Non-Axisymmetric g-Mode and p-Mode Instability in a Hydrodynamic Thin Accretion Disk

Abstract

It has been suggested that quasi-periodic oscillations of accreting X-ray sources may relate to the modes named in the title. We consider non-axisymmetric linear perturbations to an isentropic, isothermal, unmagnetized thin accretion disk. The radial wave equation, in which the number of vertical nodes (n) appears as a separation constant, admits a wave-action current that is conserved except, in some cases, at corotation. Waves without vertical nodes amplify when reflected by a barrier near corotation. Their action is conserved. As was previously known, this amplification allows the n=0 modes to be unstable under appropriate boundary conditions. In contrast, we find that waves with n >0 are strongly absorbed at corotation rather than amplified; their action is not conserved. Therefore, non-axisymmetric p-modes and g-modes with n>0 are damped and stable even in an inviscid disk. This eliminates a promising explanation for quasi-periodic oscillations in neutron-star and black-hole X-ray binaries.

A new version of the paper. The technical error in version 1 has been corrected

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• Evidence for Harmonic Relationships in the High Frequency QPOs of XTE J1550-564 and GRO J1655-40
• The Excitation, Propagation and Dissipation of Waves in Accretion Discs: The Non-linear Axisymmetric Case

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