Black Hole Growth in Dark Matter and theMBH‐σ Relation

Abstract

In this paper, we consider the growth of seed black holes immersed in dark matter halos. We investigate first the adiabatic growth in various initial distribution functions (isothermal; power law; and Navarro, Frenk, and White) and find the resulting density, radial velocity, and anisotropy profiles. In addition, we estimate the growth rate for a given black hole mass in the corresponding adiabatically modified dark matter distribution function. Only in the isothermal case is there a convincing black hole mass-age relation. By calculating the line-of-sight velocity dispersion for the various cases as a function of the black hole mass, we find the predicted adiabatic MBH-σ relation, which never approaches the recently observed power law. We conclude by abandoning adiabaticity, suggesting that the black hole grows proportionally to the dark matter halo itself on a dynamic timescale. This allows us to relate the observed MBH-σ relation to the cosmological power spectrum on galactic scales by using dimensional scaling arguments.