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 cross section , \sigma _ { { } _ { xp } } , independent of the relative velocity of the colliding particles , can not produce stable thermal balance .
In this case , avoiding an unrealistic increase of the central temperatures yields the upper bound \sigma _ { { } _ { xp } } < 10 ^ { -25 } { cm } ^ { 2 } ( m _ { x } / m _ { p } ) , where m _ { x } and m _ { p } are the DMP and proton mass , respectively .
A stable balance , however , can be achieved for a power law dependence on the relative velocity , V , of the form , \sigma _ { { } _ { xp } } \propto V ^ { a } with a < -3 .
An advantage of this heating mechanism is that it preserves the metal gradients observed in clusters .