Epicyclic Oscillations of Fluid Bodies: Newtonian Nonslender Torus

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© 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A.
, , Citation Omer M. Blaes et al 2007 ApJ 665 642 DOI 10.1086/519782

0004-637X/665/1/642

Abstract

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 νzr = 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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10.1086/519782