Cross section alignment of oblate grains

This paper provides a quantitative account of a recently introduced mechanism of mechanical alignment of suprathermally rotating grains. These rapidly rotating grains are essentially not susceptible to random torques arising from gas-grain collisions, as the timescales for such torques to have significant effect are orders of magnitude greater than the mean time between crossovers. Such grains can be aligned by gaseous torques during short periods of crossovers and/or due to the difference in the rate at which atoms arrive at grain surface. The latter is a result of the difference in orientation of a grain in respect to the supersonic how. This process, which we call cross section alignment, is the subject of our present paper. We derive expressions for the measure of cross section alignment for oblate grains and study how this measure depends upon the angle between the interstellar magnetic field and the gaseous flow and upon the grain shape.