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**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
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