Synthetic Modelling of Polarized Dust Emission in Intermediate-Mass YSOs: I: Constraining the Role of Iron Inclusions and Inelastic Relaxation on Grain Alignment with ALMA Polarization

Iron inclusions embedded inside dust grains play a crucial role in both internal alignment via Barnett relaxation and external alignment via the MAgnetically Enhanced RAdiative Torque (MRAT) mechanism. Moreover, inelastic relaxation is predicted to dominate over Barnett relaxation in driving the internal alignment of micron-sized and very large grains above 10μ m (VLGs). Yet, a detailed modeling of polarized thermal dust emission from Class 0/I Young Stellar Objects (YSOs) taking into account these effects and their observational constraints are still lacking. In this paper, we perform synthetic dust polarization modeling for MHD simulations of an intermediate-mass YSOs using our updated POLARIS code developed by Giang et al. (2022). Synthetic polarization results are then post-processed with CASA to confront ALMA observations. We found that to reproduce the high polarization degree of p ~ 5-30% observed in protostellar envelopes by ALMA, micron-sized and VLGs must contain iron inclusions with Ncl ~ 5 - 10⁴ iron atoms per cluster, assuming $30%$ of iron abundance locked inside dust grains under the cluster form. Inside the inner ~ 500 au region, it requires inelastic relaxation, larger iron inclusions of Ncl ~ 10²-10⁴, and grain growth beyond ≥ 10μ m to reproduce ~ 3-10% of polarization observed by ALMA. But given such a combination, the internal alignment and MRAT efficiency acting on VLGs still decrease toward the center, which produces the decrease of $p(%)$ with increasing gas density, reaching p ~ 1% inside the disk. Additionally, our results show that the high polarization by ALMA toward YSOs is not totally an artifact caused by the interferometric filtering, but it could be explained by the efficient magnetic alignment of SPM grains by MRAT mechanism.