Quasiperiodic oscillations and Tomimatsu-Satoδ=2space-time

Abstract

We model the space-time of low-mass x-ray binaries with the Tomimatsu-Sato $\ensuremath{\delta}=2$ metric and study the properties of the orbital and the epicyclic frequencies. The numerical analysis shows that the properties of the characteristic frequencies of oscillation do not differ qualitatively from those of the Kerr black hole. Estimates for the angular momenta of the three stellar mass black hole candidates GRO $1655\ensuremath{-}40$, XTE $1550\ensuremath{-}564$, and GRS $1915+105$ are made with the application of the nonlinear resonance model. We find agreement between the predictions based on the $3\ensuremath{\mathbin:}2$ nonlinear resonance model for a Tomimatsu-Sato $\ensuremath{\delta}=2$ background and the current estimates found in the literature.