Theoretical models of polarized dust emission from protostellar cores

We model the polarized thermal dust emission from protostellar cores that are assembled by supersonic turbulent flows in molecular clouds. Self-gravitating cores are selected from a three-dimensional simulation of supersonic and super-Alfvénic magnetohydrodynamic (MHD) turbulence. The polarization is computed in two ways. In model A it is assumed that dust properties and grain alignment efficiency are uniform; in model B it is assumed that grains are not aligned at visual extinction larger than A_V;0 = 3 mag, consistent with theoretical expectations for grain alignment mechanisms. Instead of using a specific set of grain properties, we adopt a maximum degree of polarization P_max = 15%. Results are therefore sensitive mainly to the topology of the magnetic field (model A) and to the gas distribution that determines the distribution of A_V (model B). Furthermore, the radiative transfer in the MHD model is solved with a non-LTE Monte Carlo method, to compute spectral maps of the J = 1-0 transition of CS. The CS spectral maps are used to estimate the turbulent velocity, as in the observations. The main results of this work are the following: (1) Values of P between 1% and 10% (up to almost P_max) are typical, despite the super-Alfvénic nature of the turbulence. (2) A steep decrease of P with increasing values of the submillimeter dust continuum intensity I is always found in self-gravitating cores selected from the MHD simulations if grains are not aligned above a certain value of visual extinction A_V,0 (model B). (3) The same behavior is hard to reproduce if grains are aligned independently of A_V (model A). (4) The Chandrasekhar-Fermi formula, corrected by a factor F ≈ 0.4, provides an approximate estimate of the average magnetic field strength in the cores. Submillimeter dust continuum polarization maps of quiescent protostellar cores and Bok globules have recently been obtained. They always show a decrease in P with increasing value of I consistent with the predictions of our model B. We therefore conclude that submillimeter polarization maps of quiescent cores do not map the magnetic field inside the cores at visual extinction larger than A_V,0 ≈ 3 mag. The use of such maps to constrain models of protostellar core formation and evolution is questionable. This conclusion suggests that there is no inconsistency between the results from optical and near-IR polarized absorption of background stars and the observed polarization of submillimeter dust continuum from quiescent cores. In both cases, grains at large visual extinction appear to be virtually unaligned.