Polarized dust emission of magnetized molecular cloud cores

We compute polarization maps for molecular cloud cores modeled as magnetized singular isothermal toroids, under the assumption that the emitting dust grains are aspherical and aligned with the large-scale magnetic field. We show that, depending on the inclination of the toroid with the line-of-sight, the bending of the magnetic field lines resulting from the need to counteract the inward pull of gravity naturally produces a depolarization effect toward the centre of the map. We compute the decrease of polarization degree with increasing intensity for different viewing angles and frequencies, and we show that an outward increasing temperature gradient, as expected in starless cores heated by the external radiation field, enhances the decrease of polarization. We compare our results with recent observations, and we conclude that this geometrical effect, together with other mechanisms of depolarization, may significantly contribute to the decrease of polarization degrees with intensity observed in the majority of molecular cloud cores. Finally, we consider the dependence of the polarization degree on the dust temperature gradient predicted for externally heated clouds, and we briefly comment on the limits of the Chandrasekhar-Fermi formula to estimate the magnetic field strength in molecular cloud cores.