Orientation of Rotating Grains

The Monte Carlo method previously developed by Purcell for following the dynamical behavior of rotating grains has been used to obtain extensive data on the orientation of such grains in a magnetic field. Rectangular grains of square cross-section have been considered in this work. The approximate theory of Jones and Spitzer for grain orientation has been extended and roughly confirmed by the Monte Carlo runs. The alignment of the angular monentum J with respect to the magnetic field B is predicted quite accurately by the revised theory, but the alignment of A, the axis of fourfold symmetry, with re- spect to B is less accurate; the alignment parameter QA, defined as ~ times the excess of cos2 (A, B) over its isotropic value, is under some conditions more than twice the value obtained from the simple theory. On the other hand, the Monte Carlo runs indicate that for B fixed, QA decreases as the length of a grain increases, and the assumption of aligned infinite cylinders considerably overestimates the amount of polarization that can be produced. Correction factors are given which make possible accurate theoretical predictions of QA over a wide range of parameters. These results indicate that the magnetic-field strength required to explain the observed polarization of starlight, as a result of extinction produced by elongated, magnetically aligned grains, is about twice as great as the value previously assumed, and must exceed 1O~ gauss if paramagnetic relaxation is re- sponsible for the alignment, as suggested originally by Davis and Greenstein. Evidence that B averages at most 3 X 10-6 gauss in interstellar space suggests that alignment, if it is to be explained by magnetic interactions, must be attributed to enhanced magnetic relaxation resulting from the cooperative effects of adjacent iron atoms within grains, producing either ferromagnetism or superparamagnetism. Alignment of grains by cosmic rays and by absorption and reemission of photons is also considered in some detail. It does not appear likely that the alignment mechanisms so far proposed which are asso- ciated with these two effects can be important in typical interstellar situations