Observational Constraints on the Self Interacting Dark Matter Scenario and the Growth of Supermassive Black Holes

We consider the consequences of SIDM for a velocity dependent cross section per unit mass. Accretion of SIDM onto seed black holes can produce supermassive black holes that are too large for certain combinations of parameters,which is used to obtain a new constraint on the dark matter interaction. Constraints due to other considerations are presented and previous ones are generalized. The black hole constraint is extremely sensitive to the slope \alpha, of the inner density profile of dark halos. For the most probable value of \alpha=1.3, there exists a narrow range in parameter space, 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, \alpha=1.7. This gives a tighter constraint, which would exclude SIDM as a possible solution to the purported problems with CDM 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 which reproduces the supermassive black hole masses and their observed correlations with the velocity dispersion of the host bulges. Specifically, the fourth power dependence of black hole mass on velocity dispersion is a direct consequence of the power spectrum having an index of n=-2. 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.