Stability Of Accretion Disks Research Articles

Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion

Abstract The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with a special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of the Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal magnetorotational instability (MRI). Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearing box simulations and find very good agreement with the results derived from linear theory. Because the modes under consideration are also exact solutions of the nonlinear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the nonlinear evolution in some regions of protoplanetary disks.

Newtonian analogue of Schwarzschild–de Sitter spacetime: Influence on the local kinematics in galaxies

The late time accelerated expansion of the Universe demands that even in local galactic scales it is desirable to study astrophysical phenomena, particularly relativistic accretion related phenomena in massive galaxies or in galaxy mergers and the dynamics of the kiloparsecs-scale structure and beyond, in the local galaxies in Schwarzschild--de Sitter (SDS) background, rather than in Schwarzschild or Newtonian paradigm. Owing to the complex and nonlinear character of the underlying magnetohydrodynamical equations in general relativistic (GR) regime, it is quite useful to have a Newtonian analogous potential containing all the important GR features that allows us to treat the problem in Newtonian framework for study of accretion and its related processes. From the principle of conserved Hamiltonian of the test particle motion, here, a three dimensional Newtonian analogous potential has been obtained in spherical geometry corresponding to SDS/Schwarzschild--anti--de Sitter spacetime, that reproduces almost all of the GR features in its entirety with remarkable accuracy. The derived potential contains an explicit velocity dependent term of the test particle that renders an approximate relativistic modification of Newtonian-like potential. The complete orbital dynamics around SDS geometry and the epicyclic frequency corresponding to SDS metric have been extensively studied in the Newtonian framework using the derived potential. Applying the derived analogous potential it is found that the current accepted value of $\mathrm{\ensuremath{\Lambda}}\ensuremath{\sim}{10}^{\ensuremath{-}56}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$ moderately influences both sonic radius as well as Bondi accretion rate, especially for spherical accretion with smaller values of adiabatic constant and temperature, which might have interesting consequences on the stability of accretion disk in active galactic nuclei/radio galaxies.

The role of toroidal magnetic field in the stability of accretion disks with alpha viscosity and other viscosities

The standard thin accretion disk model predicts that the inner regions of alpha model disks, where radiation pressure is dominant, are thermally and viscously unstable. However, observations show that the bright X-ray binaries and AGN accretion disks, corresponding to radiation-pressure thin disks, are stable. In this paper, we reconsider the linear and local instability of accretion disks in the presence of a toroidal magnetic field. In the basic equations, we consider physical quantities such as advection, thermal conduction, arbitrary viscosity, and an arbitrary cooling function also. A fifth order diffusion equation is obtained and is solved numerically. The solutions are compared to non-magnetic cases. The results show that the toroidal magnetic field can make the thermal instability in radiation pressure-dominated slim disks disappear if ϕm≥0.3. However, it causes a more thermal instability in radiation pressure alpha disks without advection. Also, we consider the thermal instability in accretion disks with other values of the viscosity and obtain a general criterion for thermal instability in the long-wavelength limit and in the presence of a toroidal magnetic field.

Stability of Accretion Discs around Magnetized Stars

We study the stability of accretion disc around magnetised stars. Starting from the equations of magnetohydrodynamics we derive equations for linearized perturbation of geometrically thin, optically thick axisymmetric accretion disc with an internal dynamo around magnetized stars. The structure and evolution of such discs are governed by an evolution equation for matter surface density ∑(R,T). Using the time-dependent equations for an accretion disc we do a linear stability analysis of our steady disc solutions in the presence of the magnetic field generated due to an internal dynamo.

The stability of accretion discs with inflow driven purely by magnetic winds

A model is presented for an accretion disc in which the inflow is driven purely by the angular momentum removed in a centrifugally accelerated magnetic wind. Turbulent discs around compact stars are considered, with the required magnetic field being generated in the disc by a simple dynamo. The turbulent magnetic Prandtl number, Np, measures the ratio of turbulent viscosity to turbulent magnetic diffusivity. Formally, the hypothetical limit Np 0 corresponds to the magnetic wind torque dominating the viscous torque, but in practice the inflow is magnetically controlled for Np≲ 0.1. The suggestion by previous authors that purely magnetic wind-driven discs may be unstable is investigated. A detailed steady solution is found which allows perturbations to the thermal balance and vertical equilibrium to be calculated, and hence the effect of perturbations to the magnetic diffusivity, η, to be assessed. For a standard parametrized form of η, the wind-driven angular momentum balance is found to be linearly unstable. An increase in the inflow rate leads to increased bending of the poloidal magnetic field and an enhanced wind mass loss rate. This increases the angular momentum loss rate which drives further inflow. There is a resultant increase in η, due to the temperature perturbation, but this does not relieve field bending sufficiently to prevent the instability.

Mass-losing accretion discs around supermassive black holes

We study the effects of outflow/wind on the gravitational stability of accretion discs around supermassive black holes using a set of analytical steady-state solutions. Mass-loss rate by the outflow from the disc is assumed to be a power-law of the radial distance and the amount of the energy and the angular momentum which are carried away by the wind are parameterized phenomenologically. We show that the mass of the first clumps at the self-gravitating radius linearly decreases with the total mass-loss rate of the outflow. Except for the case of small viscosity and high accretion rate, generally, the self-gravitating radius increases as the amount of mass-loss by the outflow increases. Our solutions show that as more angular momentum is lost by the outflow, then reduction to the mass of the first clumps is more significant.

The structure and stability of accretion disks surrounding black holes with anomalous viscosity

Abstract.The solution of the steady state of accretion disks surrounding non-rotating black holes is solved by numerical simulations, where we adopt a promising viscosity prescription (i.e. anomalous magnetic viscosity). We can describe the disk more exactly than other studies, because the viscosity we adopted is close to the truth accretion disk. In contrast to previous studies, the curve of the Mach number behaves differently owing to the decline of the local sound velocity with increasing radii.The stability of these disks has been examined. We find that the O-mode (out-mode) is always unstable and its growth rate decreases monotonically with increasing wavelength, in the inner disk and in the outer disk. The I-mode (in-mode) is unstable in the outer disk, but stable in the inner disk when the wavelength is greater than a special value.

Unstable magnetohydrodynamical continuous spectrum of accretion disks

We present a detailed study of localised magnetohydrodynamical (MHD) instabilities occuring in two--dimensional magnetized accretion disks. We model axisymmetric MHD disk tori, and solve the equations governing a two--dimensional magnetized accretion disk equilibrium and linear wave modes about this equilibrium. We show the existence of novel MHD instabilities in these two--dimensional equilibria which do not occur in an accretion disk in the cylindrical limit. The disk equilibria are numerically computed by the FINESSE code. The stability of accretion disks is investigated analytically as well as numerically. We use the PHOENIX code to compute all the waves and instabilities accessible to the computed disk equilibrium. We concentrate on strongly magnetized disks and sub--Keplerian rotation in a large part of the disk. These disk equilibria show that the thermal pressure of the disk can only decrease outwards if there is a strong gravitational potential. Our theoretical stability analysis shows that convective continuum instabilities can only appear if the density contours coincide with the poloidal magnetic flux contours. Our numerical results confirm and complement this theoretical analysis. Furthermore, these results show that the influence of gravity can either be stabilizing or destabilizing on this new kind of MHD instability. In the likely case of a non--constant density, the height of the disk should exceed a threshold before this type of instability can play a role. This localised MHD instability provides an ideal, linear route to MHD turbulence in strongly magnetized accretion disk tori.

Stability of Accretion Disks around Rotating Black Holes: A Pseudo–General‐Relativistic Fluid Dynamical Study

We discuss the solution of an accretion disk when the black hole is chosen to be rotating. We study how the fluid properties are affected for different rotation parameters of the black hole. We know that no cosmic object is static in the universe. Here the effect of the rotation of the black hole on spacetime is considered, following an earlier work of the author, where the pseudo-Newtonian potential was prescribed for the Kerr geometry. We show that, with the inclusion of rotation of the black hole, the valid disk parameter region dramatically changes, and the disk becomes unstable. Also we discuss the possibility of shocks in accretion disks around rotating black holes. When the black hole is chosen to be rotating, the sonic locations of the accretion disk get shifted or disappear, making the disk unstable. To bring it into the stable situation, the angular momentum of the accreting matter has to be reduced/enhanced (for co/counterrotating disk) by means of some physical process.

Stability of Accretion Disks in Presence of Nucleosynthesis

We study the effect of nuclear reaction on a thin, axisymmetric, differentially rotating, inviscid, steady accretion flow around a black hole from an analytical point of view. We find that for most of the reasonable disk parameters, when $p-p$-reaction, dissociation of deuterium and helium are taken into account, the transonic region of the disk continues to have the inner sonic point and if the temperature of the flow at the injection sonic point could be raised (by say, some heating processes) the flow would to pass through this inner sonic point. Otherwise, the flow may be unstable. We use the sonic point analysis to study the solution. In the rest of the disk parameters the inner sonic point is absent altogether and the flow will definitely be unstable.

The stability of accretion disks to short wavelength perturbations

The stability of accretion disks against short wavelength perturbations is analyzed. The disk is shown to be unstable to slow thermal perturbations propagating in the z-direction for sufficiently high values of the stress parameter ..cap alpha.. and sufficiently low values of the ratio of gas to total pressure. The acoustic flux from the ''middle region'' of the disk is estimated and discussed.

The role of viscosity and cooling mechanisms in the stability of accretion disks

A dispersion relation for linearized perturbation of a geometrically thin accretion disk is derived for an arbitrary viscosity law and cooling mechanism. Using this equation, we formulate the necessary and sufficient conditions for the stability of a disk. The conditions which are imposed on the viscosity and the cooling process are general and can be used as an a priori check if a particular choice of mechanisms leads to a stable disk. It is shown that the conditions cannot be satisfied by any one of the relevant cooling mechanisms with the standard viscosity law. Small variations in this law lead, however, to a stable configuration.

Structure and Stability of Accretion-Disk around a Black-Hole

Structure and stability of a stationary thin-disk formed around a black-hole are studied using the conventional formula for the viscous stress. The disk is classified into an optically thick case, an optically thin case and an intermediat.e case in which the comptonization plays an important role. Thermal and ·secular stabilities are examined in each of the above three cases. High temperatures . in excess of 10°'K are expected in the optically thin case and in the comptonization dominant case. However, it is shown that in these case_s the disk is unstable for the thermal perturbation. § I. Introduction It has been known that some of Xcray sources consist close binary systems. Among these X-ray sources, especially Cyg X-1 is of great interest since it is believed as a black-hole candidate. Boltonn anaiysed spectroscopic and photometric data of HD 226868, which was highly believed to be associated with Cyg X-1, and found that the mass of the invisible component was greater than 7.4 M®. Even if the lower limit of the above mass is assumed for Cyg X-1, it is far massive than the upper limit of a stable neutron star ( r-.../2M®). Moreover, recently Roths­ child et a1. 2' and Oda et al. 3' presented evidence for millisecond pulses from Cyg X-1. It seems that these short time variations also indicate the existence of a black-hole. In a close binary system the material overflowing from the primary star. has a considerable amount of angular momentum against the secondary star, probably a black-hole for Cyg X-1. As a result the centrifugal force prevents the infall of the material toward the secondary star when it balances with the gravitational force; The material rotates in a circular orbit. If there exists an effective outward trans­ porting mechanism for angular momentum, the material keeping nearly Keplerian motion falls gradually toward the secondary star. A gaseous disk is formed around the secondary star and X-ray emission is expected since gravitational energy is released by the infalling material. Pringle and Rees,4' Shakura and Sunyaev5' and Novikov and Thorne 6' studied the structure of such a disk, and discussed the X-ray spectrum emitted from the surface of the disk. As for the transporting mechanisms for angular momentum Shakura et al. assumed turbulent and magnetic viscous forces. Tn terms· of them the tan­ gential viscous stress Pr6 is expressed as