The Role of Magnetic Fields in Star Formation, from Cloud to Disk Scales

In this thesis I present three works concerning the modeling of polarized emission in star forming environments.
Apropos to the thesis title, each of these projects focuses on a different physical scale, spanning the range from a molecular cloud (~5 pc), to Class 0/I disk-envelope systems (~1000+ au), to a Class II evolved protoplanetary disk (~200 au).
In each project I develop a model for the 3-dimensional physical environment of interest, either through analytic modeling or with magnetohydrodynamic (MHD) simulations, then use radiative transfer software to simulate emission that an observer would see from a detector placed some appropriate distance away from the source.

In Chapter 1, I provide a concise summary of the astrophysical picture of star formation theory.
I also discuss some of the key physics behind the magnetohydrodynamics that underpin the simulation work that was used as the basis for many of my synthetic observations.
I then go on to introduce the observational techniques that are used to probe magnetic fields, with particular focus on the methods modeled in my thesis.
This includes linearly polarized far-infrared and (sub)millimter emission from dust grains that align orthogonal to the magnetic field and the circularly polarized line emission that arises from the splitting of energy levels (i.e., the Zeeman Effect) for some molecular species in the presence of a magnetic field.
To provide observational context, this is followed by a brief introduction to several observing facilities that have been used to study polarization in star forming environments.
Finally, I describe the general modeling approach and workflow that I use for each of my projects.

In Chapter 2, I present modeled results for Zeeman Effect observations of a typical protoplanetary disk.
First we construct an analytic 3D disk model based on AS 209, a typical nearby Class II disk with known emission of cyanide (CN, a molecular species that is sensitive to the Zeeman Effect).
We then use the POLARIS radiative transfer code to produce synthetic circular polarization observations for several disk setups and observational scenarios to test how different parameterizations affect the results.
We find that different magnetic field configurations (e.g., purely vertical versus purely toroidal) are distinguishable based on the morphology of the circularly polarized emission.
Spatially resolved Stokes V channel maps are particularly useful for this purpose.
We also note that the traditional method for inferring magnetic field strength from Zeeman observations, by fitting the Stokes V signal to the derivative of the Stokes I, should be approached with caution in protoplanetary disk environments due to substructure in the magnetic field.
This work was in part motivated by the newly available circular polarization mode on the Atacama Large Millimeter/submillimeter Array (ALMA), so we also beam convolve our results to offer a more direct comparison with anticipated data.

In Chapter 3, I present molecular cloud scale linear polarization modeling work that I performed in collaboration with the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST) team.
We compare the orientation of magnetic field structure as inferred from synthetic dust polarization with the orientation of molecular gas structure inferred from radiative transfer simulations of rotational line emission in 3-dimensional, turbulent collapsing-cloud MHD simulations.
To quantitatively compare the results for each of the nine molecular tracers we simulated, we apply the histogram of relative orientations (HRO) technique.
We then beam convolve our results and compare with observational work done by the BLAST team of the Vela C molecular cloud.
Our simulated HROs suggest that Vela C data are consistent with a dynamically important magnetic field.

In Chapter 4, I present more Zeeman Effect CN modeling, this time using MHD models of the envelope of a stellar mass protostar and a massive protostar.
One of the principal conclusions of our disk-scale Zeeman work (Chapter 2 of this thesis) is that toroidal magnetic substructure in the disk can significantly reduce the intensity of the circularly polarized emission due to cancellation in the line-of-sight component of the magnetic field.
This is liable to make the task of detecting disk-scale Zeeman emission with current instruments (i.e., ALMA) a very difficult enterprise.
However, in the envelopes of younger (Class 0/I) sources we expect the magnetic field to perhaps be more uniform, subverting this complication.
In this work we find that, indeed, the envelopes of our simulated disk-envelope systems have more favorable conditions for producing detectable emission with fractional polarization above the nominal 1.8% limit of the ALMA circular polarimeter.
This suggests that Zeeman programs that target the envelopes of deeply-embedded sources, especially those with known CN emission, can be a fruitful way to access magnetic field information in young stellar objects.

In Chapter 5, I give a short summary of the thesis as a whole and discuss some potential related avenues for future study.