Radiatively-inefficient accretion disks

Here we briefly discuss an important class of accretion disks models that have received much attention in recent years -- the radiatively-inefficient disks. Such disks, in which the radiative-efficiency $\eta$ becomes small, can occur when the accretion rate is either very low or very high. The physics is rather different in these two cases. For low accretion rates, the accreting plasma becomes so tenuous that the electrons and ions may lose thermal contact with each other (assuming that they are principally coupled via Coulomb collisions). The ions are very poor radiators; thus if most of the accretion energy is channeled to the ions rather than the electrons, it will not be radiated and instead remain as thermal energy advected along within the accretion flow [162,163]. In the so-called Advection Dominated Accretion Flows (ADAFs), this energy is advected right through the event horizon [164,165,166]. Such models were in fact first proposed to explain the hard state spectrum of Cyg X-1 [162], but were later applied to AGN [163], and they have been used to model the Galactic Center [167,168,169].

It was later realized that the situation described by these low luminosity ADAF models was dynamically unlikely -- the viscous transport of energy within this flow could readily unbind material further out, possibly leading to a powerful wind [170] or strong convection [171]. These suggestions remain controversial [113] and are the subject of active research [172,173,174], but in any case, such a flow is likely to be extremely hot (electron temperatures of $\sim 10^9{\rm\thinspace K}$) and optically-thin.

Although these models possess the sphere+disk geometry (the inner region is advection dominated while the outer region represents a standard disk), ADAF models postulate that a large fraction of the seed photons for Comptonization come from synchrotron radiation internal to the radiatively inefficient flow [175]. In addition, their low-levels of emission are concentrated towards small radii [164], while their outer radii have been postulated to extend anywhere from 10-$10^4\,GM/c^2$ [176]. In the context of the disk atmosphere modeling described below, most (but not all) variants of the ADAF model predict weak spectral lines from the innermost regions of the accretion flow.

For very high accretion rates, comparable to that needed to produce the Eddington luminosity, the accretion inflow time scale can become less than the time it takes for radiation to diffuse out of the disk, and hence the photons can become trapped in the accretion flow [177]. The inability of these disks to radiate the gravitational potential energy, together with the viscous transport of energy and strong radiation pressures present, will almost certainly lead to strong outflows. The appearance of such disks is highly uncertain -- it is unclear whether an X-ray emitting corona forms, and whether the atmosphere of such a disk is in a state capable of producing X-ray reflection spectral signatures. At the very least, it is highly unlikely that strong line features will emanate from the innermost, highly relativistic regions of the accretion flow.