object

Accretion disk

An accretion disk is a structure of orbiting matter formed around a massive central body, such as a black hole, by gravitational attraction.
46 related articles · 5 formulas · 6 who worked here

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

The accretion disk of a supermassive black hole can outshine all the stars of its host galaxy, while the hole itself remains completely dark.

Concept graph →

Formulas

$$P = ackslash eta ackslash dot{M} c^2$$
Power released by accretion onto a compact object.
What is in the formula
Pvariableaccretion power — power watt
ηvariableefficiency of mass-to-energy conversion
Ṁvariablemass accretion rate — mass flow rate kilogram per second
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
p=\eta_a\eta_φ\dot{m}_{bh}c^2 · 2606.02700v1
$$T(r) = \left( \frac{3 G M \dot{M}}{8 \pi \sigma r^3} \right)^{1/4}$$
Temperature radial profile for an accretion disk.
What is in the formula
T(r)variabledisk temperature at radius r — temperature kelvin
rvariableradial distance from the central object — radius metre
Mvariablemass of the central object — mass kilogram
\dot{M}variablemass accretion rate — mass flow rate kilogram per second
GconstantConstant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\sigmaconstantConstant relating blackbody radiated power to temperature. — stefan boltzmann constant = 5.670374419e-8 watt per square metre per kelvin to the fourth
t(r)=(\frac{3gm_1\dot{m}}{8πσr^3})^{1/4} · 2607.12971
$$r_A = \left(\frac{\mu^4}{2 G M \dot{M}^2}\right)^{1/7}$$
Radius where magnetic pressure equals ram pressure in accretion.
What is in the formula
r_AvariableAlfvén radius — radius metre
μvariableMagnetic dipole moment of the star — magnetic dipole moment ampere square metre
GvariableGravitational constant — gravitational constant cubic metre per kilogram per second squared
MvariableMass of the accreting star — mass kilogram
ṀvariableMass accretion rate — mass accretion rate kilogram per second
r_a\simeq(\frac{μ^4}{2gm\dot{m}^2})^{1/7} · 2607.21846v1
$$\dot{M} = 4\pi\lambda\frac{(G M)^2 \rho_\infty}{(c_s^2 + v_{\text{rel}}^2)^{3/2}}$$
Accretion rate onto a gravitating body depends on mass, gas density, and relative speed.
What is in the formula
\dot{M}variablemass accretion rate — mass accretion rate kilogram per second
Mvariablemass of the gravitating body — mass kilogram
\rho_\inftyvariableambient gas density at infinity — mass density kilogram per cubic metre
c_svariablesound speed in the gas — speed metre per second
v_{\text{rel}}variablerelative velocity of the body through the gas — velocity metre per second
GconstantNewtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\lambdaconstantdimensionless accretion efficiency factor of order unity — accretion efficiency = 1
\dot{m}_{\rmtarget}=4πλ\frac{(gm_{\rmbh})^2ρ_\infty}{(c_s^2+v_{\rmrel}^2)^{3/2}} · 2607.00349
$$L_{\rm acc} = \frac{G M \dot{M}}{R}$$
Luminosity released by accretion onto a compact object.
What is in the formula
L_{\rm acc}variableaccretion luminosity — luminosity watt
Mvariablemass of the accreting object — mass kilogram
\dot{M}variablemass accretion rate — mass flow rate kilogram per second
Rvariableradius at which accretion energy is released — radius metre
GconstantConstant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
l_{\rmacc}=\frac{gm_1\dot{m}}{r_1} · 2607.12971

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