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Register a new userHybrid viscosity and the magnetoviscous instability in hot, collisionless accretion disks
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Added by
Prasad Subramanian Dr
Publication date
2008
fields
Physics
and research's language is
English
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We aim to illustrate the role of hot protons in enhancing the magnetorotational instability (MRI) via the ``hybrid viscosity, which is due to the redirection of protons interacting with static magnetic field perturbations, and to establish that it is the only relevant mechanism in this situation. It has recently been shown by Balbus cite{PBM1} and Islam & Balbus cite{PBM11} using a fluid approach that viscous momentum transport is key to the development of the MRI in accretion disks for a wide range of parameters. However, their results do not apply in hot, advection-dominated disks, which are collisionless. We develop a fluid picture using the hybrid viscosity mechanism, that applies in the collisionless limit. We demonstrate that viscous effects arising from this mechanism can significantly enhance the growth of the MRI as long as the plasma $beta gapprox 80$. Our results facilitate for the first time a direct comparison between the MHD and quasi-kinetic treatments of the magnetoviscous instability in hot, collisionless disks.
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We show that the standard model for geometrically thin accretion disks (alpha-disks) leads to inconsistencies if selfgravity plays a role. This problem arises from the parametrization of viscosity in terms of local sound velocity and vertical disk scale height. A viscosity prescription based on turbulent flows at the critical effective Reynolds number allows for consistent models of thin selfgravitating disks, and recovers the alpha-disk solution as the limiting case of negligible selfgravity. We suggest that such selfgravitating disks may explain the observed spectra of protoplanetary disks and yield a natural explanation for the radial motions inferred from the observed metallicity gradients in disk galaxies.
We propose a generalized accretion disk viscosity prescription based on hydrodynamically driven turbulence at the critical effective Reynolds number. This approach is consistent with recent re-analysis by Richard & Zahn (1999) of experimental results on turbulent Couette-Taylor flows. This new $beta$-viscosity formulation is applied to both selfgravitating and non-selfgravitating disks and is shown to yield the standard $alpha$-disk prescription in the case of shock dissipation limited, non-selfgravitating disks. A specific case of fully selfgravitating $beta$-disks is analyzed. We suggest that such disks may explain the observed spectra of protoplanetary disks and yield a natural explanation for the radial motions inferred from the observed metallicity gradients in disk galaxies. The $beta$-mechanism may also account for the rapid mass transport required to power ultra luminous infrared galaxies.
When an accretion disk falls prey to the runaway instability, a large portion of its mass is devoured by the black hole within a few dynamical times. Despite decades of effort, it is still unclear under what conditions such an instability can occur. The technically most advanced relativistic simulations to date were unable to find a clear sign for the onset of the instability. In this work, we present three-dimensional relativistic hydrodynamics simulations of accretion disks around black holes in dynamical space-time. We focus on the configurations that are expected to be particularly prone to the development of this instability. We demonstrate, for the first time, that the fully self-consistent general relativistic evolution does indeed produce a runaway instability.
Axisymmetric magnetorotational instability (MRI) in viscous accretion disks is investigated by linear analysis and two-dimensional nonlinear simulations. The linear growth of the viscous MRI is characterized by the Reynolds number defined as $R_{rm MRI} equiv v_A^2/ uOmega $, where $v_A$ is the Alfv{e}n velocity, $ u$ is the kinematic viscosity, and $Omega$ is the angular velocity of the disk. Although the linear growth rate is suppressed considerably as the Reynolds number decreases, the nonlinear behavior is found to be almost independent of $R_{rm MRI}$. At the nonlinear evolutionary stage, a two-channel flow continues growing and the Maxwell stress increases until the end of calculations even though the Reynolds number is much smaller than unity. A large portion of the injected energy to the system is converted to the magnetic energy. The gain rate of the thermal energy, on the other hand, is found to be much larger than the viscous heating rate. Nonlinear behavior of the MRI in the viscous regime and its difference from that in the highly resistive regime can be explained schematically by using the characteristics of the linear dispersion relation. Applying our results to the case with both the viscosity and resistivity, it is anticipated that the critical value of the Lundquist number $S_{rm MRI} equiv v_A^2/etaOmega$ for active turbulence depends on the magnetic Prandtl number $S_{{rm MRI},c} propto Pm^{1/2}$ in the regime of $Pm gg 1$ and remains constant when $Pm ll 1$, where $Pm equiv S_{rm MRI}/R_{rm MRI} = u/eta$ and $eta$ is the magnetic diffusivity.
We present a non-linear numerical model for a geometrically thin accretion disk with the addition of stochastic non-linear fluctuations in the viscous parameter. These numerical realizations attempt to study the stochastic effects on the disk angular momentum transport. We show that this simple model is capable of reproducing several observed phenomenologies of accretion driven systems. The most notable of these is the observed linear rms-flux relationship in the disk luminosity. This feature is not formally captured by the linearized disk equations used in previous work. A Fourier analysis of the dissipation and mass accretion rates across disk radii show coherence for frequencies below the local viscous frequency. This is consistent with the coherence behavior observed in astrophysical sources such as Cygnus X-1.
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