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Dust forming around planets is called an accretion disc.
Accretion disc (or accretion disk) is a structure formed by material falling into a gravitational source. Conservation of angular momentum requires that, as a large cloud of material collapses inward, any small rotation it may have will increase. Centripetal force causes the rotating cloud to collapse into a disc, and tidal effects will tend to align this disc's rotation with the rotation of the gravitational source in the middle. Viscosity within the disc generates heat and saps Orbital momentum, causing material in the disc to spiral inward until it impacts in an accretion shock on the central body if the body is a star, or slips toward the Event horizon if the central body is a black hole.
Accretion discs are a ubiquitous phenomenon in astrophysics; active galactic nuclei, protoplanetary discs, and Gamma ray bursts are only a few phenomena in which they are thought to occur. These discs very often give rise to jets coming out of the axis of rotation of the disc. The mechanism that produces these jets is not understood.
The most spectacular accretion discs found in nature are those of active galactic nuclei and 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-rays just outside of the Event horizon. The huge luminosity of quasars is believed to be a result of friction caused by gas and dust falling into the accretion discs of supermassive black holes, which can convert about 10 percent of the mass of an object into energy as compared to around 0.5 percent for nuclear fusion processes.
Often, in binary systems with one black hole, observations show matter being pulled from the visible star when it exceeds its Roche lobe and falling into the black hole's accretion disc. The largest and most voracious black holes known are those which form the cores of quasars, whose accretion discs emit more radiation than entire galaxies of stars.
protoplanetary discs are referred to as accretion disks when viewed as material falling into the central protostar.
The viscosity in an accretion disc cannot be ordinary gas viscosity, as this is too small by many orders of magnitude. Shakura and Sunyaev (1973) constructed a simple prescription which parametrised the ignorance of exactly what was causing the viscosity? into a parameter,a so
? = acsH
wherecs is the sound speed, andH is the disc thickness. This assumption can be derived by assuming that the accretion disc is highly turbulent, noting that the size of the largest turbulent cells is of the order of the disk height, and observing that the turbulent velocities must be less than the sound speed.
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 thea parameter. Many of the observables depend only weakly ona, so this theory is predictive even though it has a free parameter.
Using Kramers' law for the opacity it is found that
whereTc and? are the mid-plane temperature and density respectively. is the accretion rate, in units of ,m1 is the mass of the central accreting object in units of a solar mass, ,R10 is the radius of a point in the disc, in units of1010cm, and , where is the radius where angular momentum stops being transported inwards.
This theory breaks down when gas pressure is not significant. For example, if the accretion rate approaches the Eddington limit, radiation pressure becomes important and the disk will "puff up" into a torus or some other three dimensional solution like an Advection Dominated Accretion Flow (ADAF). Another extreme is the case of Saturn's rings, where the disk is so gas poor its angular momentum transport is dominated by solid body collisions and disk-moon gravitational interactions.
Accretion disc: Magneto-Rotational Instability.
The Rayleigh stability criterion,
holds everywhere in an accretion disc with a Keplerian angular velocity profile. This means that the disk is stable to hydrodynamic perturbations, and the fluid flow is expected to be laminar. For there to be turbulence, as required for thea-disc model this implies that there is some form of nonlinear hydrodynamic instability, or angular momentum transport is due to some other mechanism.
Balbus and Hawley (1991) proposed a mechanism which involves magnetic fields to generate the turbulence. The key point is that Magnetohydrodynamics is subtly different from that of hydrodynamics. The tension forces of a magnetic field have no correspondence in the hydrodynamic regime.
A weak magnetic field acts like a spring. If there is a weak radial magnetic field in an accretion disc, then two gas volume elements will experience a force acting on them. The inner element will have a force acting to slow it down. This causes it to lose energy and angular momentum and move inwards, where paradoxically, due to orbital mechanics it speeds up. The reverse happens to the outer gas element, which moves outwards and slows down. As a consequence, the magnetic field 'spring' is stretched, transferring angular momentum in the process. The radial magnetic field is eventually wound into a toroidal field as the disk rotates differentially.
The Parker instability causes regions with higher than average magnetic flux to be buoyant. Thus the toroidal field will tend to rise out of the disc plane, forming a poloidal component. The radial instability then causes small radial kinks in the poloidal field to grow exponentially, completing the dynamo. This process is called the magneto-rotational instability (MRI). This instability has timescale approximately the same as the disc orbital time scale.
Unfortunately, since the MRI is global in character it makes analytic models of accretion discs difficult to obtain. Instead, people now concentrate on numerical magnetohydrodynamic simulations to discover the workings of these astrophysical objects.
References to Accretion disc.
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