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.