It can be shown that in the presence of such a spring-like tension the Rayleigh stability criterion is replaced by
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.
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)
Accretion disk QPOs: Quasi-periodic oscillations happen in many accretion disks, with their periods appearing to scale as the inverse of the mass of the central object. Why do these oscillations exist? Why are there sometimes overtones, and why do these appear at different frequency ratios in different objects?