Received May 21 Accepted December 8. Create citation alert. Journal RSS feed. Select your desired journals and corridors below. You will need to select a minimum of one corridor. Analytical studies and numerical simulations of time-dependent axially symmetric flows onto black holes have shown that it is possible to produce stationary shock waves with a stable position for both ideal inviscid and moderately viscous accretion disks.
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We perform several two-dimensional numerical simulations of accretion flows in the equatorial plane to study shock stability against nonaxisymmetric azimuthal perturbations. We find a peculiar new result. A very small perturbation seems to produce an instability as it crosses the shock, but after some small oscillations, the shock wave suddenly transforms into an asymmetric closed pattern and stabilizes with a finite radial extent, despite the fact that the inflow and outflow boundary conditions are perfectly symmetric.
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Related links. Shearing box simulations have also proven valuable in studying radiation-dominated disks. As we said, though, there are limits imposed by the finite size of the shearing box.
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The minimum physics required for a global simulation of an accretion disk are gravity and hydrodynamics assuming the disk is dense enough for the continuum approximation to hold. Since many disks have masses that are small compared to the mass of the central compact object, the self-gravity of the disk can often be ignored. Therefore, in the next three sections, gravity will simply mean that of the central black hole.
Wilson was able to confirm the additional centrifugal support that the infalling material experienced due to the rotating black hole. The cases showed greater time variability and illustrated the power of direct numerical simulations to extend our understanding of black hole accretion.
Thus, the inclusion of magnetic fields in numerical simulations of relativistic accretion disks is important. Perhaps the two most important contributions so far from relativistic MHD simulations of accretion disks have been: 1 elucidating the behavior of MRI turbulent disks in the vicinity of black holes, and 2 exploring the many interrelations between magnetic fields and relativistic jets. In most other cases, radiative processes must somehow be accounted for.
Probably the most glaring shortcoming of almost all numerical simulations of accretion disks and many other phenomena in astrophysics to date is the unrealistic treatment of radiation, which is most often simply ignored. This is not due to a lack of appreciation of its importance on the part of numericists, but simply a reflection of the fact that there are very few efficient ways to treat radiation computationally in multiple dimensions.
The optically-thin limit is an exception. In this case, the radiative cooling only enters the energy and momentum conservation equations as a source term. A few steps toward the goal of relativistic radiation MHD simulations of black hole accretion disks have also been taken in recent years. Simulations of accretion disks, though, must await the generalization of this method to treat radiation both in the optically thick and thin limits. In most simulations of accretion disks around black holes, the self-gravity of the disk is ignored.
In many cases this is justified as the mass of the disk is often much smaller than the mass of the black hole. This is also much simpler as it allows one to treat gravity as a background condition, either through a Newtonian potential or a relativistic metric the so-called Cowling approximation in relativity. However, there are plausible astrophysical scenarios in which this approximation is not valid. Two of the more interesting are: 1 a tidally disrupted neutron star accreting onto a stellar-mass black hole; and 2 an overlying stellar envelope accreting onto a nascent black hole during the final dying moments of a massive star.
Treating a self-gravitating disk in general relativity requires a code that can simultaneously evolve the spacetime metric by solving the Einstein field equations and the matter, magnetic, and radiation fields. These studies have confirmed earlier results that the runaway instability does not develop. In this section we touch on a few highlights from this area of research. Some of this work has focused on confirming predictions from analytic theory. In cases where several wavenumbers were unstable, multiple planets would begin to form but then nonlinear mode-mode coupling would cause them to merge.
For wide tori, particularly when the tori extended beyond their Roche limits, overflowed their cusps, and accreted into the hole, the PPI saturated at low amplitude or was prevented from growing altogether. Another interesting note is that most of the global numerical simulations of MRI turbulent disks have used a Polish doughnut as the starting condition. On the other hand, simulations show that magnetic fields do tend to dominate regions outside the disk, including in the hot, magnetized corona that sandwiches the disk and in the evacuated, highly magnetized funnel region.
Despite the increased complexity of the disk when MRI-driven turbulence is at play, many features and properties remain strikingly similar to what is revealed in hydrodynamic-only studies. The inner torus is predominantly a hydrodynamic structure, as it is largely gas pressure supported.
Generically, this inner torus consists of a sequence of equidensity and equipressure surfaces with a pressure maximum at , a cusp at , and a roughly parabolic, evacuated, though magnetized, funnel along the rotation axis. Early numerical simulations of black hole accretion disks nearly all focused on thick disks.
This was mostly for computational convenience as thicker disks require fewer resources than thin ones. In recent years, though, the resources have become available to start testing thinner disks. This prescription conveniently makes the same assumption that the Novikov—Thorne model does: that all energy dissipated as heat in the disk is radiated away locally on roughly the orbital timescale.
This is probably reasonable for an appropriate range of mass accretion rates, though it will be good to test this assumption with future global radiation-MHD simulations. To some extent, this is an extension of the Polish-doughnut simulations of the last decade, yet goes beyond it in at least two important respects: 1 the simulations cover a significantly larger spatial range a few hundreds of versus a few tens ; and 2 the simulations explore much longer temporal evolution hundreds of thousands of versus tens of thousands. The result of this is that the simulations are able to explore steady-state accretion out to much larger radii as opposed to.
More can be expected from this work in the coming years. The ratio of these modes is important as the highest-frequency QPOs in black hole low-mass X-ray binaries are observed to occur in this ratio. It is unclear what the implications of this are.
Numerical Simulation Of Viscous Shocked Accretion Flows Around Black Holes
It may be that some missing physics, such as radiation transport, plays a fundamental role in exciting QPOs. This is an important open problem in numerical simulations of black hole accretion disks. In recent years several numerical simulations have demonstrated the generation of jets self-consistently from simulations of disks.
A few researchers have claimed to produce jetted outflows from purely hydrodynamic interactions.
However, such simulations usually require very special starting conditions and the jets tend to be transient features of the flow; therefore, it is unlikely these are related to the well-collimated expansive jets observed in many black hole systems. Among MHD simulations, some distinction should be drawn between those that impose large scale magnetic fields that extend beyond the domain of the simulation and those that, at least initially, impose a self-contained magnetic field.
In the first case, the disk is often treated merely as a boundary condition for the evolution of large-scale magnetic field. Shibata and Uchida [ , ] used this technique to show that jets could be driven both by a pinching of the fields due to radial inflow through the disk and by the force caused when twisted fields unwind.
This limits the range of power expected for realistic AGN spins to a factor of a few tens at most — too small to explain the observed differences. There has also been some work recently trying to understand a different jet dichotomy — one that is observed in black hole low-mass X-ray binaries LMXBs. Recently, work has begun to focus on highly magnetized disk configurations, for which some modes of the MRI may be suppressed. They found that, indeed, the densest inner regions of the disk collapse down to a cool, thin, magnetically-supported structure. If the field has a consistent net flux, then doing so will necessarily increase the strength of the field near the hole due simply to the smaller area through which the flux must thread.
Hide Subsections. First, there is quite a lot of physics involved: relativistic gravity, hydrodynamics, magnetic fields, and radiation being the most fundamental. Then there is the issue that accretion disks are inherently multi-dimensional objects. The computational expense of including extra dimensions in a numerical simulation is not a trivial matter.
Simply going from one to two dimensions still assuming axisymmetry for a disk increases the computational expense by a very large factor or more. Going to three-dimensions and relaxing all symmetry requirements increases the computational expense yet again by a similar factor.
Simulations of this size have only become feasible within the last decade and still only with a subset of the physics one is interested in and usually with a very limited time duration. The simulations all begin with the same initial conditions, but have different energy conservation and cooling treatments: The upper-left panel conserves internal energy and ignores cooling; the upper-right panel conserves internal energy and includes cooling; the lower-left panel conserves total energy and ignores cooling; the lower-right panel conserves total energy and includes cooling.
The very different end states illustrate the importance of properly capturing thermodynamic processes. The bars show the variability of. The lines represent the predicted dependencies , where is the adiabatic index. The density contours are linearly spaced between and 0.
Image reproduced by permission, copyright by AAS. The individual plots are labeled by model. In each case the Keplerian distribution for a test particle, , is shown as a dashed line. The scale is logarithmic and is the same for all panels; the color maps saturate in the axial funnel. The body of the accretion disk is identified with overlaid density contours at , , , and of.
In all cases, the magnetic pressure is low in the disk, comparable to gas pressure in the corona above and below the disk, and high in the funnel region. Note, though, that the contours on the left are linearly spaced, while those on the right are logarithmically spaced. Thus, the gradients represented on the left are shallower than those on the right. The dashed vertical line marks the ISCO.
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