Engineering topics

Balbus, Steven A.

Publications and source records attributed to Balbus, Steven A..

14 records

NASA NTRS1994

Local shear instabilities in weakly ionized, weakly magnetized disks

We extend the analysis of axisymmetric magnetic shear instabilities from ideal magnetohydrodynamic (MHD) flows to weakly ionized plasmas with coupling between ions and neutrals caused by collisions, ionization, and recombination. As part of the analysis, we derive the single-fluid MHD dispersion relation without invoking the Boussinesq approximation. This work expands the range of applications of these instabilities from fully ionized accretion disks to molecular disks in galaxies and, with somewhat more uncertainty, to protostellar disks. Instability generally requires the angular velocity to decrease outward, the magnetic field strengths to be subthermal, and the ions and neutrals to be sufficiently well coupled. If ionization and recombination processes can be neglected on an orbital timescale, adequate coupling is achieved when the collision frequency of a given neutral with the ions exceeds the local epicyclic freqency. When ionization equilibrium is maintained on an orbital timescale, a new feature is present in the disk dynamics: in contrast to a single-fluid system, subthermal azimuthal fields can affect the axisymmetric stability of weakly ionized two-fluid systems. We discuss the underlying causes for this behavior. Azimuthal fields tend to be stabilizing under these circumstances, and good coupling between the neutrals and ions requires the collision frequency to exceed the epicyclic frequency by a potentially large secant factor related to the magnetic field geometry. When the instability is present, subthermal azimuthal fields may also reduce the growth rate unless the collision frequency is high, but this is important only if the field strengths are very subthermal and/or the azimuthal field is the dominant field component. We briefly discuss our results in the context of the Galactic center circumnuclear disk, and suggest that the shear instability might be present there, and be responsible for the observed turbulent motions.

Blaes, Omer M.↗

NASA NTRS1993

A limitation of the generation of magnetic fields

Simple arguments are put forward to show that the currents produced in disks by radiative or other types of drag forces on electrons must give rise to extraordinarily small magnetic fields. The field strengths are consistent with earlier (more complex) treatments of this class of problem, but inconsistent with the claims of recent papers in the literature. The discrepancies involve the treatment of self-induction. Ion-electron inductive coupling limits the generated magnetic field to have an associated ion Larmor radius greater than or of order of the radius of the disk, a result which follows most directly from conservation of canonical ion momentum, p + eA/c. An explicit time-dependent model for the buildup of the field leads to the same conclusion. If internal velocity gradient scales are smaller than the ion Larmor radius, and the plasma is not collision dominated, standard dynamo amplification within the disk is hardly likely to be effective. But to explain the Galactic field, dynamo amplification in a collisional plasma is also likely to be problematic. The difficulties posed by the existence of ordered Galactic-scale magnetic fields are made all the more acute by the simplicity and the scope of the discussed field limitation.

Balbus, Steven A.↗

NASA NTRS1993

A flux-limited treatment for the conductive evaporation of spherical interstellar gas clouds

In this work, we present and analyze a new analytic solution for the saturated (flux-limited) thermal evaporation of a spherical cloud. This work is distinguished from earlier analytic studies by allowing the thermal conductivity to change continuously from a diffusive to a saturated form, in a manner usually employed only in numerical calculations. This closed form solution will be of interest as a computational benchmark. Using our calculated temperature profiles and mass-loss rates, we model the thermal evaporation of such a cloud under typical interstellar medium (ISM) conditions, with some restrictions. We examine the ionization structure of the cloud-ISM interface and evaluate column densities of carbon, nitrogen, oxygen, neon, and silicon ions toward the cloud. In accord with other investigations, we find that ionization equilibrium is far from satisfied under the assumed conditions. Since the inclusion of saturation effects in the heat flux narrows the thermal interface relative to its classical structure, we also find that saturation effects tend to lower predicted column densities.

Dalton, William W.↗

NASA NTRS1992

A powerful local shear instability in weakly magnetized disks. III - Long-term evolution in a shearing sheet. IV - Nonaxisymmetric perturbations

The nonlinear evolution of the recently identified accretion disk magnetic shear instability is investigated through a series of numerical simulations. Finite-difference computations of the equations of compressible MHD are carried out on an axisymmetric shearing sheet system with periodic boundary conditions designed to approximate a local region within an accretion disk. Initial field configurations that include some net vertical component evolve into a nonlinear, exponentially growing solution with large poloidal velocities and magnetic fields with energies comparable to the thermal energy density. The stability of a purely azimuthal field configuration is examined, and it is found that nonaxisymmetric instability is present, but with a growth time measured in tens of orbital periods. In general, the most rapid growth occurs for very small radial and azimuthal wavenumbers, leading to coherent magnetic field structure in planes parallel to the disk. It is suggested that this instability is a key ingredient for the generation of magnetic fields in disks.

Hawley, John F.↗

NASA NTRS1992

Is the Oort A-value a universal growth rate limit for accretion disk shear instabilities?

A weak-field local MHD instability that is of importance to accretion disks is examined. The maximum growth rate of the instability is found to be not only independent of the magnetic field strength but independent of field geometry as well. In particular, all Keplerian disks are unstable in the presence of any weak poloidal field, with the ratio of the maximum growth rate to disk angular velocity given by 3/4. The maximum growth rate of any weak field configuration that is not purely toroidal is given by the local Oort A-value of the disk. The behavior is studied by using a form of the dynamical Hill equations. It is conjectured that the Oort A-value is an upper bound to the growth rate of any instability feeding upon the free energy of differential rotation.

Balbus, Steven A.↗

NASA NTRS1991

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution

A broad class of astronomical accretion disks is presently shown to be dynamically unstable to axisymmetric disturbances in the presence of a weak magnetic field, an insight with consequently broad applicability to gaseous, differentially-rotating systems. In the first part of this work, a linear analysis is presented of the instability, which is local and extremely powerful; the maximum growth rate, which is of the order of the angular rotation velocity, is independent of the strength of the magnetic field. Fluid motions associated with the instability directly generate both poloidal and toroidal field components. In the second part of this investigation, the scaling relation between the instability's wavenumber and the Alfven velocity is demonstrated, and the independence of the maximum growth rate from magnetic field strength is confirmed.

Balbus, Steven A.↗

NASA NTRS1991

On magnetothermal instability in cluster cooling flows

Lagrangian techniques appropriate to a local calculation are used to show that a weak ordered magnetic field can result in a generic condensational mode in cluster cooling flows. However, thermal instability appears possible only if the conductivity is well below its Spitzer value, for all nonradial wavenumbers. Wavenumbers not subject to conductive damping are subject to buoyant oscillations. It is shown that when instability is present, lateral magnetic confinement of high thermal pressure regions in the plasma by radial magnetic field lines is responsible in at least equal measure with radially directed magnetic tension for the suppression of oscillations and the reappearance of local condensational modes. The general importance of even very modest magnetic fields for destabilizing thermal time scale perturbations is emphasized.

Balbus, Steven A.↗

NASA NTRS1990

Resonant excitation of internal gravity waves in cluster cooling flows

Orbital motions of galaxies in X-ray clusters will resonantly excite internal gravity waves (g-waves) that propagate in the plasma. The resonance corresponds to a match between the local Brunt-Vaisala oscillation frequency in the plasma and the appropriate Fourier component of the galactic gravitational potential. Radiated internal waves have an inward group velocity that carries them to the central region of the flow where they become tightly wrapped, geometrically amplified, and eventually dissipated. Waves transport energy and angular momentum, but probably not in amounts large enough to grossly alter the structure of a cooling flow, should one be present. All physical flow variables are finite at the resonance, and all energy and angular momentum deposited by a galaxy is carried inward by the waves. Nonlinear density and velocity fluctuations are likely to result from wave amplitude growth in the central regions of the flow, and a connection with the formation of emission-line filaments is a possibility.

Balbus, Steven A.↗

NASA NTRS1990

Radiative thermal conduction fronts

The discovery of the O VI interstellar absorption lines in our Galaxy by the Copernicus observatory was a turning point in our understanding of the Interstellar Medium (ISM). It implied the presence of widespread hot (approx. 10 to the 6th power K) gas in disk galaxies. The detection of highly ionized species in quasi-stellar objects' absorption spectra may be the first indirect observation of this hot phase in external disk galaxies. Previous efforts to understand extensive O VI absorption line data from our Galaxy were not very successful in locating the regions where this absorption originates. The location at interfaces between evaporating ISM clouds and hot gas was favored, but recent studies of steady-state conduction fronts in spherical clouds by Ballet, Arnaud, and Rothenflug (1986) and Bohringer and Hartquist (1987) rejected evaporative fronts as the absorption sites. Researchers report here on time-dependent nonequilibrium calculations of planar conductive fronts whose properties match well with observations, and suggest reasons for the difference between the researchers' results and the above. They included magnetic fields in additional models, not reported here, and the conclusions are not affected by their presence.

Borkowski, Kazimierz J.↗

NASA NTRS1990

Radiative magnetized thermal conduction fronts

The evolution of plane-parallel magnetized thermal conduction fronts in the interstellar medium (ISM) was studied. Separating the coronal ISM phase and interstellar clouds, these fronts have been thought to be the site of the intermediate-temperature regions whose presence was inferred from O VI absorption-line studies. The front evolution was followed numerically, starting from the initial discontinuous temperature distribution between the hot and cold medium, and ending in the final cooling stage of the hot medium. It was found that, for the typical ISM pressure of 4000 K/cu cm and the hot medium temperature of 10 to the 6th K, the transition from evaporation to condensation in a nonmagnetized front occurs when the front thickness is 15 pc. This thickness is a factor of 5 smaller than previously estimated. The O VI column densities in both evaporative and condensation stages agree with observations if the initial hot medium temperature Th exceeds 750,000 K. Condensing conduction fronts give better agreement with observed O VI line profiles because of lower gas temperatures.

Borkowski, Kazimierz J.↗

NASA NTRS1990

Large scale interstellar gasdynamics in disk galaxies

The dynamical behavior of interstellar gas in spiral arm potentials and the nature of H I warps in disk galaxies is reviewed. Recent millimeter wave interferometry results of M 51, which are supportive in detail of a density wave structure for this galaxy are discussed. It is argued that spiral arms, when present, must be an important triggering mechanism for star formation, even though global star formation rates are insensitive to spiral structure. The effect of the unusual velocity shear fields near spiral arms on the development of small disturbances is discussed. The success of recent investigations treating H I warps as a discrete normal mode of a combined disk-halo system is highlighted. In this picture, the axes of the halo and the disk are misaligned, and warping modes correspond to what would be a zero frequency trivial tilt of the entire disk in the absence of a halo.

Balbus, Steven A.↗

NASA NTRS1989

Theory of local thermal instability in spherical systems

The gasdynamical properties of local thermal instability in optically thin astrophysical plasmas as it occurs in spherical accretion and winds is investigated. In a medium characterized by both thermal and hydrostatic equilibrium, if the cooling function is not an explicit function of position and does not display isentropic thermal instability, then isobaric thermal instability by the Field criterion is present if and only if convective instability is present by the Schwarzschild criterion. In this case, thermal overstability cannot occur. Convective instability by the Schwarzschild criterion will also occur in accretion flows locally dominated by external heating or in marginally unbound, radiatively cooling outflows. A very general Lagrangian equation for the development of nonradial thermal instability in flows with spherical symmetry is derived and is solved analytically in certain regimes. The results are applied to cluster X-ray cooling flows.

Balbus, Steven A.↗

NASA NTRS1988

On thermal instability and hydrostatic equilibrium in cooling flows

The nature of thermal instability in cluster cooling flows is investigated. The radial modes of a spherical static system are discussed, and it is shown that only the acoustical modes are present at short wavelengths and that there are no isobaric thermal instabilities. The analysis is expanded to include nonradial modes, and it is demonstrated that there are azimuthal high wavenumber thermal modes which can indeed become unstable according to the classical Field (1965) criterion. A new convective instability criterion is derived, and thermal instability and its limitations are briefly discussed.

Balbus, Steven A.↗

NASA NTRS1986

Star-gas density waves in spiral galaxies

The steady state dynamics of spiral galaxies is analyzed as a two-component system consisting of stars and gas within the framework of the WKB density wave theory. The gravitational influence of the gas is included for the first time in a steady state calculation. The full set of equations for a star-gas galaxy is presented, and the equations are analyzed for small-amplitude forcing. Wave properties near the solar circle are examined, and it is found that the large-scale gas shock disappears for gas content above 8 percent. Instead, gas density profiles change to highly symmetric shapes as a result of the action of the gas self-gravity. The stellar wave is damped by the torque exerted by the gas.

Lubow, Stephen H.↗