B-fields And dust in interstelLar fiLAments using Dust POLarization (BALLAD-POL): II. Testing the Radiative Torque Paradigm in Musca and OMC-1

Polarization of starlight and thermal dust emission caused by aligned dust grains is a valuable tool to characterize magnetic fields (B-fields) and constrain dust properties. However, the physics of grain alignment is not fully understood. To test the popular paradigm of radiative torque (RAT) theory, including RAT alignment (RAT-A) and disruption (RAT-D), we use dust polarization data observed by {\it Planck} and SOFIA/HAWC+ toward two filaments with contrasting physical conditions: Musca, a quiet filament, and OMC-1, a highly dynamic filament due to feedback. We analyze various relations of the observed polarization fraction, $P$, with gas column density, $\NHt$, dust temperature, $\Td$, and polarization angle dispersion function, $\S$. We found that $P$ decreases with increasing $\S$ and increasing $\NHt$, as expected from RAT-A. On the other hand, the $P-\Td$ relation is more complicated; it is a linear correlation at low $\Td$ but turns into an anti-correlation when $\Td$ reaches a certain high value. Next, we compute the polarization fraction on a pixel-by-pixel with B-fields in the plane of the sky using the DustPOL code based on RAT, incorporate the depolarization effect by B-field tangling using $\S$, and compare the realistic polarization model with observations of Musca and OMC-1. For Musca with well-ordered B-fields, our numerical model reproduces the decline of $P$ toward the filament spine (aka. polarization hole), having high $\NHt$ and low $\Td$, indicating the loss of grain alignment efficiency due to RAT-A. For OMC-1, with stronger B-field variations and higher $\Td$, our model can reproduce the observed $P-\Td$ and $P-N(\rm H_{2})$ relations only if the depolarization effect resulting from B-field tangling and RAT-D effect are taken into account. Our results provide more robust observational evidence for the RAT paradigm, particularly the recently discovered RAT-D.