Formation and Evolution of the Self-Interacting Dark Matter Halos

We have derived the first, fully-cosmological, similarity solutions for CDM halo formation in the presence of nongravitational collisionality, which provides an analytical theory of the effect of the self-interacting dark matter (SIDM) hypothesis on halo density profiles. Collisions transport heat inward, which produces a constant-density core, while continuous infall pumps energy into the halo to stabilize the core against gravothermal catastrophe. These solutions improve upon earlier attempts to model the formation and evolution of SIDM halos, offer deeper insight than existing N-body experiments, and yield a more precise determination of the dependence of halo density profile on the value of the CDM self-interaction cross section. Different solutions arise for different values of the dimensionless collisionality parameter Q = s rho_b r_v \~ r_v/l_mfp, where s is the scattering cross section per unit mass, rho_b is the cosmic mean matter density, r_v is halo virial radius and l_mfp is the collision mean free path. The maximum flattening of central density occurs for an intermediate value of Q, Q_th, at which the halo is maximally relaxed to isothermality. The density profiles with constant-density cores preferred by dwarf and LSB rotation curves are best fit by the maximally-flattened (Q=Q_th) solution. If we assume that dwarfs and LSB galaxies formed at their typical collapse epoch in LCDM, then the value of s which makes Q=Q_th is s ~ 200 cm^{2}/g, much higher than previous estimates, s ~ 0.5-5 cm^{2}/g, based on N-body experiments. If s is independent of collision velocity, then the same value s ~ 200 cm^{2}/g would make Q>Q_th for clusters, which typically formed only recently, resulting in relatively less flattening of their central density profile and a smaller core.