Astrophysical black hole

An astrophysical black hole is a black hole studied through its formation, accretion, mergers, dynamical environment, and electromagnetic or gravitational-wave signatures.

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 $t_{\mathrm{Sal}}=\eta t_E/[(1-\eta )f_{\mathrm{Edd}}]$.

An intermediate-mass black hole has a mass between stellar remnants and supermassive black holes, approximately $10^2$--$10^5{M}_{\odot }$.

A supermassive black hole has a mass of roughly $10^6{M}_{\odot }$ or more and commonly occupies the nucleus of a massive galaxy.

Active-galactic-nucleus feedback transfers radiative or mechanical energy and momentum from black-hole accretion to surrounding galactic gas.

A dusty radiation-pressure-driven shell is swept up when ultraviolet radiation from an active nucleus is absorbed by dust and reradiated in the infrared. Single scattering supplies up to roughly $L/c$ of momentum flux, while trapped infrared photons can enhance it by the infrared optical depth.

The dust transparency radius is where a swept shell's ultraviolet optical depth equals one. For a gas fraction $f_g$ in a singular isothermal sphere, $R_{\tau }={\kappa }_{\mathrm{UV}}{f}_g{\sigma }^2/(2\pi G)$.

A tidal disruption event occurs when a star passes close enough to a black hole that differential gravity tears it apart outside the capture boundary, producing returning debris and often a luminous flare.

For a star of mass $M_{\ast }$ and radius $R_{\ast }$ near a black hole of mass $M_{\mathrm{BH}}$, the Newtonian tidal disruption radius is $r_t\simeq R_{\ast }(2M_{\mathrm{BH}}/M_{\ast }{)}^{1/3}$ under a peak-to-center tidal-acceleration convention.

The Hills mass is the black-hole mass above which a given star crosses the capture boundary before being tidally disrupted. For a Schwarzschild capture radius $2G{M}_{\mathrm{BH}}/c^2$, it is $c^3{R}_{\ast }^{3/2}/(2G^{3/2}{M}_{\ast }^{1/2})$ with the corresponding tidal-radius convention.

A black-hole seed is an early black hole from which a later massive black hole can grow by accretion and mergers.

A Population III remnant seed forms when a massive metal-free star collapses, typically leaving a light seed of order $10$--$10^2{M}_{\odot }$ depending on stellar mass loss and pair-instability effects.

A runaway stellar-collision seed forms when mass segregation and repeated mergers in a dense young cluster create a very massive star that collapses to a black hole of roughly $10^2$--$10^4{M}_{\odot }$.

A direct-collapse black-hole seed forms when rapidly inflowing primordial gas avoids fragmentation, builds a supermassive star or quasistar, and collapses to a seed of roughly $10^4$--$10^6{M}_{\odot }$.