Prof Steven Balbus FRS, FInstP

Abstract:

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 Holland 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. © 2001. The American Astronomical Society. All rights reserved.

Abstract:

The stratification of entropy and the stratification of angular momentum are closely analogous. The analogy has been developed for a number of different problems in the fluid literature, but its consequences for the behavior of turbulent accretion disks are less appreciated. 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 "backward" relative to the sense one would expect from a simple enhanced diffusion approach. Reversed angular momentum transport has already been seen in numerical simulations; contragradient thermal diffusion should be amenable to numerical verification as well. These arguments also bear on the observed nonlinear local stability of isolated Keplerian disks: locally generated turbulence in such a disk would require simultaneous inward and outward angular momentum transport, which is, of course, impossible. 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 plasma must be sufficiently dilute that heat is channeled only along field lines. The criterion for convective instability goes from one of upwardly decreasing entropy to one of upwardly decreasing temperature. The instability remains formally viable if radiative heat transport is also present, but the equilibrium is much more unstable if Coulomb transport is dominant. In that case, the maximum growth rate is of the order of 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.