Electron scattering and the distances to cluster cooling flows

Cluster cooling flows have electron-scattering optical depths which are estimated to be about 0.01. Many of the cluster-dominant galaxies centered in cluster cooling flows have active nuclei, and about 1 percent of the luminosity from the active nuclei should appear as diffuse, scattered radiation. It is shown here that detection of this scattered radiation at radio wavelengths can provide a measure of the distance to the cluster that is independent of the Hubble constant. Observations of the scattered surface brightness profile can also be used to test for clumpiness in the gas, for variations in the central radio source on time scales less than 100,000 yr, and for the degree of beaming of radiation from the central source.