Electron Scattering and the Distances to Cluster Cooling Flows

Cluster cooling flows have electron scattering optical depths which are estimated to be about 10^-2^. Many of the cluster dominant galaxies centered in cluster cooling flows have active nuclei, and about 1% of the luminosity from the active nuclei should appear as diffuse, scattered radiation. Due to significant amounts of diffuse emission in other wavebands, this scattered radiation is most likely to be observable at radio wavelengths. Distinguishing between scattered radiation and other sources of diffuse emission poses a serious problem. However, the scattered emission should have the same spectral index as the central source, should be axisymmetric, and should have a surface brightness distribution which can be predicted from the observed X-ray surface brightness. We show that detection of this scattered radiation 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 ~ 10^5^ yr, and for the degree of beaming of radiation from the central source.