Consequences of Short-Range Interactions between Dark Matter and Protons in Galaxy Clusters

Protons gain energy in short-range collisions with heavier dark matter particles (DMPs) of comparable velocity dispersion. We examine the conditions under which the heating of baryons by scattering off DMPs can offset radiative cooling in the cores of galaxy clusters. Collisions with a constant momentum transfer cross section, σ_xp, independent of the relative velocity of the colliding particles, cannot produce stable thermal balance. In this case, avoiding an unrealistic increase of the central temperatures yields the upper bound σ_xp<10^-25 cm²(m_x/m_p), where m_x and m_p are the DMP and proton mass, respectively. However, in clusters with T>2 keV, a stable balance can be achieved for a power-law dependence on the relative velocity, V, of the form σ_xp~V^a, with a<~-3. An advantage of this heating mechanism is that it preserves the metal gradients observed in clusters.