Searcharxiv⌕ Search

arXiv subjects

Steven A. Balbus

Publications and source records attributed to Steven A. Balbus.

52 records · Page 3Linked to original sources
arXiv2003

Numerical simulations of self-gravitating magnetized disks

We present the first global simulations of self-gravitating magnetized tori. The simulations are performed with Zeus-2D and GLOBAL. We find the magnetorotational instability (MRI) to behave similarly in a self-gravitating environment as in previous simulations of non self-gravitating systems: enhancement of turbulent angular momentum transport follows the linear phase. The torus quickly develops a two component structure composed of an inner thick disk in Keplerian rotation and an outer massive disk. We compare this result with zero mass global simulations in 2D, and also present preliminary results of 3D simulations.

astro-ph↗
arXiv2003

Ambipolar Diffusion in the Magnetorotational Instability

The effects of ambipolar diffusion on the linear stability of weakly ionised accretion discs are examined. Earlier work on this topic has focused on axial magnetic fields and perturbation wavenumbers. We consider here more general field and wavenumber geometries, and find that qualitatively new results are obtained. Provided a radial wavenumber and azimuthal field are present along with their axial counterparts, ambipolar diffusion will always be destabilising, with unstable local modes appearing at well-defined wavenumber bands. The wavenumber corresponding to the maximum growth rate need not, in general, lie along the vertical axis. Growth rates become small relative to the local angular velocity when the ion-neutral collision time exceeds the orbital time. In common with Hall electromotive forces, ambipolar diffusion destabilises both positive and negative angular velocity gradients. In at least some cases, therefore, uniformly rotating molecular cloud cores may reflect the marginally stable state of the ambipolar magnetorotational instability.

astro-ph↗
arXiv2003

Turbulent Energy Transport in Nonradiative Accretion Flows

Just as correlations between fluctuating radial and azimuthal velocities produce a coherent stress contributing to the angular momentum transport in turbulent accretion disks, correlations in the velocity and temperature fluctuations produce a coherent energy flux. This nonadvective energy flux is always of secondary importance in thin radiative disks, but cannot be neglected in nonradiative flows, in which it completes the mean field description of turbulence. It is, nevertheless, generally ignored in accretion flow theory, with the exception of models explicitly driven by thermal convection, where it is modeled phenomenologically. This flux embodies both turbulent thermal convection as well as wave transport, and its presence is essential for a proper formulation of energy conservation, whether convection is present or not. The sign of the thermal flux is likely to be outward in real systems, but the restrictive assumptions used in numerical simulations may lead to inward thermal transport, in which case qualitatively new effects may be exhibited. We find, for example, that a static solution would require inward, not outward, thermal transport. Even if it were present, thermal convection would be unlikely to stifle accretion, but would simply add to the outward rotational energy flux that must already be present.

astro-ph↗
arXiv2003

Enhanced Angular Momentum Transport in Accretion Disks

The status of our current understanding of angular momentum transport in accretion disks is reviewed. The last decade has seen a dramatic increase both in the recognition of key physical processes and in our ability to carry through direct numerical simulations of turbulent flow. Magnetic fields have at once powerful and subtle influences on the behavior of (sufficiently) ionized gas, rendering them directly unstable to free energy gradients. Outwardly decreasing angular velocity profiles are unstable. The breakdown of Keplerian rotation into MHD turbulence may be studied in some numerical detail, and key transport coefficients may be evaluated. Chandra observations of the Galactic Center support the existence of low luminosity accretion, which may ultimately prove amenable to global three-dimensional numerical simulation.

astro-ph↗
arXiv2003

Gap Formation by Planets in Turbulent Protostellar Disks

The processes of planet formation and migration depend intimately on the interaction between planetesimals and the gaseous disks in which they form. The formation of gaps in the disk can severely limit the mass of the planet and its migration toward the protostar. We investigate the process of gap formation through magnetohydrodynamic simulations in which internal stress arises self-consistently from turbulence generated by the magnetorotational instability. The simulations investigate three different planetary masses and two disk temperatures to bracket the tidal (thermal) and viscous gap opening conditions. The results are in general qualitative agreement with previous simulations of gap formation, but show significant differences. In the presence of MHD turbulence, the gaps produced are shallower and asymmetrically wider than those produced with pure hydrodynamics. The rate of gap formation is also slowed, with accretion occurring across the developing gap. Viscous hydrodynamics does not adequately describe the evolution, however, because planets capable of producing gaps also may be capable of affecting the level MHD turbulence in different regions of the disk.

astro-ph↗
arXiv2002

When is Uniform Rotation an Energy Minimum?

A simple variational calculation is presented showing that a uniformly rotating barotropic fluid in an external potential attains a true energy minimum if and only if the rotation profile is everywhere subsonic. If regions of supersonic rotation are present, fluid variations exist that could take the sytem to states of lower energy. In any given system, these states may or may not be dynamically accessible, but their existence is important. It means that extending the degrees of freedom available to the fluid (say by weak magnetic fields) may open a path to fluid instabilities. Whether astrophysical gaseous nebula tend toward states of uniform rotation or toward more Keplerian core-disk systems appears to be largely a matter of whether the rotation profile is transonic or not. The suggestion is made that the length scale associated with coherent molecular cloud cores is related to the requirement that the cores be stable and rotate subsonically.

astro-ph↗
arXiv2002

Numerical Simulations of MHD Turbulence in Accretion Disks

We review numerical simulations of MHD turbulence. The last decade has witnessed fundamental advances both in the technical capabilities of direct numerical simulation, and in our understanding of key physical processes. Magnetic fields tap directly into the free energy sources in a sufficiently ionized gas. The result is that adverse angular velocity and adverse temperature gradients, not the classical angular momentum and entropy gradients, destabilize laminar and stratified flow. This has profound consequences for astrophysical accretion flows, and has opened the door to a new era of numerical simulation experiments.}

astro-ph↗
arXiv2002

The Dynamical Structure of Nonradiative Black Hole Accretion Flows

We analyze three-dimensional magnetohydrodynamic (MHD) simulations of a nonradiative accretion flow around a black hole using a pseudo-Newtonian potential. The flow originates from a torus initially centered at 100 gravitational (Schwarzschild) radii. Accretion is driven by turbulent stresses generated self-consistently by the magnetorotational instability. The resulting flow has three well-defined dynamical components: a hot, thick, rotationally-dominated Keplerian disk; a surrounding magnetized corona with vigorous circulation and outflow; and a magnetically-confined jet along the centrifugal funnel wall. Inside of 10 gravitational radii, the disk becomes very hot, more toroidal, and highly intermittent. These results contrast sharply with quasi-spherical, self-similar viscous models. There are no significant dynamical differences between simulations that include resistive heating and those that do not. We conclude by deducing some simple radiative properties of our solutions, and apply the results to the accretion-powered Galactic center source Sgr A*.

astro-ph↗
arXiv2002

On the Nature of Angular Momentum Transport in Nonradiative Accretion Flows

The principles underlying a proposed class of black hole accretion models are examined. The flows are generally referred to as ``convection-dominated,'' and are characterized by inward transport of angular momentum by thermal convection and outward viscous transport, vanishing mass accretion, and vanishing local energy dissipation. We examine the viability of these ideas by explicitly calculating the leading order angular momentum transport of axisymmetric modes in magnetized, differentially rotating, stratified flows. The modes are destabilized by the generalized magnetorotational instability. There are no inward transporting modes at all unless the magnitude of the (imaginary) Brunt frequency is comparable to the epicyclic frequency, a condition requiring substantial levels of dissipation. When inward transporting modes do exist, they appear at long wavelengths, unencumbered by magnetic tension. Moreover, very general thermodynamic principles prohibit the complete recovery of irreversible dissipative energy losses, a central feature of convection-dominated models. Dissipation of the free energy of differential rotation inevitably requires outward angular momentum transport. Our results are in good agreement with global MHD simulations, which find significant levels of outward transport and energy dissipation, whether or not destabilizing entropy gradients are present.

astro-ph↗
arXiv2001

Convective and Rotational Stability of a Dilute Plasma

The stability of a dilute plasma to local convective and rotational disturbances is examined. A subthermal magnetic field and finite thermal conductivity along the field lines are included in the analysis. Stability criteria similar in form to the classical Høiland inequalities are found, but with angular velocity gradients replacing angular momentum gradients, and temperature gradients replacing entropy gradients. These criteria are indifferent to the properties of the magnetic field and to the magnitude of the thermal conductivity. Angular velocity gradients and temperature gradients are both free energy sources; it is not surprising that they are directly relevant to the stability of the gas. Magnetic fields and thermal conductivity provide the means by which these sources can be tapped. Previous studies have generally been based upon the classical Høiland criteria, which are inappropriate for magnetized, dilute astrophysical plasmas. In sharp contrast to recent claims in the literature, the new stability criteria demonstrate that marginal flow stability is not a fundamental property of accreting plasmas thought to be associated with low luminosity X-ray sources.

astro-ph↗
arXiv2001

A Magnetohydrodynamic Nonradiative Accretion Flow in Three Dimensions

We present a global magnetohydrodynamic (MHD) three dimensional simulation of a nonradiative accretion flow originating in a pressure supported torus. The evolution is controlled by the magnetorotational instability which produces turbulence. The flow forms a nearly Keplerian disk. The total pressure scale height in this disk is comparable to the vertical size of the initial torus. Gas pressure dominates only near the equator; magnetic pressure is more important in the surrounding atmosphere. A magnetically dominated bound outflow is driven from the disk. The accretion rate through the disk exceeds the final rate into the hole, and a hot torus forms inside 10 r_g. Hot gas, pushed up against the centrifugal barrier and confined by magnetic pressure, is ejected in a narrow, unbound, conical outflow. The dynamics are controlled by magnetic turbulence, not thermal convection, and a hydrodynamic alpha model is inadequate to describe the flow. The limitations of two dimensional MHD simulations are also discussed.

astro-ph↗
arXiv1999

Stability, Instability, and "Backwards'' Transport in Accretion Disks"

The stratification of entropy and the stratification of angular momentum are closely analogous. Of particular interest is the behavior of disks in which angular momentum transport is controlled by convection, and heat transport by dynamical turbulence. In both instances we argue that the transport must proceed ``backwards'' relative to the sense one would expect from a simple enhanced diffusion approach. Reversed angular momentum transport has already been seen in numerical simulations; contra-gradient thermal diffusion should be amenable to numerical verification as well. These arguments also bear on the observed nonlinear local stability of isolated Keplerian disks. We also describe a diffusive instability that is the entropy analogue to the magnetorotational instability. It affects thermally stratified layers when Coulomb conduction and a weak magnetic field are present. The criterion for convective instability goes from one of upwardly decreasing entropy to one of upwardly decreasing temperature. The maximum growth rate is of order the inverse sound crossing time, independent of the thermal conductivity. The indifference of the growth rate to the conduction coefficient, its simple dynamical scaling, and the replacement in the stability criterion of a conserved quantity (entropy) gradient by a free energy (temperature) gradient are properties similar to those exhibited by the magnetorotational instability.

astro-ph↗
arXiv1999

Solar Nebula Magnetohydrodynamics

The dynamical state of the solar nebula depends critically upon whether or not the gas is magnetically coupled. The presence of a subthermal field will cause laminar flow to break down into turbulence. Magnetic coupling, in turn, depends upon the ionization fraction of the gas. The inner most region of the nebula ($\lesssim 0.1$ AU) is magnetically well-coupled, as is the outermost region ($\gtrsim 10$ AU). The magnetic status of intermediate scales ($\sim 1$ AU) is less certain. It is plausible that there is a zone adjacent to the inner disk in which turbulent heating self-consistently maintains the requisite ionization levels. But the region adjacent to the active outer disk is likely to be magnetically ``dead.'' Hall currents play a significant role in nebular magnetohydrodynamics. Though still occasionally argued in the literature, there is simply no evidence to support the once standard claim that differential rotation in a Keplerian disk is prone to break down into shear turbulence by nonlinear instabilities. There is abundant evidence---numerical, experimental, and analytic---in support of the stabilizing role of Coriolis forces. Hydrodynamical turbulence is almost certainly not a source of enhanced turbulence in the solar nebula, or in any other astrophysical accretion disk.

astro-ph↗
arXiv1998

Local Hydrodynamic Stability of Accretion Disks

We employ a variety of numerical simulations in the local shearing box system to investigate in greater depth the local hydrodynamic stability of Keplerian differential rotation. In particular we explore the relationship of Keplerian shear to the nonlinear instabilities known to exist in simple Cartesian shear. The Coriolis force is the source of linear stabilization in differential rotation. We exploit the formal equivalence of constant angular momentum flows and simple Cartesian shear to examine the transition from stability to nonlinear instability. The manifestation of nonlinear instability in shear flows is known to be sensitive to initial perturbation and to the amount of viscosity; marginally (linearly) stable differentially rotating flows exhibit this same sensitivity. Keplerian systems, however, are completely stable; the strength of the stabilizing Coriolis force easily overwhelms any destabilizing nonlinear effects. In fact, nonlinear effects speed the decay of applied turbulence by producing a rapid cascade of energy to high wavenumbers where dissipation occurs. Our conclusions are tested with grid resolution experiments and by comparison with results from a code that employs an alternative numerical algorithm. The properties of hydrodynamic differential rotation are contrasted with magnetohydrodynamic differential rotation. The kinetic stress couples to the vorticity which limits turbulence, while the magnetic stress couples to the shear which promotes turbulence. Thus magnetohydrodynamic turbulence is uniquely capable of acting as a turbulent angular momentum transport mechanism in disks.

astro-ph↗
arXiv1998

On Nonshearing Magnetic Configurations in Differentially Rotating Disks

A new class of disk MHD equilibrium solutions is described, which is valid within the standard local (``shearing sheet'') approximation scheme. These solutions have the following remarkable property: velocity streamlines and magnetic lines of force rotate rigidly, even in the presence of differential rotation. This situation comes about because the Lorentz forces acting upon modified epicycles compel fluid elements to follow magnetic lines of force. Field line (and streamline) configurations may be elliptical or hyperbolic, prograde or retrograde. These structures have previously known hydrodynamical analogs: the ``planet'' solutions described by Goodman, Narayan, & Goldreich. The primary focus of this investigation is configurations in the disk plane. A related family of solutions lying in a vertical plane is briefly discussed; other families of solutions may exist. Whether these MHD structures are stable is not yet known, but could readily be determined by three-dimensional simulations. If stable or quasi-stable, these simple structures may find important applications in both accretion and galactic disks.

astro-ph↗