Radiative Transfer Effects on the Stability of Sound Waves in a Polytropic Atmosphere

Abstract

From a perturbation analysis of the boundary value problem that describes the behavior of optically thin disturbances to a polytropic atmosphere initially in hydrostatic and radiative equilibrium, we derive criteria for the overstability of acoustic modes. Our criteria are more general than those found by Spiegel, which are strictly valid only if the radiative cooling time is uniform over the atmosphere, i.e., if the polytropic index m = 6. Our criteria for overstability are valid for any value of m. Applying our results to the Sun and giant stars, we find that sound waves in the envelope of the Sun do not appear to be unstable but that instability may occur in the envelopes of red giants. We note that, if acoustic waves become overstable as a star evolves into a giant, then the acoustic power in the envelopes of cool giants will be greater than one would have expected on the basis of the predictions of Lighthill theory. We propose that chromospheric heating in nonmagnetic stars (such as old giants in globular clusters) contains a significant component that arises from acoustic overstability.