= Solution
<Supermassive black holes> are compact galactic nuclei with masses typically of millions to billions of solar masses. \b[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 $r_{\rm infl}\sim GM_\bullet/\sigma_\star^2$; resolving it helps dynamical <mass> estimates.
Accretion converts binding energy into radiation,
$$
L=\eta\dot M_{\rm in}c^2,\qquad\boxed{L_E=\frac{4\pi GM_\bullet c}{\kappa_{\rm es}}.}
$$
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 $(1-\eta)\dot M_{\rm in}$. 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.<Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies by John Kormendy and Luis C. Ho>[Dynamical evidence, bulge-dependent correlations and different feedback regimes]{ref}
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