Past exam of the formation of Structure in the Universe course of the University of Cambridge / 2015 / Paper 1 / 1 / b

Supermassive black holes are compact galactic nuclei with masses typically of millions to billions of solar masses. Their gravitational influence is measured from the motion of surrounding matter; accretion luminosity is evidence of feeding, not a necessary property of every black hole. Keplerian stellar orbits near the Galactic Centre and molecular-maser rotation curves in other nuclei provide particularly direct compact-mass constraints. A rough black-hole sphere of influence is $r_{\mathrm{infl}}\sim G{M}_{\bullet }/{\sigma }_{\star }^2$; resolving it helps dynamical mass estimates.

Accretion converts binding energy into radiation,The latter is the Eddington luminosity for isotropic radiation opposed by electron-scattering opacity, not an absolute luminosity ceiling for every geometry. The retained black-hole mass grows at $(1-\eta ){\dot{M}}_{\mathrm{in}}$. Sustained feeding can produce an active galactic nucleus, whereas gas-poor nuclei may be faint. Loss of gas angular momentum is a central feeding problem.

Black-hole mass correlates with classical-bulge stellar velocity dispersion through the M-sigma relation. Accretion-powered radiation, winds and jets can heat or remove gas, linking nuclear growth to galaxy evolution. Such correlations do not establish one universal feedback history, and disks and pseudobulges do not follow the same tight relations as classical bulges. Seed formation, accretion and mergers all contribute; seed masses and feeding histories remain model dependent.^[ref]