Radiative torques on interstellar grains. III. Dynamics with thermal relaxation

In the previous papers in this series, we found that radiative torques can play a major role in the alignment of grains with the interstellar magnetic field. Since the radiative torques can drive the grains to suprathermal rotational speeds, in previous work we made the simplifying assumption that the grain principal axis of greatest moment of inertia is always parallel to the grain angular momentum. This enabled us to describe many of the features of the grain dynamics. However, this assumption fails when the grains enter periods of thermal rotation, which occur naturally in the radiative torque alignment scenario. In the present paper we relax this assumption and explore the consequences for the grain dynamics. We develop a treatment to follow the grain dynamics, including thermal fluctuations and "thermal flipping," and show results for one illustrative example. By comparing with a treatment without thermal fluctuations, we see that inclusion of thermal fluctuations can lead to qualitative changes in the grain dynamics. In future installments in this series, we will use the more complete dynamical treatment developed here to perform a systematic study of grain alignment by radiative torques and test the model against observations of starlight polarization and polarized thermal emission from dust.