Origins of (sub)Millimeter Disk Polarization

Magnetic fields are believed to play a crucial role in the dynamics and evolution of protoplanetary disks. Polarized (sub)millimeter dust emission has been established as a reliable tool to probe the magnetic field on the relatively large scales of molecular clouds, dense star-forming cores and protostellar envelopes, based on the well-known mechanism of magnetically aligned grains. However, this canonical mechanism fails to explain the first spatially resolved disk polarization detected in a T Tauri star, HL Tau, through the Combined Array for Research in Millimeter-wave Astronomy (CARMA). We are thus motivated to search for alternative explanations. The goal of this thesis is to explore the origins of the disk polarization, with an emphasis on dust scattering.

We start by developing a semi-analytic theory for the dust scattering-induced polarization in a disk inclined to the line of sight under the simplification that the disk is both optically and geometrically thin. We show that dust scattering can naturally explain the two main features of the HL Tau disk polarization observed by CARMA: (1) the polarized intensity distribution is elongated along the major axis, and (2) the polarization orientation is along the minor axis. Both are unavoidable consequences of a simple geometric effect. The broad agreement between the simplified theory and the CARMA data played an important role in establishing dust scattering as a viable alternative to magnetic grain alignment for producing disk polarization. Furthermore, in order to produce polarization at the observed level of about 1%, the scattering grains must have sizes of order several tens of um, which are much larger than those in the general interstellar medium (of order 0.1 um or less). The dust polarization is thus a powerful tool for probing the grain growth in the disk, the crucial first step towards the formation of planetesimals and ultimately planets.

We then study the interplay between the polarization produced by dust scattering and that by magnetically aligned (ellipsoidal) grains under the same simplification. The scattering of (sub)millimeter light by aligned ellipsoidal grains is computed through the so-called “electrostatic approximation.” We show that the interplay can produce polarization patterns that are very different from those produced by the two mechanisms individually, including a “butterfly-shaped” pattern with two “null” (zero polarization) points. We find tentative evidence for this composite pattern in the Very Large Array (VLA) 8 mm polarization data of the deeply embedded protostar NGC 1333 IRAS4A1. If confirmed, it would imply not only that magnetic fields exist on the disk scale but also that they are strong enough to align the large grains responsible for the 8 mm emission.

We quantify the effects of the optical depth on the scattering-induced polarization through a combination of analytic illustration, approximate semi-analytic modeling using formal solutions to the radiative transfer equation, and Monte Carlo simulations. We find that for an inclined, optically thick disk with a finite geometric thickness, the near side will be brighter than the far side in polarized intensity. It is a robust signature that can be used to distinguish the scattering-induced polarization from that by other mechanisms, such as aligned grains. This asymmetry is weaker in a well-settled (dust) disk with a smaller thickness. As such, it can be used to probe the dust settling, a process important for the grain growth and dust dynamics.

The last part of the thesis presents ongoing work on another mechanism for disk polarization, the radiative alignment. It was recently proposed as an explanation of the elliptical polarization pattern observed by the Atacama Large Millimeter/submillimeter Array (ALMA) in the HL Tau disk at 3 mm. We show that the radiative alignment produces a circular (or concentric), rather than elliptical, polarization pattern. An elliptical pattern can be produced if the dust grains are aligned aerodynamically.However, both mechanisms predict a strong azimuthal variation in the polarized intensity, which is not observed. We conclude that neither of these two mechanisms alone can explain the data and the origin of the ALMA 3 mm polarization in HL Tau remains a mystery. The flood of ALMA data and relatively early stage of theoretical development should make the field of disk polarization an exciting area of research that is poised for rapid growth.