Scaling relations between super-massive black holes, galaxies and dark matter halos

Abstract

The observed correlations between the masses of supermassive black holes (SMBH), MBH, with a gravitational influence on parsec scales, and properties of the host galaxy, measured on kiloparsec scales, strongly suggest that the SMBH and galaxy co-evolve. These correlations are likely to be a reflection of a more fundamental connection between MBH and the depth of the potential wells that just fail to prevent gas blow-out, due to feedback from rapid accretion during a quasar-phase. The potential wells in question were dominated by dark matter, and a general method is lacking to connect the stellar properties at z = 0 to properties of their dark matter halos, both at z = 0 and higher redshifts. The work presented here develops a method to make these connections self-consistently.

Models of two-component spherical galaxies are used to establish scaling relations linking properties of spheroids at z = 0 (stellar masses, effective radii and velocity dispersions) to properties of the dark matter halo (virial masses and circular speeds), also at z = 0. These models are constrained by combining results from the literature connecting the masses and radii of dark matter halos to each other and stellar masses, with data samples for large, early-type galaxies. The z = 0 properties are then connected to dark matter properties at z > 0 by accounting for the halo redshift evolution. A critical SMBH mass prediction, with dependence on the maximum circular-speed in a protogalactic dark matter halo (MBH ? V 4 d,pk), is considered. Combining this with the scaling relations between z = 0 properties and halo properties at z > 0 transforms this theoretical relation into predictions for the observable SMBH correlations.

A new prediction is also derived, extending on the MBH ? V 4 d,pk relation expected from momentum-driven outflows, allowing for the presence of stars and gas not tracing
the dark matter. This new prediction is also compared to the observed correlations at z = 0.