A luminosity-temperature relation for cluster X-ray sources

Abstract

Luminosity-temperature (L-T) relations are derived for a self-gravitating isothermal gas sphere and for an isothermal gas sphere in hydrostatic equilibrium with the total mass of a cluster of galaxies. The relationships are compared with X-ray data for 13 clusters of galaxies. The L-T relation for the self-gravitating isothermal gas sphere is found to predict X-ray luminosities that are considerably larger than those observed, and the corresponding model is ruled out. It is shown, however, that the L-T relation for the isothermal gas sphere in hydrostatic equilibrium with total cluster mass is consistent with X-ray observations for reasonable choices of the ratio between central density and confining-mass density. Core radii or gas temperatures are predicted for five of the 13 clusters considered.