The Mass Frequency-Function in Open Clusters

According to the first author, a = 4 . 0, and from the data given by Salpeter, a = 3 . 5. Salpeter has further shown that if the rate of star formation has been uniform since the beginning of our galaxy, the present distribution function is the result of evolutionary changes applied to an original function of the same form, but with a = 2 . 35. It must be remarked, however, that this hypothesis and the others that Salpeter has used cannot be checked independently. Therefore, it is of interest to analyze a different kind of material. If possible, one should select a system in which all stars were formed simultaneously, so that no hypothesis about the rate of creation is required. Such systems are provided by the open clusters. For the present study we have used three clusters : the Pleiades, Praesepe, and the Hyades. For these clusters we have a fairly complete knowledge of the cluster members and of the absolute magnitudes that are necessary for the calculation of the mass frequency-function. Perhaps it would have been possible to include other clusters (Coma Berenices, h and % Persei), but we have preferred to use only the best known clusters. The distance moduli for the individual star clusters, the identification lists of cluster members and the sources for the visual magnitudes of the stars are those given by Mawridis.3 Table I gives the most important data. The procedure of reduction adopted was as follows : using the mass-luminosity relation, we made star counts for intervals of