Previous abstract Next abstract

Session 12 - Stellar Evolution - Theory.
Display session, Wednesday, January 07
Exhibit Hall,

[12.08] Acoustic Overstability of Plane Parallel Polytropes: An Astrophysical Thermoacoustic Engine

O. M. Umurhan, E. A. Spiegel (Columbia U.)

We examine the stability of nonadiabatic acoustic modes in a plane parallel atmosphere in a constant gravitational field where the source of nonadiabaticity is thermal conduction with constant coefficient. This prescription filters out the effects of the \kappa-mechanism. The static state is described by polytrope solutions where the density is related to the linear temperature profile via a power law relation described by the usual polytropic index m. We solve the resulting fourth order boundary-value/eigenvalue problem describing perturbations by utilizing a variety of asymptotic and numerical methods. Disturbances are shown to be unstable under a variety of parameter regimes including conditions where the background polytrope is either super- or subadiabatic. Two main instabilities emerge and in one of them its resemblance to the thermoacoustic engine is drawn. We also find that it is most clearly heard when the conduction parameter is strong. For this extreme circumstance marginal stability conditions are derived and are used to motivate and derive weakly nonlinear amplitude equations for this problem.

Program listing for Wednesday