Barnett relaxation in thermally rotating grains

We present an exact formulation of the physics of Barnett relaxation. Our formulation is based on a realistic kinetic model of the relaxation mechanism, which includes the alignment of the grain angular momentum in body coordinates by Barnett dissipation, disalignment by thermal fluctuations, and coupling of the angular momentum to the gas via gas damping. We solve the Fokker-Planck equation for the measure of internal alignment using numerical integration of the equivalent Langevin equation for Brownian rotation. The accuracy of our results is calibrated by comparing our numerical solutions with exact analytic results obtained for special cases. We describe an analytic approximation for the measure of alignment that fits our numerical results for cases of practical interest.