Limits on collisional dark matter from elliptical galaxies in clusters

The dynamical evolution of galaxies in clusters would be modified if dark matter were self-interacting. Heat conduction from the hot cluster halo would lead to evaporation of the relatively cooler galactic halos. The stellar distribution would adiabatically expand as it readjusted 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 fdm = 25%-50% of the total, as indicated by current observations, the elliptical galaxies in clusters would be offset from the fundamental plane relation beyond 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 less than or similar to sigma (p)/m(p) less than or similar to 10(4) cm(2) g(-1), 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> proportional to v(2 delta), a new problem of evaporation of dark matter arises in 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.