# Accretion disk

Accretion disk in an X-ray binary star (artist's impression)

In astrophysics, an accretion disk is a disk rotating around a central object that transports ( accretes ) matter towards the center . It can consist of atomic gas, differently strong ionized gas ( plasma ) or interstellar dust .

## description

Accretion disks range in diameter from a few hundred astronomical units to hundreds of parsecs for active galactic nuclei . The matter stored in the accretion discs can exceed the mass of the accreting object by one to two orders of magnitude. These disks are described as self-gravitating disks because they are stabilized and held together by the gravitational force of the matter stored in them.

The temperature of a ring of an accretion disc is a function of density , viscosity and the speed of rotation . It therefore rises in the direction of the center and can reach up to several million Kelvin in the transition layer .

As a first approximation, the radiation profile of an accretion disk is composed of the radiation of many rings of different temperatures at different distances from the accretion object and ranges from infrared to hard X-ray radiation .

## Occur

Typical accretion disks are found around young stars during and some time after star formation ; these include the T-Tauri stars , Herbig-Ae / Be stars and the FU Orionis stars .

In older stars, accretion disks occur in binary star systems in which there is a mass flow from a donor to a compact object. These systems include the star classes of the symbiotic stars , the cataclysmic binary stars and the X-ray binary stars . The accreting compact objects are neutron stars , black holes and white dwarfs . Rarely, they are main sequence stars in algol stars , beta-lyrae stars and double-period variables .

In the accretion disks around the central black holes of galaxies , radii and mass transfer rates that are several orders of magnitude larger have been found. Depending on the perspective and accretion rate, they manifest themselves as quasars , active galactic nuclei or Seyfert galaxies .

In accretion disks around neutron stars and black holes, potential gravitational energy is converted, so that the differentially rotating disks light up brightly due to the viscosity. Depending on the compactness , the quotient of the mass and radius of the object, this mechanism can be up to 20 times as effective as the generation of radiation by nuclear processes, e.g. B. by nuclear fusion . In addition, a so-called jet often forms from the intertwined matter .

## Forms of accretion flows

ADAF stands for advection-dominated accretion flow, by which one understands an inflated flow of matter made of hot, thin gas, which assumes an approximately spherical shape around the central object collecting matter. Astronomy depends on the existence of these hot accretion flows around cosmic objects such as neutron stars or black holes in order to be able to explain how high-energy X-ray spectra come about.

#### Particle movements

The speed field in ADAF is sub-Keplersch, i. This means that for a given radius the rotation is only about 40% of the Kepler's circumferential speed at this radius. The radial speed, i.e. the speed of incidence in the direction of the central object, is comparable to this sub-Kepler rotation speed. ADAFs typically develop at low accretion rates. Relatively little matter falls on the accretor per unit of time. At high accretion rates, other accretion solutions dominate, such as the standard disk or the so-called slim disks.

### Standard disk (SSD)

Shakura-Sunyaev Disk (SSD)

The standard disc as an accretion solution was discovered in 1973 by Nikolai Shakura and Rashid Sunyaev. Therefore the standard accretion disk (SAD for short) is also called Shakura-Sunyaev-Disk or SSD. A short time later, the SSD solution was generalized relativistically . The standard disk is one of many accretion flows based on pure hydromechanics without magnetic fields and describes a flow of matter that rotates around a central, cosmic object. The flow of matter collects in a flat disk, the so-called accretion disk. In contrast to the ADAF, the standard disc can be found in different forms in all accretion flows - regardless of the accretion rate. This statement is indicated at least in a unifying accretion unification scheme.

#### properties

Orbital velocities for different distances with ${\ displaystyle v \ propto 1 / {\ sqrt {R}}}$

The flow rotates in a flat, geometrically thin disk of matter. The ratio of disk height H and typical disk radius R is called the scale height; for standard disks this is much smaller than 1. Rotating matter has angular momentum . The accretion flow has to flatten out to a disk because this state is energetically more favorable and is dictated by the conservation of angular momentum. The disk shape or axis symmetry is precisely the corresponding symmetry property to the angular momentum obtained.

Gas and dust disks generally do not rotate as a rigid body , but differentially . One can measure the orbital velocity as a function of the radius by means of spectral red and blue shifts. Accretion disks around stars or multiple star systems, in which the orbital velocity depends on the radius according to Kepler's 3rd law ( ), are also known as Kepler disks . For these it applies that the disk itself contains so little mass that its rotation is practically only determined by the central star or the central stars. ${\ displaystyle v \ propto 1 / {\ sqrt {R}}}$

The speed of rotation increases with the approach to the central object. However, there is an innermost edge of the disk, because stable rotation collapses on the marginally stable path. This inner edge is also called the innermost stable circular orbit (ISCO). The slow movement of incidence towards the central object is called "radial drift".

The disk material moves under the microscope like a viscous liquid in a turbulent manner - that is, disordered. In contrast, the Kepler speed profile is an ordered, macroscopic movement. It means that neighboring rings of disc material rotate at different speeds. These liquid rings are in communication with one another, just as the particles are loosely held together in a liquid. But the rotation moves the rings against each other. During this shear, turbulent kinetic energy is withdrawn from the disc material and converted into thermal energy.

In general, the conversion of energy into thermal energy is called dissipation . The dissipation in standard disks is a consequence of the turbulent, hydrodynamic viscosity. The temperature profile in the standard disk is precisely known on the basis of the Shakura & Sunyaev model. The disk temperature T follows a power law and increases inward with the radius r, but it decreases with the mass M of the central object. The maximum temperature at the inner edge generally depends on the mass of the central object, the accretion rate and the location of the inner edge (ISCO). A typical maximum temperature near a supermassive black hole of 100 million solar masses is about one million Kelvin . This corresponds to about a tenth of the central temperature of the sun . These high temperatures show that the disc material is often a plasma . Atomic and molecular standard disks are only conceivable at lower temperatures. Nevertheless, one often speaks of cold standard panes. This designation arose because there is an even hotter accretion flow, the ADAF. The radiation from the standard pane is thermal. The thin disk can be thought of as broken up into rings, each of which has a certain temperature. Each ring can be treated like a Planckian heat radiator , which assumes its radiation maximum at a certain wavelength . The entire spectrum of the standard disc is accordingly the sum of all rings.

The optical luminosity of the standard disk is proportional to the mass of the collecting central object. In addition, the luminosity also increases with the accretion rate. The accretion flow loses energy through the emission of electromagnetic heat radiation. The cooling is particularly efficient with standard panes. This means that the thermal energy of the material flow is almost completely emitted as radiant energy. This, together with the rotation, ensures that the accretion flow collapses and standard disks are thin, flattened accretion flows. This compacts the disc material. Electromagnetic radiation can hardly propagate inside the pane because it is constantly scattered, absorbed, re-emitted and reabsorbed by the radiation transport. Standard disks are, therefore, more or less opaque ( opaque ) for electromagnetic waves. This property of opacity in standard panes gave them the attribute optically thick.

#### Particle movements

In summary, one can say that in accretion flows like the standard disks, forms of energy are converted into one another. At the beginning there is gravitational energy, a potential energy that matter has some distance from the accretor. In the case of standard disks, this energy of the position is first converted into rotational energy. Shear and turbulence convert it into thermal energy. Finally, there is a conversion into radiant energy. This last transformation process is the decisive one for astronomy, because in this way the cosmic objects become noticeable from a great distance.

### Further accretion flows

The NRAF model (non-radiative accretion flow) has been established since 1999 and is currently being intensively pursued. In principle, the acronym NRAF subsumes all accretion flows that cannot be cooled or heated by radiation. The hot accretion flow can form an advective torus inside, close to the gravitating object.

The first NRAF models were purely hydrodynamic. The models were later refined by taking magnetic fields into account. Then an essential ingredient in the model is ideal magnetohydrodynamics . This is the simplest form of MHD that is not dissipative. Viscosities and heat conduction are not taken into account. This has the numerical advantage that the system of equations is much simpler. But even the ideal MHD shows an important mechanism: the already indicated magneto-rotational instability or magnetic rotational instability (MRI). This instability was discovered by Balbus and Hawley in 1991. This led to the alternative name Balbus-Hawley instability. MRI is essential to understand why matter from an accretion disk can fall into a black hole despite the high angular momentum. The MRI ensures very efficient angular momentum transport. The associated magnetic turbulence is much more important than the hydrodynamic turbulence. For this MHD instability to work, you only need a rotating object, e.g. B. a torus or a slim accretion disk, and a weak magnetic field that penetrates this object.

An alternative to the SSD-ADAF scenario is called TDAT, which stands for (truncated disk - advective tori), i.e. truncated disks - advective tori . The TDAT model (Hujeirat & Camenzind 2000) is characterized by the fact that a flat accretion disc ends at significantly larger radii than the marginally stable path. Further inside there is a hot ADAF. Many advection-dominated models have been proposed in recent years. Models such as ADIOS (advection-dominated inflow / outflow solutions) are known, in which significant outflows ( winds ) are also taken into account. In CDAF (convection-dominated accretion flow), the convection of the accreted plasma plays an important role.

## Mechanism of Accretion

Friction and shear forces result from the differential rotation around the central object (the inner areas rotate faster due to Kepler's laws ) . Through these and other turbulent processes in the disk, particles are transported in the direction of the central object, so that it gains mass (accretes). To do this, the particles have to dissipate their angular momentum to the outside ( conservation of angular momentum ) by transferring it to other particles, which are then “pushed away” from the central object.

The molecular viscosity is too small to be responsible for the transfer of angular momentum in the required order of magnitude. Therefore, it is believed that the disc becomes turbulent and this creates viscosity. In the case of weakly ionized disks, the magnetic fields that the ions inevitably carry with them play an important role: they cause instability ( magneto-rotation instability  (MRI)), which lead to turbulence in the disk and thus to dynamic viscosity. The theory for describing plasmas in magnetic fields is magnetohydrodynamics  (MHD).

### Disc Instability Model

Accretion disks oscillate between two states in a number of star classes, which is also known as the Disc Instability Model :

• a high viscosity (i.e., high internal friction ), high rate of accretion (i.e., high mass transfer rate) state; In this case, the disk heats up due to the high viscosity, which leads to a sharp increase in electromagnetic radiation.
• a state of low viscosity and low accretion rate.

The viscosity of the material in the disk changes by a factor of 10 between the two states.

This change of state occurs both in close binary stars (such as dwarf novae , AM-Canum-Venaticorum stars and X-ray binary stars of low mass) and in single stars such as the FU Orionis stars , which in phases with low accretion rates as T-Tauri -Stars to be classified. The change of state occurs regardless of the chemical composition; The accretion disk in the AM-CVn stars consists almost exclusively of helium and is mostly dominated by hydrogen in the other cases .

With the help of the disc instability model , the eruptions in the star classes can be described quite well, but so far no physical cause is known for the sudden change in viscosity.

## Emergence

A gas cloud can only then contract under the influence of gravity if there is some form of friction between meeting particles of different speed; otherwise the particles would retain the same kinetic energy on average even after collisions and would therefore no longer take a place further down in the potential well (i.e. drift closer to the center). The greater the relative speeds of the particles , the greater the dissipation .

If the entire contracting cloud has a significant total angular momentum, encounters parallel to the axis of rotation take place on average at a higher speed than perpendicular to the axis. As a result, the movements parallel to the axis are slowed down more than those whose orbital angular momentum coincides with the total angular momentum (i.e. than the movements perpendicular to the axis). As soon as the components move somewhat in one plane, the relative speed decreases significantly and a disk remains.

There are models for the creation of accretion discs. With them, radiation processes play an essential role in damping .

## literature

• Juhan Frank, Andrew R. King, Derek J. Raine: Accretion power in astrophysics (= Cambridge Astrophysics Series 8). Cambridge University Press, Cambridge u. a. 1985, ISBN 0-521-24530-3 .
• Matias Montesinos Armijo: Review: Accretion disk theory . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1203.6851v1 .

Wiktionary: accretion disc  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. Advection-Dominated Accretion around Black Holes. In: Cornell University. March 12, 1998, accessed February 14, 2019 .
2. Narayan & Yi, Advection-dominated accretion. In: The Astrophysical Journal. June 1994, accessed February 8, 2019 .
3. radiatively Inefficient Accretion Flow Simulation with Cooling: Implications for Black Hole Transients. In: Cornell University. April 4, 2013, accessed February 14, 2019 .
4. Slim accretion disk model. In: nasa.gov. 2003, accessed February 14, 2019 .
5. ^ Black holes in binary systems. In: harvard.edu. 1973, accessed February 14, 2019 .
6. Novikov & Thorne, Astrophysics of black holes. In: harvard.edu. 1973, accessed February 8, 2019 .
7. ^ Grand Unification of AGN and the Accretion and Spin Paradigms. In: Cornell University. August 26, 1999, accessed February 14, 2019 .
8. COSMOS - The SAO Encyclopedia of Astronomy | COSMOS. In: edu.au. astronomy.swin.edu.au, accessed on May 28, 2018 .
9. Innermost stable circular orbit of spinning test particle in Kerr-AdS black hole background. In: Cornell University. December 15, 2018, accessed February 14, 2019 .
10. Hydrodynamical non-radiative accretion flows in two dimensions. In: harvard.edu. December 1999, accessed March 15, 2019 .
11. ^ On the Nature of Angular Momentum Transport in Nonradiative Accretion Flows. In: The Astrophysical Journal. July 10, 2002, accessed March 15, 2019 .
12. ^ A powerful local shear instability in weakly magnetized disks. I - linear analysis. II - nonlinear evolution. In: harvard.edu. July 20, 1991, Retrieved March 15, 2019 .
13. ^ A model for the jet-disk connection in BH accreting systems. (PDF) In: Max Planck Institute for Astronomy. 2003, accessed February 14, 2019 .
14. ^ Iwona Kotko, Jean-Pierre Lasota: The viscosity parameter α and the properties of accretion disc outbursts in close binaries. In: Astronomy & Astrophysics . 545, 2012, p. A115, doi: 10.1051 / 0004-6361 / 201219618 , arxiv : 1209.0017
15. Lexicon of Astrophysics: Accretion