Abstract
AbstractThis paper develops a new statistical approach to the study of the axial rotational velocities of the stars, by considering the break-up limit or any upper limit for the equatorial rotational velocities. The main conclusions are as follows: (1) For random orientation of the axis of rotation, the frequency function of the inclinationαto the line of sight is not sina, as assumed until now. (2) For stars with the same break-up velocityvb, the distribution ofαis given by :wheref(y) is the distribution of the apparent velocitiesy=vsin α,vbeing the true rotational velocity. New integral equations governing the frequency function of α,yandvhave been derived and the correct procedure to treat observations has been discussed; a simple method is also suggested to get an approximate trend of the distribution of the true velocities directly from the observed histogram. The method of analysis proposed in this paper has been applied to a re-discussion of the rotational behaviour of a group of Be stars.
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