Numerical modeling of thermal dust polarization from aligned grains in the envelope of evolved stars with updated POLARIS

Magnetic fields are thought to influence the formation and evolution of evolved star envelopes. Thermal dust polarization from magnetically aligned grains is potentially a powerful tool for probing magnetic fields and dust properties in these circumstellar environments. In this paper, we present numerical modeling of thermal dust polarization from the envelope of IK Tau using the magnetically enhanced radiative torque (MRAT) alignment theory implemented in our updated POLARIS code. Due to the strong stellar radiation field, the minimum size required for RAT alignment of silicate grains is $\sim 0.005 - 0.05\,\rm\mu m$. Additionally, ordinary paramagnetic grains can achieve perfect alignment by MRAT in the inner regions of $r < 500\,\rm au$ due to stronger magnetic fields of $B\sim 10$ mG - 1G, producing thermal dust polarization degree of $\sim 10\,\%$. The polarization degree can be enhanced to $\sim 20-40\%$ for grains with embedded iron inclusions. We also find that the magnetic field geometry affects the alignment size and the resulting polarization degree due to the projection effect in the plane-of-sky. We also study the spectrum of polarized thermal dust emission and find the increased polarization degree toward $\lambda > 50\,\rm\mu m$ due to the alignment of small grains by MRAT. Furthermore, we investigate the impact of rotational disruption by RATs (RAT-D) and find the RAT-D effect cause a decrease in the dust polarization fraction. Finally, we compare our numerical results with available polarization data observed by SOFIA/HAWC+ for constraining dust properties, suggesting grains are unlikely to have embedded iron clusters and might have slightly elongated shapes. Our modeling results suggest further observational studies at far-infrared/sub-millimeter wavelengths to understand the properties of magnetic fields and dust in AGB envelopes.