Comment on Viscous Stability of Relativistic Keplerian Accretion Disks

Recently Ghosh (1998) reported a new regime of instability in Keplerian accretion disks which is caused by relativistic effects. This instability appears in the gas pressure dominated region when all relativistic corrections to the disk structure equations are taken into account. We show that he uses the stability criterion in completely wrong way leading to inappropriate conclusions. We perform a standard stability analysis to show that no unstable region can be found when the relativistic disk is gas pressure dominated.Comment: 9 pages, 4 figures, uses aasms4.sty, submitted for ApJ Letter

Viscous Stability of Relativistic Keplerian Accretion Disks

We investigate the viscous stability of thin, Keplerian accretion disks in regions where general relativistic (GR) effects are essential. For gas pressure dominated (GPD) disks, we show that the Newtonian conclusion that such disks are viscously stable is reversed by GR modifications in the behaviors of viscous stress and surface density over a significantly large annular region not far from the innermost stable orbit at r=\rms. For slowly-rotating central objects, this region spans a range of radii 14\lo r\lo 19 in units of the central object's mass $M$. For radiation pressure dominated (RPD) disks, the Newtonian conclusion that they are viscously unstable remains valid after including the above GR modifications, except in a very small annulus around $r\approx 14M$, which has a negligible influence. Inclusion of the stabilizing effect of the mass-inflow through the disk's inner edge via a GR analogue of Roche-lobe overflow adds a small, stable region around \rms~for RPD disks, but leaves GPD disks unchanged. We mention possible astrophysical relevance of these results, particularly to the high-frequency X-ray variabilities observed by the $Rossi$ $X-ray$ $Timing$ $Explorer$.Comment: 18 pages, 3 figures, accepted by The Astrophysical Journal Letter

Photon Bubbles and the Vertical Structure of Accretion Disks

We consider the effects of "photon bubble" shock trains on the vertical structure of radiation pressure-dominated accretion disks. These density inhomogeneities are expected to develop spontaneously in radiation-dominated accretion disks where magnetic pressure exceeds gas pressure, even in the presence of magnetorotational instability. They increase the rate at which radiation escapes from the disk, and may allow disks to exceed the Eddington limit by a substantial factor. We first generalize the theory of photon bubbles to include the effects of finite optical depths and radiation damping. Modifications to the diffusion law at low optical depth tend to fill in the low-density regions of photon bubbles, while radiation damping inhibits the formation of photon bubbles at large radii, small accretion rates, and small heights above the equatorial plane. Accretion disks dominated by photon bubble transport may reach luminosities of 10 to >100 times the Eddington limit (L_E), depending on the mass of the central object, while remaining geometrically thin. However, photon bubble-dominated disks with alpha-viscosity are subject to the same thermal and viscous instabilities that plague standard radiation pressure-dominated disks, suggesting that they may be intrinsically unsteady. Photon bubbles can lead to a "core-halo" vertical disk structure. In super-Eddington disks the halo forms the base of a wind, which carries away substantial energy and mass, but not enough to prevent the luminosity from exceeding L_E. Photon bubble-dominated disks may have smaller color corrections than standard accretion disks of the same luminosity. They remain viable contenders for some ultraluminous X-ray sources and may play a role in the rapid growth of supermassive black holes at high redshift.Comment: 38 pages, 2 figures, accepted for publication in The Astrophysical Journa

Counter-rotating Accretion Disks

We consider accretion disks consisting of counter-rotating gaseous components with an intervening shear layer. Configurations of this type may arise from the accretion of newly supplied counter-rotating gas onto an existing co-rotating gas disk. For simplicity we consider the case where the gas well above the disk midplane is rotating with angular rate $+\Omega$ and that well below has the same properties but is rotating with rate $-\Omega$. Using the Shakura-Sunyaev alpha turbulence model, we find self-similar solutions where a thin (relative to the full disk thickness) equatorial layer accretes very rapidly, essentially at free-fall speed. As a result the accretion speed is much larger than it would be for an alpha disk rotating in one direction. Counter-rotating accretion disks may be a transient stage in the formation of counter-rotating galaxies and in the accretion of matter onto compact objects.Comment: 7 pages, 3 figures, aas2pp4.sty, submitted to Ap

Surface Structure in an Accretion Disk Annulus with Comparable Radiation and Gas Pressure

We have employed a 3-d energy-conserving radiation MHD code to simulate the vertical structure and thermodynamics of a shearing box whose parameters were chosen so that the radiation and gas pressures would be comparable. The upper layers of this disk segment are magnetically-dominated, creating conditions appropriate for both photon bubble and Parker instabilities. We find little evidence for photon bubbles, even though the simulation has enough spatial resolution to see them and their predicted growth rates are high. On the other hand, there is strong evidence for Parker instabilities, and they appear to dominate the evolution of the magnetically supported surface layers. The disk photosphere is complex, with large density inhomogeneities at both the scattering and effective (thermalization) photospheres of the evolving horizontally-averaged structure. Both the dominant magnetic support and the inhomogeneities are likely to have strong effects on the spectrum and polarization of thermal photons emerging from the disk atmosphere. The inhomogeneities are also large enough to affect models of reflection spectra from the atmospheres of accretion disks.Comment: ApJ, in pres

Long-term Nonlinear Behaviour of the Magnetorotational Instability in a Localised Model of an Accretion Disc

For more than a decade, the so-called shearing box model has been used to study the fundamental local dynamics of accretion discs. This approach has proved to be very useful because it allows high resolution and long term studies to be carried out, studies that would not be possible for a global disc. Localised disc studies have largely focused on examining the rate of enhanced transport of angular momentum, essentially a sum of the Reynolds and Maxwell stresses. The dominant radial-azimuthal component of this stress tensor is, in the classic Shakura-Sunayaev model, expressed as a constant alpha times the pressure. Previous studies have estimated alpha based on a modest number of orbital times. Here we use much longer baselines, and perform a cumulative average for alpha. Great care must be exercised when trying to extract numerical alpha values from simulations: dissipation scales, computational box aspect ratio, and even numerical algorithms all affect the result. This study suggests that estimating alpha becomes more, not less, difficult as computational power increases.Comment: 10 pages, 10 figures, 2 tables, accepted by MNRA

Non-Steady State Accretion Disks in X-Ray Novae: Outburst Models for Nova Monocerotis 1975 and Nova Muscae 1991

We fit outbursts of two X-ray novae (Nova Monocerotis 1975=A0620-00 and Nova Muscae GS 1991=1124-683) using a time-dependent accretion disk model. The model is based on a new solution for a diffusion-type equation for the non-steady-state accretion and describes the evolution of a viscous alpha-disk in a binary system after the peak of an outburst, when matter in the disk is totally ionized. The accretion rate in the disk decreases according to a power law. We derive formulas for the accretion rate and effective temperature of the disk. The model has three free input parameters: the mass of the central object M, the turbulence parameter alpha, and the normalization parameter delta t. Results of the modeling are compared with the observed X-ray and optical B and V light curves. The resulting estimates for the turbulence parameter $\alpha$ are similar: 0.2-0.4 for A 0620-00 and 0.45-0.65 for GS 1124-683, suggesting a similar nature for the viscosity in the accretion disks around the compact objects in these sources. We also derive the distances to these systems as functions of the masses of their compact objects.Comment: 10 pages, 7 figures; style improve

A New Equilibrium for Accretion Disks Around Black Holes

Accretion disks around black holes in which the shear stress is proportional to the total pressure, the accretion rate is more than a small fraction of Eddington, and the matter is distributed smoothly are both thermally and viscously unstable in their inner portions. The nonlinear endstate of these instabilities is uncertain. Here a new inhomogeneous equilibrium is proposed which is both thermally and viscously stable. In this equilibrium the majority of the mass is in dense clumps, while a minority reaches temperatures $\sim 10^9$ K. The requirements of dynamical and thermal equilibrium completely determine the parameters of this system, and these are found to be in good agreement with the parameters derived from observations of accreting black holes, both in active galactic nuclei and in stellar binary systems.Comment: AAS LaTeX, accepted to Ap. J. Letter