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 (IA) 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 IA of micron-sized and very large grains above $10\mu m$ (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 is still lacking. In this paper, we update the POLARIS code and use it to perform synthetic dust polarization modeling for MHD simulations of an intermediate-mass YSO. Results will be post-processed with CASA to confront ALMA polarimetric observations. We found that to reproduce the high polarization degree of $p \sim 5-30\%$ observed in protostellar envelopes by ALMA, micron-sized and VLGs must contain iron inclusions with $N_{\rm cl} \sim 5 - 10^{3}$ iron atoms per cluster, assuming $30\%$ of iron abundance locked inside dust grains under the cluster form. Inside the inner $\sim 500$ au region, inelastic relaxation must participate in driving the grain internal alignment, and grains must contain larger iron inclusions of $N_{\rm cl} \sim 10^{2}-10^{4}$ and grow beyond $\geq 10\mu m$ to reproduce $\sim 3-10\%$ of dust polarization observed by ALMA. But given such a combination, the internal alignment and MRAT efficiency acting on VLGs still decrease toward the center, inducing the decrease of $p(\%)$ with increasing gas density, reaching $p \sim 1\%$ inside the disk.