Supermassive black hole (SMBH)

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

The M-sigma relation is an empirical correlation between supermassive black hole mass and the stellar velocity dispersion of its host's spheroidal component. A commonly used rough parametrization has exponent near four, but the normalization, exponent, scatter, and selection effects depend on the observed sample. It is distinct from the black-hole--bulge mass relation.

The black-hole--bulge mass relation is the empirical correlation between a galaxy's central black-hole mass and the stellar mass of its spheroidal component. Locally, the black hole is typically of order $10^{-3}$--$10^{-2}$ of the bulge mass, with substantial scatter and possible redshift evolution.

An active galactic nucleus is a compact luminous galactic nucleus powered primarily by accretion onto a supermassive black hole.

A quasar is an extremely luminous active galactic nucleus whose compact central emission can be observed across cosmological distances.

A quasar light curve records its measured brightness as a function of time. Intrinsic accretion variability, measurement noise, and gravitational lensing can all contribute structure.

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

Heating a gas reservoir reduces its Bondi accretion rate because ${\dot{M}}_B\propto {\rho }_{\infty }{c}_s^{-3}$. At fixed density, increasing the sound speed by ten reduces the rate by about a thousand and the gravitational capture radius by a hundred. Expansion and density loss can strengthen this negative feedback. Neither the density nor the cold pre-heating accretion rate is determined by the temperature change alone.

An active-galactic-nucleus wind bubble forms when a fast nuclear wind shocks against galactic gas. From inside outward it contains free wind, a reverse shock, shocked wind, a contact discontinuity, a swept-up shocked shell, a forward shock, and undisturbed interstellar gas.

An outflow is momentum driven when shocked driving material cools rapidly, so it cannot retain enough thermal energy to inflate a pressure-supported bubble. The swept shell then receives approximately the direct wind momentum flux, often of order $L/c$.

An outflow is energy driven when cooling of the shocked wind is slow. Its hot bubble stores mechanical energy and expands by pressure work on the swept-up shell.

A momentum boost is a shell momentum flux exceeding the direct input momentum flux. An energy-conserving wind of speed $v_w$ driving a shell of speed $v_s\ll v_w$ can give ${\dot{p}}_s/(L/c)$ of order $v_w/(2v_s)$.

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.

A fixed-mass shell with ultraviolet opacity ${\kappa }_{\mathrm{UV}}$ has dust transparency radius $R_{\mathrm{UV}}=\sqrt{{\kappa }_{\mathrm{UV}}{M}_{\mathrm{sh}}/(4\pi )}$. For an initially expanding shell driven by constant ultraviolet luminosity, a sharp opaque-to-transparent approximation givesHere ${\Gamma }_{\mathrm{ss}}=L{R}_0^2/(GM{M}_{\mathrm{sh}}c)$ is the initial single-scattering force ratio and ${\Gamma }_{\mathrm{IR}}={\kappa }_{\mathrm{IR}}L/(4\pi GMc)$. The trajectory must actually reach $R_{\mathrm{UV}}$. Large initial ultraviolet optical depth enhances the radiative work at fixed initial single-scattering ratio; the same conclusion does not follow unconditionally at fixed electron-scattering luminosity.

The critical luminosity of a dusty shell is the luminosity at which radiation pressure balances gravity. For shell mass $M_s$, enclosed gravitating mass $M$, and ultraviolet and infrared optical depths,

For a spherical swept shell of mass $M_s(R)$, radial speed $\dot{R}$, driving force $F_d$, and enclosed gravitating mass $M(<R)$,The derivative includes momentum needed to accelerate newly swept ambient mass.

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, $R_{\tau }={\kappa }_{\mathrm{UV}}{f}_g{\sigma }^2/(2\pi G)$.

The Soltan argument compares the cosmological energy density radiated by active galactic nuclei with the present mass density in supermassive black holes. Their ratio constrains the mass-weighted mean radiative efficiency of black-hole growth.