Our aim is to study the polarization of thermal dust emission to see if the alignment of grain by radiative torques could explain the observed relation between the degree of polarization and the intensity in dense cores. Predictions are made for polarimetry observations with the Planck satellite. Our results are based on model clouds derived from MHD simulations of magnetized turbulent flows, while the continuum radiative transfer problem is solved with Monte Carlo methods in order to estimate the three-dimensional distribution of dust emission and the radiation field strength affecting the grain alignment. The influence of grain alignment efficiency is examined in the calculated polarization maps. We are able to reproduce the P/I-relation with the grain alignment by radiative torques. The decrease in intrinsic polarization and total emission means that sub-mm polarimetry carries only little information about the magnetic fields in dense cores with high visual extinction. The interpretation of the observations will be further complicated by the unknown magnetic field geometry and the fact that what is observed as individual cores may, in fact, be a superposition of several density enhancements. According to our calculations, Planck will be able to map dust polarization reliably when A_V > 2 mag at spatial resolution of 15.
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