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Magnetic fields are thought to influence the formation and evolution ofevolved star envelopes. Thermal dust polarization from magnetically alignedgrains is potentially a powerful tool for probing magnetic fields and dustproperties in these circumstellar environments. In this paper, we presentnumerical modeling of thermal dust polarization from the envelope of IK Tauusing the magnetically enhanced radiative torque (MRAT) alignment theoryimplemented in our updated POLARIS code. Due to the strong stellar radiationfield, the minimum size required for RAT alignment of silicate grains is $\sim0.005 - 0.05\,\rm\mu m$. Additionally, ordinary paramagnetic grains can achieveperfect alignment by MRAT in the inner regions of $r < 500\,\rm au$ due tostronger magnetic fields of $B\sim 10$ mG - 1G, producing thermal dustpolarization degree of $\sim 10\,\%$. The polarization degree can be enhancedto $\sim 20-40\%$ for grains with embedded iron inclusions. We also find thatthe magnetic field geometry affects the alignment size and the resultingpolarization degree due to the projection effect in the plane-of-sky. We alsostudy the spectrum of polarized thermal dust emission and find the increasedpolarization degree toward $\lambda > 50\,\rm\mu m$ due to the alignment ofsmall grains by MRAT. Furthermore, we investigate the impact of rotationaldisruption by RATs (RAT-D) and find the RAT-D effect cause a decrease in thedust polarization fraction. Finally, we compare our numerical results withavailable polarization data observed by SOFIA/HAWC+ for constraining dustproperties, suggesting grains are unlikely to have embedded iron clusters andmight have slightly elongated shapes. Our modeling results suggest furtherobservational studies at far-infrared/sub-millimeter wavelengths to understandthe properties of magnetic fields and dust in AGB envelopes.

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