Nonlinear tidal instabilities in compressible atmospheres

The amount of dissipation caused by tidal interactions in binary stars and planetary systems is poorly understood but important in determining the orbital evolution of these systems. In particular, it is theorized that dissipation from tidal instabilities may measurably alter the gravitational waves emitted by binary neutron stars, potentially allowing detectors such as LIGO to observationally constrain the unknown interior structure of these objects. As a first step towards studying these effects in fully compressible stellar models, we present a study of the stability of a tidally deformed plane-parallel atmosphere. Using a general-purpose spectral PDE solver, we evaluate the threshold amplitude for the weakly nonlinear instability of the tidal response to coupled collections of p-modes and g-modes over multiple scale heights. We additionally perform fully nonlinear simulations to verify the predicted threshold amplitudes. This work demonstrates the feasibility of using general spectral methods to perform weakly nonlinear analyses of atmospheres with arbitrary background structures and including multiple mode families and non-adiabatic effects. We will also discuss current efforts to extend this work to spherical geometries and more realistic neutron star models.