Black-hole accretion

Black-hole accretion converts gravitational binding energy of inflowing matter into heat, radiation, outflows, and growth of the black hole.

The radiative efficiency is $\eta =L/(\dot{M}{c}^2)$. For a zero-torque thin disk it is $1-E_{\mathrm{ISCO}}$, the binding energy per unit rest mass released before matter crosses the innermost stable circular orbit.

The innermost stable circular orbit is the smallest stable circular timelike orbit around a black hole. Its radius and orbital energy depend on black-hole spin and on whether the orbit is prograde or retrograde.

Bondi accretion is steady spherical accretion from a uniform gas reservoir onto a compact gravitating object. In its adiabatic form, compression raises internal energy without providing the irreversible shear heating of a radiatively efficient disk.

An advection-dominated accretion flow is a hot, geometrically thick, radiatively inefficient flow in which most dissipated energy remains in the gas and is carried inward rather than radiated locally.

The Eddington ratio is the luminosity divided by the Eddington luminosity. At fixed radiative efficiency it also measures the accretion rate relative to the Eddington rate.

The Salpeter time is the e-folding time for Eddington-limited black-hole growth. If $t_E={\sigma }_{T}c/(4\pi G{m}_p)$, then $t_{\mathrm{Sal}}=\eta t_E/[(1-\eta )f_{\mathrm{Edd}}]$.