Physical modelling of dust polarization from magnetically enhanced radiative torque alignment in protostellar cores withpolaris

Magnetic fields ($\textbf{B}$) are an important factor that controls the star formation process. The leading method to observe $\textbf{B}$ is using polarized thermal emission from dust grains aligned with $\textbf{B}$. However, in dense environments such as protostellar cores, dust grains may have inefficient alignment due to strong gas randomizations, so that using dust polarization to trace $\textbf{B}$ is uncertain. Hoang $\&$ Lazarian (2016) demonstrated that the grain alignment by RAdiative Torques is enhanced if dust grains contain embedded iron inclusions. Here we extend POLARIS code to study the effect of iron inclusions on grain alignment and thermal dust polarization toward a protostellar core, assuming uniform magnetic fields. We found that paramagnetic grains produce a low polarization degree of $p \sim 1\%$ in the envelope and negligible $p \ll 1\%$ in the central region due to the loss of grain alignment. In contrast, grains with a high level of iron inclusions can have perfect alignment and produce high $p \sim 40\%$ in the envelope and low $p \leq 10\%$ in the central region. Grains with a moderate level of iron inclusions induce the polarization flipping from $\textbf{P}$ $\parallel$ $\textbf{B}$ at millimeter to $\textbf{P}$ $\perp$ $\textbf{B}$ at submillimeter due to the change in the internal alignment caused by slow internal relaxation. The weak alignment of very large grains of $a \geq 10\mu m$ reduces the polarization by dichroic extinction at submillimeter wavelengths. We found a positive correlation between p and the level of iron inclusions, which opens a new window to constrain the abundance of irons locked in dust through dust polarimetry.