Limits on Collisional Dark Matter from Elliptical Galaxies in Clusters

The dynamical evolution of galaxies in clusters is modified if dark matter is self-interacting. Heat conduction from the hot cluster halo leads to evaporation of the relatively cooler galactic halos. The stellar distribution would adiabatically expand as it readjusts to the loss of dark matter, reducing the velocity dispersion and increasing the half-light radius. If the dark matter content within that radius was f_dm = 25-50% of the total, as indicated by current observations, the ellipticals in clusters would be offset from the fundamental plane relation beyond the observational scatter. The requirement that their halos survive for a Hubble time appears to exclude just that range of the dark matter cross-section, 0.3 < sigma/m < 10^4 cm^2/g, thought to be optimal for reducing central halo cusps, unless f_dm < 15%. If the cross-section is allowed to vary with the relative velocity of dark matter particles, sigma \propto v^{-2 delta}, a new problem of evaporation of dark matter arises in the dwarf galaxies with low velocity dispersion. The halos of large galaxies in clusters and dwarf galaxies in the Local Group can both survive only if delta < 1.1 or delta > 1.8. In either case the problem of central density cusps remains.