Accretion disc
Encyclopedia
An accretion disc is a structure (often a circumstellar disk
) formed by diffuse material in orbital motion around a central body. The central body is typically a star. Gravity causes material in the disc to spiral inward towards the central body. Gravitational forces compress the material causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object. Accretion discs of young stars and protostar
s radiate in the infrared; those around neutron stars and black holes in the x-ray
part of the spectrum.
s all involve accretion discs. These discs very often give rise to jets coming from the vicinity of the central object. Jets are an efficient way for the star-disc system to shed angular momentum without losing too much mass.
The most spectacular accretion discs found in nature are those of active galactic nuclei and of quasars, which are believed to be massive black holes at the center of galaxies. As matter spirals into a black hole
, the intense gravitational gradient gives rise to intense frictional heating; the accretion disc of a black hole is hot enough to emit X-ray
s just outside of the event horizon
. The large luminosity of quasars is believed to be a result of gas being accreted by supermassive black holes. This process can convert about 10 percent of the mass of an object into energy as compared to around 0.5 percent for nuclear fusion
processes.
In close binary systems the more massive primary component evolves faster and has already become a white dwarf, a neutron star, or a black hole, when the less massive companion reaches the giant state and exceeds its Roche lobe
. 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 disc forms instead.
Accretion discs surrounding T Tauri star
s or Herbig stars are called protoplanetary discs because they are thought to be the progenitors of planetary systems. The accreted gas in this case comes from the molecular cloud out of which the star has formed rather than a companion star.
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
. Since the total angular momentum of the disc 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,
where
represents the angular velocity of a fluid element and 
its distance to the rotation center,
an accretion disc is expected to be a laminar flow
. This prevents the existence of a hydrodynamic
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 itself was not enough to explain the transport of angular momentum to the exterior parts of the disc. Turbulence
-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 phenomenological approach introduces an adjustable parameter
describing the effective increase of viscosity due to turbulent eddies within the disc. In 1991, with the rediscovery of the magnetorotational instability (MRI), S. A. Balbus and J. F. Hawley established that a weakly magnetized disc accreting around a heavy, compact central object would be highly unstable, providing a direct mechanism for angular-momentum redistribution.
Shakura and Sunyaev
(1973) proposed turbulence in the gas as the source of an increased viscosity. Assuming subsonic turbulence and the disc height as an upper limit for the size of the eddies, the disc viscosity can be estimated as
where
is the sound speed, 
is the disc height, and 
is a free parameter between zero (no accretion) and approximately one. Note that in turbulent motion 
, where 
is the velocity of turbulent cells relative to the mean gas motion, and 
is the size of the largest turbulent cells, which is estimated as 
and 
, where 
is the Keplerian orbital angular velocity, 
is the radial distance from the central object of mass 
.
By using the equation of hydrostatic equilibrium
, combined with conservation of angular momentum
and assuming that the disc is thin, the equations of disk structure may be solved in terms of the
parameter. Many of the observables depend only weakly on 
, so this theory is predictive even though it has a free parameter.
Using Kramers' law for the opacity it is found that
where
and 
are the mid-plane temperature and density respectively.
is the accretion rate, in units of 
,
is the mass of the central accreting object in units of a solar mass, 
, 
is the radius of a point in the disc, in units of 
, and
, where 
is the radius where angular momentum stops being transported inwards.
The Shakura-Sunyaev
-Disc model is both thermally and viscously unstable.
An alternative model, known as the
-disk, which is stable in both sense assumes that the viscosity is proportional to the gas pressure 
.
Note that in the standard Shakura-Sunyaev model, viscosity is proportional to the total pressure
since
.
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
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
, 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
.
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 disc 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 disc 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
Most astrophysical discs 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
action.
When the accretion rate is sub-Eddington and the opacity very low, an ADAF is formed. This type of accretion disc 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 disc, and very hot (close to the virial temperature). Because of their low efficiency, ADAFs are much less luminous than the Shakura-Sunyaev thin discs. ADAFs emit a power-law, non-thermal radiation, often with a strong Compton component.
, 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 discs 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 discs (name coined by Kolakowska) have only moderately super-Eddington accretion rates,
M≥MEdd, rather disc-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.
Circumstellar disk
A circumstellar disk is a torus, pancake or ring-shaped accumulation of matter composed of gas, dust, planetesimals, asteroids or collision fragments in orbit around a star. Around the youngest stars, they are the reservoirs of material out of which planets may form...
) formed by diffuse material in orbital motion around a central body. The central body is typically a star. Gravity causes material in the disc to spiral inward towards the central body. Gravitational forces compress the material causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object. Accretion discs of young stars and protostar
Protostar
A protostar is a large mass that forms by contraction out of the gas of a giant molecular cloud in the interstellar medium. The protostellar phase is an early stage in the process of star formation. For a one solar-mass star it lasts about 100,000 years...
s radiate in the infrared; those around neutron stars and black holes in the x-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
part of the spectrum.
Manifestations
Accretion discs are a ubiquitous phenomenon in astrophysics; active galactic nuclei, protoplanetary discs, and gamma ray burstGamma ray burst
Gamma-ray bursts are flashes of gamma rays associated with extremely energetic explosions that have been observed in distant galaxies. They are the most luminous electromagnetic events known to occur in the universe. Bursts can last from ten milliseconds to several minutes, although a typical...
s all involve accretion discs. These discs very often give rise to jets coming from the vicinity of the central object. Jets are an efficient way for the star-disc system to shed angular momentum without losing too much mass.
The most spectacular accretion discs found in nature are those of active galactic nuclei and of quasars, which are believed to be massive black holes at the center of galaxies. As matter spirals into a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
, the intense gravitational gradient gives rise to intense frictional heating; the accretion disc of a black hole is hot enough to emit X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s just outside of the event horizon
Event horizon
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...
. The large luminosity of quasars is believed to be a result of gas being accreted by supermassive black holes. This process can convert about 10 percent of the mass of an object into energy as compared to around 0.5 percent for nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
processes.
In close binary systems the more massive primary component evolves faster and has already become a white dwarf, a neutron star, or a black hole, when the less massive companion reaches the giant state and exceeds its Roche lobe
Roche lobe
The Roche lobe is the region of space around a star in a binary system within which orbiting material is gravitationally bound to that star. If the star expands past its Roche lobe, then the material can escape the gravitational pull of the star. If the star is in a binary system then the material...
. 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 disc forms instead.
Accretion discs surrounding T Tauri star
T Tauri star
T Tauri stars are a class of variable stars named after their prototype – T Tauri. They are found near molecular clouds and identified by their optical variability and strong chromospheric lines.-Characteristics:...
s or Herbig stars are called protoplanetary discs because they are thought to be the progenitors of planetary systems. The accreted gas in this case comes from the molecular cloud out of which the star has formed rather than a companion star.
Accretion disc physics
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
. Since the total angular momentum of the disc 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,
where
represents the angular velocity of a fluid element and its distance to the rotation center,an accretion disc is expected to be a laminar flow
Laminar flow
Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents...
. This prevents the existence of a hydrodynamic
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
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 itself was not enough to explain the transport of angular momentum to the exterior parts of the disc. Turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
-enhanced viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher 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 phenomenological approach introduces an adjustable parameter
describing the effective increase of viscosity due to turbulent eddies within the disc. In 1991, with the rediscovery of the magnetorotational instability (MRI), S. A. Balbus and J. F. Hawley established that a weakly magnetized disc accreting around a heavy, compact central object would be highly unstable, providing a direct mechanism for angular-momentum redistribution. 
-Disc Model
Shakura and SunyaevRashid Sunyaev
Rashid Alievich Sunyaev was born in Tashkent, Uzbek SSR, on March 1, 1943 to a Tatar family, and educated at the Moscow Institute of Physics and Technology and Moscow State University . He became a professor at MIPT in 1974...
(1973) proposed turbulence in the gas as the source of an increased viscosity. Assuming subsonic turbulence and the disc height as an upper limit for the size of the eddies, the disc viscosity can be estimated as
where
is the sound speed, is the disc height, and is a free parameter between zero (no accretion) and approximately one. Note that in turbulent motion , where is the velocity of turbulent cells relative to the mean gas motion, and is the size of the largest turbulent cells, which is estimated as and , where is the Keplerian orbital angular velocity, is the radial distance from the central object of mass .By using the equation of hydrostatic equilibrium
Hydrostatic equilibrium
Hydrostatic equilibrium or hydrostatic balance is the condition in fluid mechanics where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force...
, combined with conservation of angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
and assuming that the disc is thin, the equations of disk structure may be solved in terms of the
parameter. Many of the observables depend only weakly on , so this theory is predictive even though it has a free parameter.Using Kramers' law for the opacity it is found that
where
and are the mid-plane temperature and density respectively. is the accretion rate, in units of , is the mass of the central accreting object in units of a solar mass, , is the radius of a point in the disc, in units of , and, where is the radius where angular momentum stops being transported inwards.The Shakura-Sunyaev
-Disc model is both thermally and viscously unstable.An alternative model, known as the
-disk, which is stable in both sense assumes that the viscosity is proportional to the gas pressure .Note that in the standard Shakura-Sunyaev model, viscosity is proportional to the total pressure
since .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
Torus
In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...
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
Rings of Saturn
The rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometres to metres, that form clumps that in turn orbit about Saturn...
, 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
It can be shown that in the presence of such a spring-like tension the Rayleigh stability criterion is replaced by
Most astrophysical discs 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 theory
In geophysics, dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time...
action.
Analytic models of sub-Eddington accretion discs (thin discs, ADAFs)
When the accretion rate is sub-Eddington and the opacity very high, the standard thin accretion disc is formed. It is geometrically thin in the vertical direction (has a disc-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 discs 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 discs. The classic 1974 work by Shakura and Sunyaev on thin accretion discs is one of the most often quoted papers in modern astrophysics. Thin discs have been independently worked out by Lynden-Bell, Pringle and Rees. Pringle contributed in the past thirty years many key results to accretion disc theory, and wrote the classic 1981 review that for many years was the main source of information about accretion discs, and is still very useful today.When the accretion rate is sub-Eddington and the opacity very low, an ADAF is formed. This type of accretion disc 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 disc, and very hot (close to the virial temperature). Because of their low efficiency, ADAFs are much less luminous than the Shakura-Sunyaev thin discs. ADAFs emit a power-law, non-thermal radiation, often with a strong Compton component.
Analytic models of super-Eddington accretion discs (slim discs, Polish doughnuts)
The theory of highly super-Eddington black hole accretion, M>>MEdd, was developed in the 1980s by Abramowicz, Jaroszynski, PaczyńskiBohdan Paczynski
Bohdan Paczyński or Bohdan Paczynski was a Polish astronomer, a leading scientist in theory of the evolution of stars, accretion discs and gamma ray bursts....
, 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 discs cooled by advection
Advection
Advection, in chemistry, engineering and earth sciences, is a transport mechanism of a substance, or a conserved property, by a fluid, due to the fluid's bulk motion in a particular direction. An example of advection is the transport of pollutants or silt in a river. The motion of the water carries...
. 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 discs (name coined by Kolakowska) have only moderately super-Eddington accretion rates,
M≥MEdd, rather disc-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.
See also
- AccretionAccretion (astrophysics)In astrophysics, the term accretion is used for at least two distinct processes.The first and most common is the growth of a massive object by gravitationally attracting more matter, typically gaseous matter in an accretion disc. Accretion discs are common around smaller stars or stellar remnants...
- Circumstellar diskCircumstellar diskA circumstellar disk is a torus, pancake or ring-shaped accumulation of matter composed of gas, dust, planetesimals, asteroids or collision fragments in orbit around a star. Around the youngest stars, they are the reservoirs of material out of which planets may form...
- Solar NebulaSolar nebulaIn cosmogony, the nebular hypothesis is the most widely accepted model explaining the formation and evolution of the Solar System. There is evidence that it was first proposed in 1734 by Emanuel Swedenborg. Originally applied only to our own Solar System, this method of planetary system formation...
- Dynamo TheoryDynamo theoryIn geophysics, dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time...
- Planetary ringPlanetary ringA planetary ring is a ring of cosmic dust and other small particles orbiting around a planet in a flat disc-shaped region.The most notable planetary rings known in Earth's solar system are those around Saturn, but the other three gas giants of the solar system possess ring systems of their...
- SingularityGravitational singularityA gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...
- Spin-flipSpin-flipA black hole spin-flip occurs when the spin axis of a rotating black hole undergoes a sudden change in orientation due to absorption of a second black hole....