Axisymmetric waves in polytropic accretion discs

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Abstract
We extend the analysis by Lubow & Pringle of axisymmetric waves in accretion discs to the case where the structure of the disc is polytropicvertically. We numerically solve the eigenvalue equations for the modal structure and dispersion relation, and derive WKBJ relations which approximate the dispersion relation. We find new families of modes not present inthe isothermal case that are essentially due to the presence of an upper-surface of the disc, and which are analogous to g-modes well-known from stellar oscillation theory. An important difference between these discmodels and isothermal ones lies in the variation of the sound speed with height and its consequences for p-mode behaviour. The ‘two-dimensional’(z-independent) mode found by LP does not exist in the polytropic case. Thus p-modes, as they propagate outward, become increasingly concentratedtoward the disc surface, leading to non-linear dissipation.

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