Accretion disc

An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction causes 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. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of oscillation modes in accretion disks is referred to as diskoseismology.Credit: NASA/JPL-Caltech An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction causes 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. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of oscillation modes in accretion disks is referred to as diskoseismology. Accretion disks are a ubiquitous phenomenon in astrophysics; active galactic nuclei, protoplanetary disks, and gamma ray bursts all involve accretion disks. These disks very often give rise to astrophysical jets coming from the vicinity of the central object. Jets are an efficient way for the star-disk system to shed angular momentum without losing too much mass. The most spectacular accretion disks found in nature are those of active galactic nuclei and of quasars, 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, 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 wants to adopt a lower orbit. As the particle falls to this lower orbit, a portion of its gravitational potential energy 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-rays just outside the event horizon. 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. 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 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 disk forms instead. Accretion disks surrounding T Tauri stars or Herbig stars are called protoplanetary disks 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 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, where Ω {displaystyle Omega } represents the angular velocity of a fluid element and R {displaystyle R} its distance to the rotation center,an accretion disk 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 disk. 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 α {displaystyle alpha } -model (discussed below) introduces an adjustable parameter α {displaystyle 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. 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 ν = α c s H {displaystyle u =alpha c_{ m {s}}H} where c s {displaystyle c_{ m {s}}} is the sound speed, H {displaystyle H} is the scale height of the disk Shakura and Sunyaev,1973), and α {displaystyle alpha } is a free parameter between zero (no accretion) and approximately one. In a turbulent medium ν ≈ v t u r b l t u r b {displaystyle u approx v_{ m {turb}}l_{ m {turb}}} , where v t u r b {displaystyle v_{ m {turb}}} is the velocity of turbulent cells relative to the mean gas motion, and l t u r b {displaystyle l_{ m {turb}}} is the size of the largest turbulent cells, which is estimated as l t u r b ≈ H = c s / Ω {displaystyle l_{ m {turb}}approx H=c_{ m {s}}/Omega } and v t u r b ≈ c s {displaystyle v_{ m {turb}}approx c_{ m {s}}} , where Ω = ( G M ) 1 / 2 r − 3 / 2 {displaystyle Omega =(GM)^{1/2}r^{-3/2}} is the Keplerian orbital angular velocity, r {displaystyle r} is the radial distance from the central object of mass M {displaystyle M} . By using the equation of hydrostatic equilibrium, combined with conservation of angular momentum and assuming that the disk is thin, the equations of disk structure may be solved in terms of the α {displaystyle alpha } parameter. Many of the observables depend only weakly on α {displaystyle alpha } , so this theory is predictive even though it has a free parameter.