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An accretion disk is a structure (often a
circumstellar disk A circumstellar disc (or circumstellar disk) is a torus, pancake or ring-shaped accretion disk of matter composed of gas, dust, planetesimals, asteroids, or collision fragments in orbit around a star. Around the youngest stars, they are the ...
) formed by diffuse material in
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
al motion around a massive
central body A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravitationally bound, multi-object system. This object constitutes most of that system's mass and will generally be located near the syst ...
. The central body is typically a star.
Friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of ...
, uneven irradiance,
magnetohydrodynamic Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydro­magnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magneto­fluids include plasmas, liquid metals, ...
effects, and other forces induce instabilities causing orbiting material in the disk to spiral inward towards the central body. Gravitational and frictional forces compress and raise the temperature of the material, causing the emission of
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) li ...
. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and
protostar A protostar is a very young star that is still gathering mass from its parent molecular cloud. The protostellar phase is the earliest one in the process of stellar evolution. For a low-mass star (i.e. that of the Sun or lower), it lasts about 50 ...
s radiate in the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
; those around
neutron star A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. w ...
s and black holes in the
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10  nanometers, corresponding to frequencies in the range 30&nb ...
part of the
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
. The study of oscillation modes in accretion disks is referred to as diskoseismology.


Manifestations

Accretion disks are a ubiquitous phenomenon in astrophysics;
active galactic nuclei An active galactic nucleus (AGN) is a compact region at the center of a galaxy that has a much-higher-than-normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not prod ...
,
protoplanetary disk A protoplanetary disk is a rotating circumstellar disc of dense gas and dust surrounding a young newly formed star, a T Tauri star, or Herbig Ae/Be star. The protoplanetary disk may also be considered an accretion disk for the star itself, be ...
s, and
gamma ray burst In gamma-ray astronomy, gamma-ray bursts (GRBs) are immensely energetic explosions that have been observed in distant galaxies. They are the most energetic and luminous electromagnetic events since the Big Bang. Bursts can last from ten millise ...
s all involve accretion disks. These disks very often give rise to
astrophysical jet An astrophysical jet is an astronomical phenomenon where outflows of ionised matter are emitted as an extended beam along the axis of rotation. When this greatly accelerated matter in the beam approaches the speed of light, astrophysical jets be ...
s coming from the vicinity of the central object. Jets are an efficient way for the star-disk system to shed
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
without losing too much
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
. The most spectacular accretion disks found in nature are those of
active galactic nuclei An active galactic nucleus (AGN) is a compact region at the center of a galaxy that has a much-higher-than-normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not prod ...
and of
quasars A quasar is an extremely luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a mass rangi ...
, which are thought to be massive black holes at the center of galaxies. As matter enters the accretion disc, it follows a trajectory called a
tendex line A tendex line (from the Latin "tendere": To stretch) is a traversal line describing the path matter takes through the accretion disc of a black hole. A tendex line typically follows a spiral around the black hole descending to the event horizon. ...
, which describes an inward spiral. This is because particles rub and bounce against each other in a turbulent flow, causing frictional heating which radiates energy away, reducing the particles' angular momentum, allowing the particle to drift inwards, driving the inward spiral. The loss of angular momentum manifests as a reduction in velocity; at a slower velocity, the particle must adopt a lower orbit. As the particle falls to this lower orbit, a portion of its
gravitational potential energy Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (conver ...
is converted to increased velocity and the particle gains speed. Thus, the particle has lost energy even though it is now travelling faster than before; however, it has lost angular momentum. As a particle orbits closer and closer, its velocity increases, as velocity increases frictional heating increases as more and more of the particle's potential energy (relative to the black hole) is radiated away; the accretion disk of a black hole is hot enough to emit
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10  nanometers, corresponding to frequencies in the range 30&nb ...
s just outside the
event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact ob ...
. The large luminosity of quasars is believed to be a result of gas being accreted by supermassive black holes. Elliptical accretion disks formed at tidal disruption of stars can be typical in galactic nuclei and quasars. The accretion process can convert about 10 percent to over 40 percent of the mass of an object into energy as compared to around 0.7 percent for
nuclear fusion Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles ( neutrons or protons). The difference in mass between the reactants and products is manife ...
processes. In close
binary system A binary system is a system of two astronomical bodies which are close enough that their gravitational attraction causes them to orbit each other around a barycenter ''(also see animated examples)''. More restrictive definitions require that th ...
s the more massive primary component evolves faster and has already become a
white dwarf A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes ...
, a neutron star, or a black hole, when the less massive companion reaches the giant state and exceeds its
Roche lobe In astronomy, the Roche lobe is the region around a star in a binary system within which orbiting material is gravitationally bound to that star. It is an approximately teardrop-shaped region bounded by a critical gravitational equipotential ...
. A gas flow then develops from the companion star to the primary. Angular momentum conservation prevents a straight flow from one star to the other and an accretion disk forms instead. Accretion disks surrounding
T Tauri star T Tauri stars (TTS) are a class of variable stars that are less than about ten million years old. This class is named after the prototype, T Tauri, a young star in the Taurus star-forming region. They are found near molecular clouds and ide ...
s or Herbig stars are called
protoplanetary disk A protoplanetary disk is a rotating circumstellar disc of dense gas and dust surrounding a young newly formed star, a T Tauri star, or Herbig Ae/Be star. The protoplanetary disk may also be considered an accretion disk for the star itself, be ...
s because they are thought to be the progenitors of planetary systems. The accreted gas in this case comes from the
molecular cloud A molecular cloud, sometimes called a stellar nursery (if star formation is occurring within), is a type of interstellar cloud, the density and size of which permit absorption nebulae, the formation of molecules (most commonly molecular hydroge ...
out of which the star has formed rather than a companion star.


Accretion disk physics

In the 1940s, models were first derived from basic physical principles. In order to agree with observations, those models had to invoke a yet unknown mechanism for angular momentum redistribution. If matter is to fall inwards it must lose not only gravitational energy but also lose
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
. Since the total angular momentum of the disk is conserved, the angular momentum loss of the mass falling into the center has to be compensated by an angular momentum gain of the mass far from the center. In other words, angular momentum should be ''transported'' outwards for matter to accrete. According to the Rayleigh stability criterion, :\frac>0, where \Omega represents the angular velocity of a fluid element and R its distance to the rotation center, an accretion disk is expected to be a laminar flow. This prevents the existence of a
hydrodynamic In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) a ...
mechanism for angular momentum transport. On one hand, it was clear that viscous stresses would eventually cause the matter towards the center to heat up and radiate away some of its gravitational energy. On the other hand,
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
itself was not enough to explain the transport of angular momentum to the exterior parts of the disk.
Turbulence In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
-enhanced viscosity was the mechanism thought to be responsible for such angular-momentum redistribution, although the origin of the turbulence itself was not well understood. The conventional \alpha-model (discussed below) introduces an adjustable parameter \alpha describing the effective increase of viscosity due to turbulent eddies within the disk. In 1991, with the rediscovery of the magnetorotational instability (MRI), S. A. Balbus and J. F. Hawley established that a weakly magnetized disk accreting around a heavy, compact central object would be highly unstable, providing a direct mechanism for angular-momentum redistribution.


α-Disk model

Shakura and Sunyaev (1973) proposed turbulence in the gas as the source of an increased viscosity. Assuming subsonic turbulence and the disk height as an upper limit for the size of the eddies, the disk viscosity can be estimated as \nu=\alpha c_H where c_ is the
sound speed The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as wel ...
, H is the scale height of the disk, and \alpha is a free parameter between zero (no accretion) and approximately one. In a turbulent medium \nu\approx v_ l_ , where v_ is the velocity of turbulent cells relative to the mean gas motion, and l_ is the size of the largest turbulent cells, which is estimated as l_ \approx H = c_/\Omega and v_ \approx c_ , where \Omega = (G M)^ r^ is the Keplerian orbital angular velocity, r is the radial distance from the central object of mass M. By using the equation of
hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary ...
, combined with conservation of
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
and assuming that the disk is thin, the equations of disk structure may be solved in terms of the \alpha parameter. Many of the observables depend only weakly on \alpha, so this theory is predictive even though it has a free parameter. Using Kramers' opacity law it is found that :H=1.7\times 10^8\alpha^\dot^_ m_1^ R^_f^ :T_c=1.4\times 10^4 \alpha^\dot^_ m_1^ R^_f^ :\rho=3.1\times 10^\alpha^\dot^_ m_1^ R^_f^^ where T_c and \rho are the mid-plane temperature and density respectively. \dot_ is the accretion rate, in units of 10^^, m_1 is the mass of the central accreting object in units of a solar mass, M_\bigodot, R_ is the radius of a point in the disk, in units of 10^, and f=\left -\left(\frac\right)^ \right, where R_\star is the radius where angular momentum stops being transported inwards. The Shakura–Sunyaev α-disk model is both thermally and viscously unstable. An alternative model, known as the \beta-disk, which is stable in both senses assumes that the viscosity is proportional to the gas pressure \nu \propto \alpha p_. In the standard Shakura–Sunyaev model, viscosity is assumed to be proportional to the total pressure p_ = p_ + p_ = \rho c_^2 since \nu = \alpha c_ H = \alpha c_s^2/\Omega = \alpha p_/(\rho \Omega) . The Shakura–Sunyaev model assumes that the disk is in local thermal equilibrium, and can radiate its heat efficiently. In this case, the disk radiates away the viscous heat, cools, and becomes geometrically thin. However, this assumption may break down. In the radiatively inefficient case, the disk may "puff up" into a
torus In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not tou ...
or some other three-dimensional solution like an Advection Dominated Accretion Flow (ADAF). The ADAF solutions usually require that the accretion rate is smaller than a few percent of the Eddington limit. Another extreme is the case of
Saturn's rings The rings of Saturn are the most extensive ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometers to meters, that orbit around Saturn. The ring particles are made almost entire ...
, where the disk is so gas poor that its angular momentum transport is dominated by solid body collisions and disk-moon gravitational interactions. The model is in agreement with recent astrophysical measurements using gravitational lensing.


Magnetorotational instability

Balbus and Hawley (1991) proposed a mechanism which involves magnetic fields to generate the angular momentum transport. A simple system displaying this mechanism is a gas disk in the presence of a weak axial magnetic field. Two radially neighboring fluid elements will behave as two mass points connected by a massless spring, the spring tension playing the role of the magnetic tension. In a Keplerian disk the inner fluid element would be orbiting more rapidly than the outer, causing the spring to stretch. The inner fluid element is then forced by the spring to slow down, reduce correspondingly its angular momentum causing it to move to a lower orbit. The outer fluid element being pulled forward will speed up, increasing its angular momentum and move to a larger radius orbit. The spring tension will increase as the two fluid elements move further apart and the process runs away. It can be shown that in the presence of such a spring-like tension the Rayleigh stability criterion is replaced by : \frac>0. Most astrophysical disks do not meet this criterion and are therefore prone to this magnetorotational instability. The magnetic fields present in astrophysical objects (required for the instability to occur) are believed to be generated via
dynamo "Dynamo Electric Machine" (end view, partly section, ) A dynamo is an electrical generator that creates direct current using a commutator. Dynamos were the first electrical generators capable of delivering power for industry, and the foundati ...
action.


Magnetic fields and jets

Accretion disks are usually assumed to be threaded by the external magnetic fields present in the interstellar medium. These fields are typically weak (about few micro-Gauss), but they can get anchored to the matter in the disk, because of its high electrical conductivity, and carried inward toward the central star. This process can concentrate the magnetic flux around the centre of the disk giving rise to very strong magnetic fields. Formation of powerful astrophysical jets along the rotation axis of accretion disks requires a large scale poloidal magnetic field in the inner regions of the disk. Such magnetic fields may be advected inward from the interstellar medium or generated by a magnetic dynamo within the disk. Magnetic fields strengths at least of order 100 Gauss seem necessary for the magneto-centrifugal mechanism to launch powerful jets. There are problems, however, in carrying external magnetic flux inward towards the central star of the disk. High electric conductivity dictates that the magnetic field is frozen into the matter which is being accreted onto the central object with a slow velocity. However, the plasma is not a perfect electric conductor, so there is always some degree of dissipation. The magnetic field diffuses away faster than the rate at which it is being carried inward by accretion of matter. A simple solution is assuming a
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
much larger than the
magnetic diffusivity The magnetic diffusivity is a parameter in plasma physics which appears in the magnetic Reynolds number. It has SI units of m²/s and is defined as:W. Baumjohann and R. A. Treumann, ''Basic Space Plasma Physics'', Imperial College Press, 1997. :\e ...
in the disk. However, numerical simulations, and theoretical models, show that the viscosity and magnetic diffusivity have almost the same order of magnitude in magneto-rotationally turbulent disks. Some other factors may possibly affect the advection/diffusion rate: reduced turbulent magnetic diffusion on the surface layers; reduction of the ShakuraSunyaev viscosity by magnetic fields; and the generation of large scale fields by small scale MHD turbulence –a large scale dynamo. In fact, a combination of different mechanisms might be responsible for efficiently carrying the external field inwards towards the central parts of the disk where the jet is launched. Magnetic buoyancy, turbulent pumping and turbulent diamagnetism exemplify such physical phenomena invoked to explain such efficient concentration of external fields.


Analytic models of sub-Eddington accretion disks (thin disks, ADAFs)

When the accretion rate is sub-Eddington and the opacity very high, the standard thin accretion disk is formed. It is geometrically thin in the vertical direction (has a disk-like shape), and is made of a relatively cold gas, with a negligible radiation pressure. The gas goes down on very tight spirals, resembling almost circular, almost free (Keplerian) orbits. Thin disks are relatively luminous and they have thermal electromagnetic spectra, i.e. not much different from that of a sum of black bodies. Radiative cooling is very efficient in thin disks. The classic 1974 work by Shakura and Sunyaev on thin accretion disks is one of the most often quoted papers in modern astrophysics. Thin disks were independently worked out by Lynden-Bell, Pringle and Rees. Pringle contributed in the past thirty years many key results to accretion disk theory, and wrote the classic 1981 review that for many years was the main source of information about accretion disks, and is still very useful today. A fully general relativistic treatment, as needed for the inner part of the disk when the central object is a black hole, has been provided by Page and Thorne, and used for producing simulated optical images by Luminet and Marck, in which, although such a system is intrinsically symmetric its image is not, because the relativistic rotation speed needed for centrifugal equilibrium in the very strong gravitational field near the black hole produces a strong Doppler redshift on the receding side (taken here to be on the right) whereas there will be a strong blueshift on the approaching side. Due to light bending, the disk appears distorted but is nowhere hidden by the black hole. When the accretion rate is sub-Eddington and the opacity very low, an ADAF is formed. This type of accretion disk was predicted in 1977 by Ichimaru. Although Ichimaru's paper was largely ignored, some elements of the ADAF model were present in the influential 1982 ion-tori paper by Rees, Phinney, Begelman and Blandford. ADAFs started to be intensely studied by many authors only after their rediscovery in the mid-1990 by Narayan and Yi, and independently by Abramowicz, Chen, Kato, Lasota (who coined the name ADAF), and Regev. Most important contributions to astrophysical applications of ADAFs have been made by Narayan and his collaborators. ADAFs are cooled by advection (heat captured in matter) rather than by radiation. They are very radiatively inefficient, geometrically extended, similar in shape to a sphere (or a "corona") rather than a disk, and very hot (close to the virial temperature). Because of their low efficiency, ADAFs are much less luminous than the Shakura–Sunyaev thin disks. ADAFs emit a power-law, non-thermal radiation, often with a strong Compton component.


Analytic models of super-Eddington accretion disks (slim disks, Polish doughnuts)

The theory of highly super-Eddington black hole accretion, ''M''≫''M''Edd, was developed in the 1980s by Abramowicz, Jaroszynski, Paczyński, Sikora and others in terms of "Polish doughnuts" (the name was coined by Rees). Polish doughnuts are low viscosity, optically thick, radiation pressure supported accretion disks cooled by advection. They are radiatively very inefficient. Polish doughnuts resemble in shape a fat torus (a doughnut) with two narrow funnels along the rotation axis. The funnels collimate the radiation into beams with highly super-Eddington luminosities. Slim disks (name coined by Kolakowska) have only moderately super-Eddington accretion rates, ''M''≥''M''Edd, rather disk-like shapes, and almost thermal spectra. They are cooled by advection, and are radiatively ineffective. They were introduced by Abramowicz, Lasota, Czerny and Szuszkiewicz in 1988.


Excretion disk

The opposite of an accretion disk is an excretion disk where instead of material accreting from a disk on to a central object, material is excreted from the center outwards on to the disk. Excretion disks are formed when stars merge.


See also

* Accretion *
Astrophysical jet An astrophysical jet is an astronomical phenomenon where outflows of ionised matter are emitted as an extended beam along the axis of rotation. When this greatly accelerated matter in the beam approaches the speed of light, astrophysical jets be ...
* Blandford–Znajek process * Circumstellar disc * *
Dynamo theory In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can ...
*
Gravitational singularity A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is so intense that spacetime itself breaks down catastrophically. As such, a singularity is by definition no longer part of the regular sp ...
*
Ring system A ring system is a disc or ring, orbiting an astronomical object, that is composed of solid material such as dust and moonlets, and is a common component of satellite systems around giant planets. A ring system around a planet is also known as ...
* Quasi-star * Solar nebula * Spin-flip


References

* *


External links


Professor John F. Hawley homepage



Accretion Discs on Scholarpedia
* {{DEFAULTSORT:Accretion Disk - Black holes Unsolved problems in physics Vortices Concepts in astronomy Articles containing video clips