Open AccessSlow pressure modes in thin accretion discs
Author(s) -
Saini Tarun Deep,
Gulati Mamta,
Sridhar S.
Publication year - 2009
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2009.15602.x
Subject(s) - physics , barotropic fluid , wkb approximation , wavenumber , eigenvalues and eigenvectors , accretion (finance) , astrophysics , power law , spectral index , spectral density , normal mode , classical mechanics , azimuth , instability , computational physics , spectral line , mechanics , optics , quantum mechanics , statistics , mathematics , vibration
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.