Davis-Greenstein alignment of oblate spheroidal grains

We present extensive calculations on the efficiency of grain alignment by t he Davis-Greenstein (DG) mechanism. We model the grains as oblate spheroids with arbitrary axis ratios. Our description of the grain dynamics includes (i) magnetic dissipation and the inverse process driven by thermal fluctua tions in the grain magnetization, (ii) gas-grain collisions and thermal eva poration of molecules from the grain surface, (iii) the transformation of r otational energy into heat by the Barnett effect and the inverse process dr iven by thermal fluctuations, and (iv) rapid Larmor precession of the grain angular momentum about the interstellar magnetic held. For ordinary parama gnetic grains, we calculate the Rayleigh reduction factor, R, for > 1000 co mbinations of the three dimensionless parameters which characterize the ali gnment. For superparamagnetic grains, we calculate R from an exact analytic solution for the relevant distribution function. Our results are compared with classical studies of DG alignment, which did not include the Barnett e ffect. We calibrate the accuracy of a recently proposed perturbative approx imation, which includes the Barnett effect, and show that it yields R value s with a mean error of approximate to 17 per cent.