Do the electrons and ions in X-ray clusters share the same temperature?

The virialization shock around an X-ray cluster primarily heats the ions, since they carry most of the kinetic energy of the infalling gas. Subsequently, the ions share their thermal energy with the electrons through Coulomb collisions. We quantify the expected temperature difference between the electrons and ions as a function of radius and time, based on a spherical self-similar model for the accretion of gas by a cluster in an Omega = 1, h(50) = 1 universe. Clusters with X-ray temperatures T(x) = 4-10 x 10(7) K show noticeable differences between their electron and ion temperatures at radii greater than or similar to 2 Mpc. High-resolution spectroscopy with future X-ray satellites such as Astro-E may be able to determine the ion temperature in intracluster gas from the width of its X-ray emission lines and compare it to the electron temperature as inferred from the free-free emission spectrum. Any difference between these temperatures can be used to date the period of time that has passed since the infalling gas joined the cluster.