Mathematics – Probability
Scientific paper
Sep 1969
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1969natur.223.1140p&link_type=abstract
Nature, Volume 223, Issue 5211, pp. 1140-1142 (1969).
Mathematics
Probability
40
Scientific paper
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.
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