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Davis-Greenstein alignment of oblate spheroidal grains

We present extensive calculations on the efficiency of grain alignment by the Davis-Greenstein 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 fluctuations in the grain magnetization; (ii) gas-grain collisions and thermal evaporation of molecules from the grain surface; (iii) the transformation of rotational energy into heat by the Barnett effect and the inverse process driven by thermal fluctuations; and (iv) rapid Larmor precession of the grain angular momentum about the interstellar magnetic field. For ordinary paramagnetic grains, we calculate the Rayleigh reduction factor, R, for more than 1000 combinations of the 3 dimensionless parameters which characterise the alignment. For superparamagnetic grains, we calculate R from an exact analytic solution for the relevant distribution function. We calibrate the accuracy of a recently-proposed perturbative approximation and show that it yields R values with a mean error of about 17 percent.