Scaling Relations of Halo Cores for Self-Interacting Dark Matter

Understand

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.