Shock formation in stellar perturbations and tidal shock waves in binaries

Gundlach, Carsten and Murphy, Jeremiah W. (2011) Shock formation in stellar perturbations and tidal shock waves in binaries. Monthly Notices of the Royal Astronomical Society, 416 (2), 1284-1291. (doi:10.1111/j.1365-2966.2011.19126.x).

Abstract

We investigate whether tidal forcing can result in sound waves steepening into shocks at the surface of a star. To model the sound waves and shocks, we consider adiabatic non-spherical perturbations of a Newtonian perfect fluid star. Because tidal forcing of sound waves is naturally treated with linear theory, but the formation of shocks is necessarily non-linear, we consider the perturbations in two regimes. In most of the interior, where tidal forcing dominates, we treat the perturbations as linear, while in a thin layer near the surface we treat them in full non-linearity but in the approximation of plane symmetry, fixed gravitational field and a barotropic equation of state. Using a hodograph transformation, this non-linear regime is also described by a linear equation. We show that the two regimes can be matched to give rise to a single-mode equation which is linear but models non-linearity in the outer layers. This can then be used to obtain an estimate for the critical mode amplitude at which a shock forms near the surface. As an application, we consider the tidal waves raised by the companion in an irrotational binary system in circular orbit. We find that shocks form at the same orbital separation where Roche lobe overflow occurs, and so shock formation is unlikely to occur.

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Contributors

Author: Carsten Gundlach

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