Epicyclic Oscillations of Fluid Bodies: Newtonian Nonslender Torus

We study epicyclic oscillations of fluid tori around black holes (in the Paczynski-Wiita potential) and derive exact analytic expressions for their radial and vertical eigenfrequendes [unk] and v2 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 v2/ [unk] = 3/2, which is important for the theory of high-frequency quasi-periodic oscillations (QPOs), occurs when the fluid tori epicyclic frequencies [unk] and v2 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.