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Epicyclic Oscillations of Fluid Bodies: Newtonian Nonslender Torus

Journal article
Authors Omer Blaes
Eva Šrámková
Marek A Abramowicz
Włodek Kluźniak
Ulf Torkelsson
Published in Astrophysical Journal
Volume 665
Issue 1
Pages 642-653
ISSN 0004-637X
Publication year 2007
Published at Department of Physics (GU)
Pages 642-653
Language en
Keywords Accretion, Accretion Disks, Black Hole Physics, Hydrodynamics, X-Rays: Binaries
Subject categories High energy astrophysics, Theory of relativity, gravitation


We study epicyclic oscillations of fluid tori around black holes (in the Paczyński-Wiita potential) and derive exact analytic expressions for their radial and vertical eigenfrequencies νr and νz to second-order accuracy in the width of the torus. We prove that pressure effects make the eigenfrequencies smaller than those for free particles. However, the particular ratio νz/νr=3/2, which is important for the theory of high-frequency quasi-periodic oscillations (QPOs), occurs when the fluid tori epicyclic frequencies νr and νz are about 15% higher than the ones corresponding to free particles. Our results therefore suggest that previous estimates of black hole spins from QPOs have produced values that are too high.

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