absorption and emission polarization components.

109 Figure A-1. Polarization profiles. The solid line is the absorptive polarization profile and the dashed line is the emissive polarization profile adopted from Aitken et al. (2004).

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118 BIOGRAPHICAL SKETCH Han Zhang was born in Jining, hometown of the ancient Chinese philosopher Confucius,

China, 1991. Her childhood dream was to be a great artist like Leonardo da Vinci. After living in her hometown for 18 years, she went to Beijing and became a student in astronomy at

Beijing Normal University, one of the four universities that had astronomy majors in China at that time. She started a cosmology research project when she was a sophomore and she found that she enjoyed exploring the unknown and solving problems. After graduation from college in 2013, she moved to Gainesville, FL, to pursue her Ph.D. degree in astronomy, under the supervision of Prof. Charles M. Telesco. She very much enjoyed her life in Gainesville and liked the small town a lot. She got opportunities to travel around the world during the ﬁve years in graduate school. She received her Ph.D. from the University of Florida in the summer of 2018.

After she completes her Ph.D., she will continue pursuing her dream as an astronomer.

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