Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the limit cycle instability in magnetized accretion discs
152
0
0.0
(
0
)
Authors
A. Merloni
Ask ChatGPT about the research
No Arabic abstract
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
rate research
Read More
We examine the properties of strongly magnetized accretion discs in a global framework, with particular focus on the evolution of magnetohydrodynamic instabilities such as the magnetorotational instability (MRI). Work by Pessah and Psaltis showed that MRI is stabilized beyond a critical toroidal field in compressible, differentially rotating flows and, also, reported the appearance of two new instabilities beyond this field. Their results stemmed from considering geometric curvature effects due to the suprathermal background toroidal field, which had been previously ignored in weak-field studies. However, their calculations were performed under the local approximation, which poses the danger of introducing spurious behavior due to the introduction of global geometric terms in an otherwise local framework. In order to avoid this, we perform a global eigenvalue analysis of the linearized MHD equations in cylindrical geometry. We confirm that MRI indeed tends to be highly suppressed when the background toroidal field attains the Pessah-Psaltis limit. We also observe the appearance of two new instabilities that emerge in the presence of highly suprathermal toroidal fields. These results were additionally verified using numerical simulations in PLUTO. There are, however, certain differences between the the local and global results, especially in the vertical wavenumber occupancies of the various instabilities, which we discuss in detail. We also study the global eigenfunctions of the most unstable modes in the suprathermal regime, which are inaccessible in the local analysis. Overall, our findings emphasize the necessity of a global treatment for accurately modeling strongly magnetized accretion discs.
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.
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.
(Abridged) We analyse the stability and evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are power-law functions of cylindrical radius. We employ two different hydrodynamic codes to perform 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the viscosity. We present a stability analysis of the problem that we use to interpret the simulation results. We find that disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of modes with wavenumber ratios |k_R/k_Z| >> 1 when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time scale. These discs are subject to the Goldreich-Schubert-Fricke (GSF) or `vertical shear linear instability. Development of the instability involves excitation of vertical breathing and corrugation modes in the disc, with the corrugation modes in particular being a feature of the nonlinear saturated state. Instability operates when the dimensionless disc kinematic viscosity nu < 10^{-6} (Reynolds numbers Re>H c_s/nu > 2500). In 3D the instability generates a quasi-turbulent flow, and the Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches alpha ~ 6 x 10^{-4} by the end of the simulation. The vertical shear instability in disc models which include realistic thermal physics has yet to be examined. Should it occur, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance.
Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long standing puzzle. These flows are linearly stable. Here we explore the evolution of perturbation in such flows in the presence of an additional force. Such a force, which is expected to be stochastic in nature hence behaving as noise, could be result of thermal fluctuations (however small be), Brownian ratchet, grain-fluid interactions and feedback from outflows in astrophysical discs etc. We essentially establish the evolution of nonlinear perturbation in the presence of Coriolis and external forces, which is modified Landau equation. We show that even in the linear regime, under suitable forcing and Reynolds number, the otherwise least stable perturbation evolves to a very large saturated amplitude, leading to nonlinearity and plausible turbulence. Hence, forcing essentially leads a linear stable mode to unstable. We further show that nonlinear perturbation diverges at a shorter timescale in the presence of force, leading to a fast transition to turbulence. Interestingly, emergence of nonlinearity depends only on the force but not on the initial amplitude of perturbation, unlike original Landau equation based solution.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
