MNRAS 000,1–17 (0000) Preprint 13 April 2021 Compiled using MNRAS LATEX style file v3.0 Characterising the Magnetic Fields of Nearby Molecular Clouds using Submillimeter Polarization Observations Colin H Sullivan,1,2¢ L. M. Fissel,2,3 P. K. King,1,4,5 C.-Y. Chen,1,4 Z.-Y. Li,1 and J. D. Soler6 1Department of Astronomy, University of Virginia, Charlottesville VA, 22904 2National Radio Astronomy Observatory, Charlottesville, VA, 22904 3Department of Physics, Engineering Physics, and Astronomy, Queen’s University, Kingston, ON, Canada, K7L 3N6 4Johns Hopkins University Applied Physics Laboratory, Laurel, MD, 20723 5Lawrence Livermore National Laboratory, Livermore, 7000 East Ave, Livermore, CA 94550, USA 6Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany Accepted 2021 February 23. Received 2021 February 21; in original form 2019 October 30 ABSTRACT Of all the factors that influence star formation, magnetic fields are perhaps the least well understood. The goal of this paper is to characterize the 3D magnetic field properties of nearby molecular clouds through various methods of statistically analyzing maps of polarized dust emission. Our study focuses on nine clouds, with data taken from the Planck Sky Survey as well as data from the BLASTPol observations of Vela C. We compare the distributions of polarization fraction (p), dispersion in polarization angles (S), and hydrogen column density (#H) for each of our targeted clouds. To broaden the scope of our analysis, we compare the distributions of our clouds’ polarization observables with measurements from synthetic polarization maps generated from numerical simulations. We also use the distribution of polarization fraction measurements to estimate the inclination angle of each cloud’s cloud- scale magnetic field. We obtain a range of inclination angles associated with our clouds, ◦ ◦ varying from 16 to 69 . We establish inverse correlations between ? and both S and #H in almost every cloud, but we are unable to establish a statistically robust S vs #H trend. By comparing the results of these different statistical analysis techniques, we are able to propose a more comprehensive view of each cloud’s 3D magnetic field properties. These detailed cloud analyses will be useful in the continued studies of cloud-scale magnetic fields and the ways in which they affect star formation within these molecular clouds. Key words: Polarization – Magnetic Fields – ISM: Clouds 1 INTRODUCTION difficult. The long observation times required also make Zeeman observations impractical for producing cloud-scale maps. Molecular Clouds (MCs) are the birthplaces of stars. These clouds are typically cold (10-30K) and have dense sub-regions within them As an alternative, linearly polarized thermal dust emission is that may collapse under gravity to form stars. The evolution and commonly used to create large-scale maps to study MC-scale mag- arXiv:2104.04673v1 [astro-ph.GA] 10 Apr 2021 efficiency of star formation within MCs are regulated by a number of netic fields. This technique relies heavily on the orientation of their factors, primarily gravity, turbulence, and magnetic fields (McKee dust grains, as dust grains tend to align with their minor axes ori- & Ostriker 2007). Among these physical processes, magnetic fields ented parallel to the local magnetic field lines. This alignment is are perhaps the least well understood, and this is largely because most likely caused by radiative torques from the local radiation magnetic fields are very difficult to observe directly. Although the field (see Andersson et al. 2015 for a review). This process cre- line-of-sight component of a magnetic field can be measured by ates a net linear polarization orientation of the emitted light that is Zeeman spectral line splitting (Crutcher 2012), the width of the perpendicular to the magnetic field direction projected on the sky. line splitting is typically much less than the thermally broadened By measuring linear polarization of the sub-mm radiation emit- line width, which makes detection of Zeeman splitting extremely ted by dust grains within the molecular cloud and rotating the polar- ization orientation by 90◦, we can map the corresponding magnetic field orientation projected on the plane of sky. These measured ori- entation values represent the averaged magnetic field orientation ¢ E-mail: [email protected] within the volume of the cloud probed by the telescope beam, and © 0000 The Authors 2 C. Sullivan et al. are most sensitive to regions of high dust emissivity and efficient generated using the Athena MHD code (Chen et al. 2016), with the grain alignment. goal of reproducing the correlations between ?, #H, and S found In addition to the inferred plane-of-sky magnetic field orienta- in observations of the Vela C GMC in Fissel et al.(2016). In order tion, there are several other polarization parameters that can be used to reproduce the high levels of S, large range of ?, and the level to study the structure and geometry of magnetic fields in molecular of anti-correlation between ? and S, the authors speculated that clouds. The polarization fraction (?) of the emission is the frac- Vela C must have either a weak magnetic field or a stronger field tion of observed radiation that is linearly polarized. ? is sensitive that is highly inclined with respect to the plane of the sky. Other to the efficiency with which grains are aligned with respect to the studies analyzing the orientation of cloud structure with respect to magnetic field, the degree of disorder in the plane-of-sky magnetic the magnetic field (Soler et al. 2017, Fissel et al. 2019) have sug- field within the dust column probed by the polarimeter, and the gested that Vela C has a reasonably strong cloud-scale magnetic inclination angle of the cloud’s magnetic field with respect to the field, and so it seems more likely that Vela C’s magnetic field must plane of the sky. In addition, the local polarization angle dispersion be significantly inclined with respect to the plane of the sky (King (S) is used to measure the disorder in the projected magnetic field et al. 2018, Chen et al. 2019). orientation at a given location in the cloud (Fissel et al. 2016). In Here, we extended the comparisons of the ?, #H, and S dis- addition to these polarimetric properties, we also consider the hy- tributions to a larger sample size of molecular clouds by including drogen column density (#H) in our analysis. This quantity is used Planck 353 GHz polarization observations of eight nearby clouds. as a proxy for the total mass surface density of our clouds, and is In this way, we will determine if the results of King et al.(2018) thus useful for characterising the gas substructure of MCs. are consistent with a larger sample size of nearby MCs. The eight Lower resolution polarization studies, such as the 1◦ reso- Planck clouds included in this study are all nearby and relatively low 5 lution, all-sky analysis of Planck Collaboration XIX(2015), or the mass, while Vela C is more distant and massive ("Vela ¡ 10 " ). BLASTPol 20.5 resolution study of the Vela C giant molecular cloud Significantly higher resolution (2.50 as opposed to 150 for the Planck (GMC) (Fissel et al. 2016), have identified several correlations be- observations) means that Vela C has a linear resolution almost equal tween p, S, and #H. The first trend is a negative correlation between to the closest of the Planck clouds. Linear resolution and other such p and S: as S increases, p decreases. This trend could be related cloud-specific quantities are listed in Table1. to the differences in the 3D geometry of the magnetic field in dif- In this paper, we use our increased sample size to provide more ferent parts of the cloud as ? is proportional to cos2 W, where W is stringent tests of the analyses presented in King et al.(2018, 2019), the inclination angle of the magnetic field with respect to the plane Chen et al.(2019), Fissel et al.(2019). We also compare our results of the sky (Hildebrand 1988). For cloud sightlines where the mag- to multiple intermediate-results Planck papers, specifically Planck netic field is nearly parallel to the line-of-sight, ? values tend to Collaboration XX et al.(2015), Planck Collaboration XIX(2015) be lower, and upon projection onto the plane-of-sky the angles can and Planck Collaboration et al.(2020). This paper is organized as vary greatly between adjacent sightlines, leading to large values of follows: Section2 - Observations and Data Reduction; Section3 S. - Comparison of polarization properties between different clouds; In addition, a weak, disordered magnetic field provides little Section4 - Comparison with synthetic polarization observations resistance to turbulent motions, and can be easily driven to a highly of 3D MHD simulations reported in King et al.(2018); Section disordered state, which produces large values for S. This in turn 5 - Conclusions. In AppendixA, we discuss how our results are leads to significantly lower p values. Strong magnetic fields are able influenced by different methods selecting cloud sightlines. to resist turbulent motions that are perpendicular to their field lines, and thus tend to have lower values for S. Low p and high S values can therefore indicate a weak/disordered magnetic field and/or a 2 OBSERVATIONS & DATA REDUCTION nearly line-of-sight magnetic field orientation, while high p values and low S values can indicate a strongly ordered magnetic field In this paper, we analyze thermal dust emission polarization obser- and/or a nearly plane-of-sky magnetic field orientation. vations of nine nearby MCs. For eight of the clouds we use 353 GHz The second observed trend that we will investigate is the anti- polarization maps from the Planck satellite, first presented in Planck correlation between polarization fraction ? and hydrogen column Collaboration XXXV(2016).