An accretion disk is a structure of orbiting matter formed around a massive central body, such as a black hole, by gravitational attraction.An accretion disk is a flattened rotating structure of gas and plasma that forms when matter flows toward a massive compact object: a black hole, neutron star, or white dwarf. Due to conservation of angular momentum, the gas does not fall straight in but enters a circular orbit and slowly drifts inward while viscous forces (e.g., magnetorotational instability) redistribute angular momentum outward. The inner edge of the disk is determined by the last stable circular orbit, which for a non-rotating black hole is three gravitational radii. Closer to the center, temperatures soar to tens of millions of degrees, and the disk emits hard X-ray and gamma radiation.
The theory of disk accretion actively developed from the 1960s. The α-disk model, which became a standard, was published by N. I. Shakura and R. A. Sunyaev in 1973. The discovery of quasars (Maarten Schmidt, 1963) pointed to accretion as the source of their incredible luminosity. X-ray binary systems (e.g., Cygnus X-1) became natural laboratories for testing the theory. Modern instruments—Hubble, Chandra, Spektr-RG—continuously refine the picture, and the Event Horizon Telescope in 2019 directly imaged for the first time the disk around the supermassive black hole in the center of M87.
In a steady state, the disk structure is determined by the balance of gravity, pressure, and rotation. For a Keplerian disk, the angular velocity Ω = √(GM/r³). The radiation flux at radius r: F(r) = (3GMṀ / 8πr³) [1 − √(r_in/r)], where Ṁ is the accretion rate, r_in is the inner radius (ISCO). The total luminosity L = GMṀ / (2r_in). Angular momentum transport is provided by magnetorotational instability (MRI), generating turbulent viscosity. In a strong gravitational field, general relativistic corrections are important: ISCO moves closer to the horizon for rotating holes, increasing energy output. Part of the energy can be extracted from the hole's rotation via the Blandford–Znajek mechanism and focused into relativistic jets.
Accretion disks are the main energy sources of quasars and X-ray radiation from binary systems with black holes and neutron stars. Studying them allows weighing black holes and investigating strong gravity.
The accretion disk of a supermassive black hole can outshine all the stars of its host galaxy, while the hole itself remains completely dark.
| P | variable | accretion power — power watt |
| η | variable | efficiency of mass-to-energy conversion |
| Ṁ | variable | mass accretion rate — mass flow rate kilogram per second |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| T(r) | variable | disk temperature at radius r — temperature kelvin |
| r | variable | radial distance from the central object — radius metre |
| M | variable | mass of the central object — mass kilogram |
| \dot{M} | variable | mass accretion rate — mass flow rate kilogram per second |
| G | constant | Constant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \sigma | constant | Constant relating blackbody radiated power to temperature. — stefan boltzmann constant = 5.670374419e-8 watt per square metre per kelvin to the fourth |
| r_A | variable | Alfvén radius — radius metre |
| μ | variable | Magnetic dipole moment of the star — magnetic dipole moment ampere square metre |
| G | variable | Gravitational constant — gravitational constant cubic metre per kilogram per second squared |
| M | variable | Mass of the accreting star — mass kilogram |
| Ṁ | variable | Mass accretion rate — mass accretion rate kilogram per second |
| \dot{M} | variable | mass accretion rate — mass accretion rate kilogram per second |
| M | variable | mass of the gravitating body — mass kilogram |
| \rho_\infty | variable | ambient gas density at infinity — mass density kilogram per cubic metre |
| c_s | variable | sound speed in the gas — speed metre per second |
| v_{\text{rel}} | variable | relative velocity of the body through the gas — velocity metre per second |
| G | constant | Newtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \lambda | constant | dimensionless accretion efficiency factor of order unity — accretion efficiency = 1 |
| L_{\rm acc} | variable | accretion luminosity — luminosity watt |
| M | variable | mass of the accreting object — mass kilogram |
| \dot{M} | variable | mass accretion rate — mass flow rate kilogram per second |
| R | variable | radius at which accretion energy is released — radius metre |
| G | constant | Constant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |













