The luminosity function obtained from bright stars

Abstract

As a preliminary step to derive the luminosity function the underlying hypothesis involved in the mean absolute magnitudes method have been analyzed. The study of the material published by Cowley, A. P., Hiltner, W. A. and Witt, A. N. (A.J., 72, 1334, 1967) shows that the hypothesis of a linear relationship between the mean absolute magnitude and H, as well as the hypothesis that such a relationship does not depend on the apparent magnitude, have little influence on the obtained values. The shape of the luminosity function is not biased either by the adopted shape of the relative distribution function of absolute magnitudes for each H, but it depends critically on the number of stars in each magnitude and proper motion interval.