Determination of True Velocity Dispersion and the Dark Matter Problem in Clusters of Galaxies

Abstract

According to the convention normally followed the redshifts of the galaxies in a cluster are assumed to be of purely dopplerian origin. The resulting velocity dispersion, when used in the virial theorem, leads to a very large proportion of dark matter to be present in the galaxy clusters. However, the recently proposed model of velocity dependent ‘cosmic’ drag cause redshifts of photons and it is necessary to develop a procedure to determine the true velocity dispersion from the gross redshift data. A method for this has been presented in the paper. Coma and Perseus clusters have been investigated using this procedure and the M/L ratios for both were found to be approximately of the order of 30, i.e., approximately the order of M/L ratios for individual galaxies. A study of the m - z relation indicates that the galaxies with higher redshifts have fainter magnitudes. Distortion of the redshift plots and the typical elongation of the core regions along the line-of-sight is also explained.