Brightest Members of Clusters of Galaxies

Abstract

THE small dispersion in the absolute magnitude of the brightest member of rich clusters of galaxies has been interpreted by Peebles¹ in terms of a statistical model based on a luminosity function common to all clusters. In this model it is assumed that the probability that there is a galaxy in a given cluster with absolute magnitude in the range M to M + dM is is a universal function for all rich clusters. This form of ψ(M) is consistent with the bright end of the cumulative luminosity function for the Coma cluster determined by Abell² with α = 1.8; M₀, which can be derived from the observed mean luminosity of the brightest cluster members, is interpreted as a measure of the total number of galaxies in the cluster and thus of the cluster mass. On these assumptions Peebles shows that the probability distribution of the absolute magnitude M₁ of the brightest member is Peebles has compared the distribution (3) with absolute magnitudes derived from the photographic photometry of eighteen brightest cluster galaxies by Humason, Mayall and Sandage³ ; he has also investigated the distribution of differences in absolute magnitude between the first brightest and the third, fifth and tenth brightest members. He concludes that the observations are compatible with the predictions of the model. Consequently, the brightest galaxies in clusters obey a statistical luminosity function smoothly extrapolated from the fainter members and there is nothing physically remarkable about their small luminosity dispersion.