The Formation and Evolution of Self-Interacting Dark Matter Halos

We study the formation and evolution of self-interacting dark matter (SIDM) halos. We find analytical, fully cosmological similarity solutions for their dynamics, which take proper account of the collisional interaction of SIDM particles, based on a fluid approximation derived from the Boltzmann equation. These similarity solutions are relevant to galactic and cluster halo formation in the cold dark matter (CDM) model. Different solutions arise for different values of the dimensionless collisionality parameter, Q=sigma*rho_b*r_s, where sigma is the SIDM particle scattering cross section per unit mass, rho_b is the cosmic mean density, and r_s is the shock radius. For all solutions, a flat-density, isothermal core is present which grows in size as a fixed fraction of r_s, pumped by cosmological infall. Accordingly, core collapse must in general be delayed until infall becomes negligible, contrary to previous analyses based on isolated halos, which predict core collapse in a Hubble time. Our solutions agree with N-body simulations, which match observed galactic rotation curves if sigma=[0.56 - 5.6]cm^2/g, implying Q=[6.2e-7 - 3.6e-5]. Similar profiles also arise for Q=[1.37e-2 - 1.7e-1], or sigma=[1.2e4 - 2.7e4]cm^2/g, a regime not previously simulated.