A dark matter scaling relation from mirror dark matter

Mirror dark matter, and other similar dissipative dark matter candidates, need an energy source to stabilize dark matter halos in spiral galaxies. It has been suggested previously that ordinary supernovae can potentially supply the required energy. By matching the energy supplied to the halo from supernovae to that lost due to radiative cooling, we here derive a rough scaling relation, $R_{SN} \propto \rho_0 r_0^2$ ($R_{SN}$ is the supernova rate and $\rho_0, \ r_0$ the dark matter central density and core radius). Such a relation is consistent with dark matter properties inferred from studies of spiral galaxies with halo masses larger than $3\times 10^{11} M_\odot$. We speculate that other observed galaxy regularities might be explained within the framework of such dissipative dark matter.