A method for mapping the temperature profile of X-ray clusters through radio observations

Many of the most luminous extragalactic radio sources are located at the centers of X-ray clusters, and so their radiation must be scattered by the surrounding hot gas. We show that radio observations of the highly polarized scattered radiation (which depends on the electron density distribution) in combination with the thermal Sunyaev-Zel'dovich effect (which measures the electron pressure distribution) can be used to determine the radial profile of the electron temperature within the host cluster. The sensitivity levels expected from current instruments will allow radio measurements of mass-weighted cluster temperature profiles to better than a ∼ 1 keV accuracy, as long as the central radio source is steady over several million years. Variable or beamed sources will leave observable signatures in the scattered emission. For clusters with a central point source brighter than ∼1 mJy, the scattered polarization signal is stronger than competing effects due to the cosmic microwave background.