Slow pressure modes in thin accretion discs

Abstract

Thin accretion discs around massive compact objects can support slow pressure modes of oscillations in the linear regime that have azimuthal wavenumber m= 1 . We consider finite, flat discs composed of barotropic fluid for various surface density profiles and demonstrate – through WKB analysis and numerical solution of the eigenvalue problem – that these modes are stable and have spatial scales comparable to the size of the disc. We show that the eigenvalue equation can be mapped to a Schrödinger-like equation. The analysis of this equation shows that all eigenmodes have discrete spectra. We find that all the models we have considered support negative frequency eigenmodes; however, the positive eigenfrequency modes are only present in power-law discs, albeit for physically uninteresting values of the power-law index β and barotropic index γ.