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Register a new userOn the Eddington limit in accretion discs
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Added by
Dominikus Heinzeller
Publication date
2006
fields
Physics
and research's language is
English
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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.
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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.
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
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.
Super-Eddington mass accretion has been suggested as an efficient mechanism to grow supermassive black holes (SMBHs). We investigate the imprint left by the radiative efficiency of the super-Eddington accretion process on the clustering of quasars using a new semi-analytic model of galaxy and quasar formation based on large-volume cosmological $N$-body simulations. Our model includes a simple model for the radiative efficiency of a quasar, which imitates the effect of photon trapping for a high mass accretion rate. We find that the model of radiative efficiency affects the relation between the quasar luminosity and the quasar host halo mass. The quasar host halo mass has only weak dependence on quasar luminosity when there is no upper limit for quasar luminosity. On the other hand, it has significant dependence on quasar luminosity when the quasar luminosity is limited by its Eddington luminosity. In the latter case, the quasar bias also depends on the quasar luminosity, and the quasar bias of bright quasars is in agreement with observations. Our results suggest that the quasar clustering studies can provide a constraint on the accretion disc model.
(abridged) MHD turbulence is known to exist in shearing boxes with either zero or nonzero net magnetic flux. However, the way turbulence survives in the zero-net-flux case is not explained by linear theory and appears as a purely numerical result. Aims: We look for a nonlinear mechanism able to explain the persistence of MHD turbulence in shearing boxes with zero net magnetic flux, and potentially leading to large-scale dynamo action. Method: Spectral nonlinear simulations of the magnetorotational instability are shown to exhibit a large-scale axisymmetric magnetic field, maintained for a few orbits. The generation process of this field is investigated using the results of the simulations and an inhomogeneous linear approach. Results: The mechanism by which turbulence is sustained in zero-net-flux shearing boxes is shown to be related to the existence of a large-scale azimuthal field, surviving for several orbits. In particular, it is shown that MHD turbulence in shearing boxes can be seen as a dynamo process coupled to a magnetorotational-type instability.
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