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 H{\o}iland 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 H{\o}iland 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.