Scaling Relations of Halo Cores for Self-Interacting Dark Matter

Using a simple analytic formalism, we demonstrate that significant dark matter self-interactions produce halo cores that obey scaling relations nearly independent of the underlying particle physics parameters such as the annihilation cross section and the mass of the dark matter particle. For dwarf galaxies, we predict that the core density $\rho_c$ and the core radius $r_c$ should obey $\rho_c r_c \approx 41 \,\text{M}_\odot \text{pc}^{-2}$ with a weak mass dependence $\sim M^{0.2}$. Remarkably, such a scaling relation has recently been empirically inferred. Scaling relations involving core mass, core radius, and core velocity dispersion are predicted and agree well with observational data. By calibrating against numerical simulations, we predict the scatter in these relations and find them to be in excellent agreement with existing data. Future observations can test our predictions for different halo masses and redshifts.