Epicyclic Oscillations of Fluid Bodies: Newtonian Nonslender Torus

TL;DR

This paper derives exact formulas for epicyclic oscillation frequencies of fluid tori around black holes, showing pressure effects lower frequencies and adjusting previous black hole spin estimates based on QPO observations.

Contribution

It provides the first analytic expressions for eigenfrequencies of fluid tori, accounting for pressure effects, and refines the interpretation of QPO data for black hole spins.

Findings

Pressure reduces epicyclic frequencies compared to free particles.

The 3/2 frequency ratio occurs at frequencies 15% higher than free particle values.

Previous black hole spin estimates from QPOs may be overestimated.

Abstract

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 eigenfrequencies nu_r and nu_z 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 nu_z/nu_r=3/2, which is important for the theory of high-frequency quasi-periodic oscillations (QPOs), occurs when the fluid tori epicyclic frequencies nu_r and nu_z 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.