Mass-spin relation of black holes obtained by twin high-frequency quasi-periodic oscillations

Abstract

The paper studies the uniqueness and the monotonicity of the mass-spin relation of black holes (BHs) the X-ray power density spectra of which contain twin high-frequency quasi-periodic oscillations in 3:2 ratio. Some of the results are valid for a relatively large class of models — the geodesic models, which attribute the observed pair of HF QPOs to the frequencies of epicyclic motion of inhomogeneities in the accretion disk surrounding the black hole, treated as point particles, or to simple linear combinations of them. It is found that for geodesic models the properties of the mass-spin relation are independent of the observed frequencies, i.e. they are independent of the particular object. For concreteness two of the most commonly used geodesic models are studied here – the 3:1 nonlinear epicyclic resonance model and its Keplerian version.