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Register a new userOn the Eddington limit for relativistic accretion discs
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Standard accretion disc model relies upon several assumptions, the most important of which is geometrical thinness. Whenever this condition is violated, new physical effects become important such as radial energy advection and mass loss from the disc. These effects are important, for instance, for large mass accretion rates when the disc approaches its local Eddington limit. In this work, we study the upper limits for standard accretion disc approximation and find the corrections to the standard model that should be considered in any model aiming on reproducing the transition to super-Eddington accretion regime. First, we find that for thin accretion disc, taking into account relativistic corrections allows to increase the local Eddington limit by about a factor of two due to stronger gravity in General Relativity (GR). However, violation of the local Eddington limit also means large disc thickness. To consider consequently the disc thickness effects, one should make assumptions upon the two-dimensional rotation law of the disc. For rotation frequency constant on cylinders $rsintheta=const$, vertical gravity becomes stronger with height on spheres of constant radius. On the other hand, effects of radial flux advection increase the flux density in the inner parts of the disc and lower the Eddington limit. In general, the effects connected to disc thickness tend to increase the local Eddington limit even more. The efficiency of accretion is however decreased by advection effects by about a factor of several.
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Although the Eddington limit has originally been derived for stars, recently its relevance for the evolution of accretion discs has been realized. We discuss the question whether the classical Eddington limit - which has been applied globally for almost all calculations on accretion discs - is a good approximation if applied locally in the disc. For this purpose, a critical accretion rate corresponding to this type of modified classical Eddington limit is calculated from thin alpha-disc models and slim disc models. We account for the non-spherical symmetry of the disc models by computing the local upper limits on the accretion rate from vertical and radial force equilibria separately. It is shown that the results can differ considerably from the classical (global) value: The vertical radiation force limits the maximum accretion rate in the inner disc region to much less than the classical Eddington value in thin alpha-discs, while it allows for significantly higher accretion rates in slim discs. We discuss the implications of these results for the evolution of accretion discs and their central objects.
X-ray reverberation is a powerful technique which maps out the structure of the inner regions of accretion disks around black holes using the echoes of the coronal emission reflected by the disk. While the theory of X-ray reverberation has been developed almost exclusively for standard thin disks, recently reverberation lags have been observed from likely super-Eddington accretion sources such as the jetted tidal disruption event Swift J1644+57. In this paper, we extend X-ray reverberation studies into the super-Eddington accretion regime, focusing on investigating the lags in the Fe K{alpha} line region. We find that the coronal photons are mostly reflected by the fast and optically thick winds launched from super-Eddington accretion flow, and this funnel-like reflection geometry produces lag-frequency and lag-energy spectra with unique characteristics. The lag-frequency spectra exhibits a step-function like decline near the first zero-crossing point. As a result, the shape of the lag-energy spectra remains almost independent of the choice of frequency bands and linearly scales with the black hole mass for a large range of parameter spaces. Not only can these morphological differences be used to distinguish super-Eddington accretion systems from sub-Eddington systems, they are also key for constraining the reflection geometry and extracting parameters from the observed lags. When explaining the X-ray reverberation lags of Swift J1644+57, we find that the super-Eddington disk geometry is preferred over the thin disk, for which we obtain a black hole mass of 5-6 million solar masses and a coronal height around 10 gravitational radii by fitting the lag spectra to our modeling.
The faintest ultraluminous X-ray sources (ULXs), those with 0.3-10 keV luminosities 1 < L_X/10^39 < 3 erg s^-1, tend to have X-ray spectra that are disk-like but broader than expected for thin accretion disks. These `broadened disk spectra are thought to indicate near- or mildly super-Eddington accretion onto stellar remnant black holes. Here we report that a sample of bright thermal-dominant black hole binaries, which have Eddington ratios constrained to moderate values, also show broadened disk spectra in the 0.3-10 keV band at an order of magnitude lower luminosities. This broadening would be missed in studies that only look above ~2 keV. While this may suggest that broadened disk ULXs could be powered by accretion onto massive stellar remnant black holes with close to maximal spin, we argue in favor of a scenario where they are at close to the Eddington luminosity, such that radiation pressure would be expected to result in geometrically slim, advective accretion disks. However, this implies that an additional physical mechanism is required to produce the observed broad spectra at low Eddington ratios.
Observational evidence accumulated over the past decade indicates that accretion discs in X-ray binaries are viscously stable unless they accrete very close to the Eddington limit. This is at odds with the most basic standard accretion disc theory, but could be explained by either having the discs to be much cooler whereby they are not radiation pressure dominated, or by a more sophisticated viscosity law. Here we argue that the latter is taking place in practice, on the basis of a stability analysis that assumes that the magneto-rotational-instability (MRI) responsible for generating the turbulent stresses inside the discs is also the source for a magnetically dominated corona. We show that observations of stable discs in the high/soft states of black hole binaries, on the one hand, and of the strongly variable microquasar GRS 1915+105 on the other, can all be explained if the magnetic turbulent stresses inside the disc scale proportionally to the geometric mean of gas and total pressure with a constant of proportionality (viscosity parameter) having a value of a few times 10^{-2}. Implications for bright AGN are also briefly discussed
Gravitational microlensing by the stellar population of lensing galaxies provides an important opportunity to spatially resolve the accretion disk structure in strongly lensed quasars. Some of the objects (like Einsteins cross) are reasonably consistent with the predictions of the standard accretion disk model. In other cases, the size of the emitting region is larger than predicted by the standard thin disk theory and practically independent on wavelength. This may be interpreted as an observational manifestation of an optically-thick scattering envelope possibly related to super-Eddington accretion with outflows.
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