Thin-disc theory with a non-zero-torque boundary condition and comparisons with simulations (original) (raw)
Related papers
Evolution of Accretion Discs around a Kerr Black Hole using Extended Magnetohydrodynamics
MNRAS 456, 1332 (2015)
Black holes accreting well below the Eddington rate are believed to have geometrically thick, optically thin, rotationally supported accretion discs in which the Coulomb mean free path is large compared to GM/c 2. In such an environment, the disc evolution may differ significantly from ideal magnetohydrodynamic predictions. We present non-ideal global axisymmetric simulations of geometrically thick discs around a rotating black hole. The simulations are carried out using a new code grim, which evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal magnetohydrodynamics. Non-ideal effects are modeled through heat conduction along magnetic field lines, and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) insta-bilities. We find that the pressure anisotropy grows to match the magnetic pressure, at which point it saturates due to the mirror instability. The pressure anisotropy produces outward angular momentum transport with a magnitude comparable to that of MHD turbulence in the disc, and a significant increase in the temperature in the wall of the jet. We also find that, at least in our axisymmetric simulations, conduction has a small effect on the disc evolution because (1) the heat flux is constrained to be parallel to the field and the field is close to perpendicular to temperature gradients, and (2) the heat flux is choked by an increase in effective collisionality associated with the mirror instability.
Monthly Notices of the Royal Astronomical Society, 2010
The standard general relativistic model of a razor-thin accretion disc around a black hole, developed by Novikov & Thorne (NT) in 1973, assumes the shear stress vanishes at the radius of the innermost stable circular orbit (ISCO) and that, outside the ISCO, the shear stress is produced by an effective turbulent viscosity. However, astrophysical accretion discs are not razor thin; it is uncertain whether the shear stress necessarily vanishes at the ISCO, and the magnetic field, which is thought to drive turbulence in discs, may contain large-scale structures that do not behave like a simple local scalar viscosity. We describe 3D general relativistic magnetohydrodynamic simulations of accretion discs around black holes with a range of spin parameters, and we use the simulations to assess the validity of the NT model. Our fiducial initial magnetic field consists of multiple (alternating polarity) poloidal field loops whose shape is roughly isotropic in the disc in order to match the isotropic turbulence expected in the poloidal plane. For a thin disc with an aspect ratio |h/r| ∼ 0.07 around a non-spinning black hole, we find a decrease in the accreted specific angular momentum of 2.9 per cent relative to the NT model and an excess luminosity from inside the ISCO of 3.5 per cent. The deviations in the case of spinning black holes are also of the same order. In addition, the deviations decrease with decreasing |h/r|. We therefore conclude that magnetized thin accretion discs in X-ray binaries in the thermal/high-soft spectral state ought to be well described by the NT model, especially at luminosities below 30 per cent of Eddington where we expect a very small disc thickness |h/r| 0.05. We use our results to determine the spin equilibrium of black hole accretion discs with a range of thicknesses and to determine how electromagnetic stresses within the ISCO depend upon black hole spin and disc thickness. We find that the electromagnetic stress and the luminosity inside the ISCO depend on the assumed initial magnetic field geometry. We consider a second geometry with field lines following density contours, which for thin discs leads to highly radially elongated magnetic field lines. This gives roughly twice larger deviations from NT for both the accreted specific angular momentum and the luminosity inside the ISCO. Lastly, we find that the disc's corona (including any wind or jet) introduces deviations from NT in the specific angular momentum that are comparable to those contributed by the disc component, while the excess luminosity of bound gas from within the ISCO is dominated by only the disc component. Based on these indications, we suggest that differences in results between our work and other similar work are due to differences in the assumed initial magnetic field geometry as well as the inclusion of disc
A Study of a Tilted Thin Inner Accretion Disk around a Spinning Black Hole
The Astrophysical Journal, 2019
The inner part of a thin accretion disk around a Kerr black hole can serve as an important tool to study the physics of the strong gravity regime. A tilt in such a disk with respect to the black hole spin axis is particularly useful for this purpose, as such a tilt can have a significant effect on the observed X-ray spectral and timing features via Lense-Thirring precession. However, the inner disk has been predicted to become aligned with the spin direction of the black hole by the well-known Bardeen-Petterson effect. Here we calculate, both analytically and numerically, the radial profile of the thin accretion disk tilt angle in the viscous regime (i.e., a > H R; α is the Shakura-Sunyaev viscosity parameter, H is the disk thickness, and R is the radial distance). We show that the inner disk may not be aligned at all for certain reasonable ranges of parameter values. This makes the inner accretion disk particularly promising to probe the black hole parameters, and the accretion process in the strong gravity region.
Monthly Notices of the Royal Astronomical Society, 2014
If accretion disc contains weak frozen-in entangled magnetic fields, their dynamical effect may be important inside the last stable orbit because of the decompression near the sonic point. Here, I consider the radial and vertical structure of a nearly free-falling flow inside the last stable orbit of a thin disc around a Kerr black hole. The thickness of such a flow is determined primarily by the vertical stress created by radial and azimuthal magnetic fields. The thickness is predicted to oscillate vertically around its equilibrium value determined by the magnetic field balance with gravity. For thin discs, this thickness is much larger than that of the accretion disc itself. Numerical simulations with HARM2d show the vertical structure is more complicated. In particular, magnetically supported disc seems to be unstable to segregation of matter into thinner streams with the vertical scale determined by thermal pressure or other processes.
Magnetohydrodynamic simulations of black hole accretion
AIP Conference Proceedings, 2001
We discuss the results of three-dimensional magnetohydrodynamic simulations, using a pseudo-Newtonian potential, of thin disk (h/r ≈ 0.1) accretion onto black holes. We find (i) that magnetic stresses persist within r ms , the marginally stable orbit, and (ii) that the importance of those stresses for the dynamics of the flow depends upon the strength of magnetic fields in the disk outside r ms . Strong disk magnetic fields (α > ∼ 0.1) lead to a gross violation of the zero-torque boundary condition at r ms , while weaker fields (α ∼ 10 −2 ) produce results more akin to traditional models for thin disk accretion onto black holes. Fluctuations in the magnetic field strength in the disk could lead to changes in the radiative efficiency of the flow on short timescales.
Development of Secular Instability in Different Disc Models of Black Hole Accretion
Proceedings of the Indian National Science Academy, 2015
Analytical treatment of black hole accretion generally presumes the stability of the stationary configuration. Various authors in the past several decades demonstrated the validity of such an assumption for inviscid hydrodynamic flow. Inviscid assumption is a reasonable approximation for low angular momentum advection dominated flow in connection to certain supermassive black holes at the centres of the galaxies (including our own) fed from a number of stellar donors. Introduction of a weak viscosity, however, may sometimes provide a more detail understanding of the observed spectrum. Recently it has been demonstrated that introduction of small amount of viscosity in the form of quasi-viscous flow makes a stationary accretion disc -where the geometric configuration of matter is described by axisymmetric flow in hydrostatic equilibrium -unstable. We perform similar analysis for other disc models (for all three possible geometric configurations of matter) for quasi-viscous models under the post-Newtonian scheme. We introduced perturbations on the stationary flow solution particularly in standing wave form and studied their time evolution to observe whether they grow with time. Our analysis shows that same sort of secular instability exists in other disc models too. We further argued that with sufficiently low value of viscosity in the realistic astrophysical perspective, the instability does not effectively jeopardize the stationary condition.
A tilted and warped inner accretion disc around a spinning black hole: an analytical solution
Monthly Notices of the Royal Astronomical Society, 2017
Inner accretion disc around a black hole provides a rare, natural probe to understand the fundamental physics of the strong gravity regime. A possible tilt of such a disc, with respect to the black hole spin equator, is important. This is because such a tilt affects the observed spectral and timing properties of the disc X-ray emission via Lense-Thirring precession, which could be used to test the theoretical predictions regarding the strong gravity. Here, we analytically solve the steady, warped accretion disc equation of Scheurer and Feiler, and find an expression of the radial profile of the disc tilt angle. In our exact solution, considering a prograde disc around a slowly spinning black hole, we include the inner part of the disc, which was not done earlier in this formalism. Such a solution is timely, as a tilted inner disc has recently been inferred from X-ray spectral and timing features of the accreting black hole H1743-322. Our tilt angle radial profile expression includes observationally measurable parameters, such as black hole mass and Kerr parameter, and the disc inner edge tilt angle W in , and hence can be ideal to confront observations. Our solution shows that the disc tilt angle in 10-100 gravitational radii is a significant fraction of the disc outer edge tilt angle, even for W in = 0. Moreover, tilt angle radial profiles have humps in ∼10-1000 gravitational radii for some sets of parameter values, which should have implications for observed X-ray features.
The Astrophysical Journal, 2009
We examine the evolution and influence of viscosity-induced diskoseismic modes in simulated black hole accretion disks. Understanding the origin and behavior of such oscillations will help us to evaluate their potential role in producing astronomically observed high-frequency quasi-periodic oscillations in accreting black hole binary systems. Our simulated disks are geometrically thin with a constant half-thickness of 5% the radius of the innermost stable circular orbit. A pseudo-Newtonian potential reproduces the relevant effects of general relativity, and an alpha-model viscosity achieves angular momentum transport and the coupling of orthogonal velocity components in an otherwise ideal hydrodynamic numerical treatment. We find that our simulated viscous disks characteristically develop and maintain trapped global mode oscillations with properties similar to those expected of trapped g-modes and inner p-modes in a narrow range of frequencies just below the maximum radial epicyclic frequency. Although the modes are driven in the inner portion of the disk, they generate waves that propagate at the trapped-mode frequencies out to larger disk radii. This finding is contrasted with the results of global magnetohydrodynamic disk simulations, in which such oscillations are not easily identified. Such examples underscore fundamental physical differences between accretion systems driven by the magneto-rotational instability and those for which alpha viscosity serves as a proxy for the physical processes that drive accretion, and we explore potential approaches to the search for diskoseismic modes in full magnetohydrodynamic disks.
Corotation Resonance and Diskoseismology Modes of Black Hole Accretion Disks
The Astrophysical Journal, 2008
We demonstrate that the corotation resonance affects only some nonaxisymmetric g-mode oscillations of thin accretion disks, since it is located within their capture zones. Using a more general (weaker radial WKB approximation) formulation of the governing equations, such g-modes, treated as perfect fluid perturbations, are shown to formally diverge at the position of the corotation resonance. A small amount of viscosity adds a small imaginary part to the eigenfrequency which has been shown to induce a secular instability (mode growth) if it acts hydrodynamically. The g-mode corotation resonance divergence disappears, but the mode magnitude can remain largest at the place of the corotation resonance. For the known g-modes with moderate values of the radial mode number and axial mode number (and any vertical mode number), the corotation resonance lies well outside their trapping region (and inside the innermost stable circular orbit), so the observationally relevant modes are unaffected by the resonance. The axisymmetric g-mode has been seen by Reynolds & Miller in a recent inviscid hydrodynamic accretion disk global numerical simulation. We also point out that the g-mode eigenfrequencies approximately obey the harmonic relation σ ∝ m for axial mode numbers |m| ≥ 1.
The general relativistic thin disc evolution equation
Monthly Notices of the Royal Astronomical Society, 2017
In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of WKB, local techniques, and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenolgical studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.