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A new analytic approximation for the luminosity function for galaxies is proposed, which shows good agreement with both a luminosity distribution for bright nearby galaxies and a composite luminosity distribution for cluster galaxies. The analytic expression is proportional to LlL*, where L* is a characteristic luminosity corresponding to a characteristic absolute magnitude M*B(O) = -20.6. For an individual cluster, the characteristic magnitude may be determined with an accuracy of 0.25 mag, suggesting its use as a standard candle. The analytic expression is used to compute an expected richness-absolute magnitude correlation for first ranked cluster galaxies and an expected dispersion, which are compared with the data of Sand age and Hardy. Subject headings: galaxies: clusters of galaxies: photometry
Paul L. Schechter (1976) studied this question.