Observational constraints on the self-interacting dark matter scenario and the growth of supermassive black holes

We consider the astrophysical consequences of the self-interacting dark matter (SIDM) scenario for a general velocity-dependent cross section per unit mass that varies as some power of velocity: sigma(DM) = sigma(0)(nu/nu(o))(-a), Accretion of SIDM onto seed black holes can produce supermassive black holes that are too large for certain combinations of sigma(o)nu(o)(a) and a, a fact that is used to obtain a new constraint on the dark matter interaction. Constraints due to other astrophysical considerations are presented and previous constraints for a constant cross section are generalized. The black hole constraint is extremely sensitive to the cusp slope,, of the inner density profile rho similar to r(-alpha) of dark halos. For the most probable value of alpha = 1.3, we find that there exists a tiny region in the parameter space for SIDM properties, with a approximate to 0.5 and (sigma(o)/1 cm(2) g(-1)) (nu(o)/100 km s(-1))(a)approximate to0.5, such that all constraints are satisfied. However, the adiabatic compression of the dark halo by baryons as they cool and contract in normal galaxies yields a steeper cusp, rho similar to r(-alpha'). We find that in both the highly collisional and collisionless limits invariance arguments require alpha' = (6 - alpha) (4 - alpha), where alpha and alpha' are the (4alpha) inner profile slope of the dark halo before and after compression, respectively. This gives the tighter constraint (sigma(o)/1 cm(2) g(-1)) (nu(o)/100 km s(-1))(a) less than or similar to 0.02, which would exclude SIDM as a possible solution to the purported problems with cold dark matter (CDM) on subgalactic scales in the absence of other dynamical processes. Nevertheless, SIDM with parameters consistent with this stronger constraint, can explain the ubiquity of supermassive black holes in the centers of galaxies. A best-fit model is presented with a=0 and (sigma(o)/1 cm(2) g(-1)) = 0.02, which reproduces the supermassive black hole masses and their observed correlations with the velocity dispersion of the host bulges. Specifically, the approximately black hole mass on galactic velocity dispersion is a direct consequence of the power spectrum of primeval perturbations having an index of n approximate to -2 and the value of a. Although the dark matter collision rates for this model are too small to directly remedy problems with CDM, mergers between dark halos harboring supermassive black holes at high redshift could ameliorate the cuspy halo problem. This scenario also explains the lack of comparable supermassive black holes in bulgeless galaxies like M33.