Exploring the accelerating black holes from the observations of quasi-periodic oscillations in X-ray binaries

Black holes in dense astrophysical environments, such as globular clusters or in the vicinity of other massive objects, may possess accelerations. Such acceleration would modulate the characteristics of the quasi-periodic oscillations (QPOs) observed in X-ray black hole binaries. In this paper, we explore the influence of spin-aligned acceleration of a black hole on QPOs observed in X-ray binaries. For this purpose, we compute the fundamental frequencies arising from the motion of test particles around an accelerating (spin-aligned) black hole and apply the relativistic precession, parametric resonance, and forced resonance models to establish their correspondence with several observed QPOs of X-ray binaries (GRO J1655-40, XTE J1550-564, XTE J1859+226, GRS 1915+105, H1743-322, M82~X-1, and Sgr~A${}^{\ast }$). We then employ the Bayesian Markov-Chain Monte Carlo method to constrain the black hole parameters. Our results show no evidence for spin-aligned acceleration in any of the analyzed sources, suggesting that most of these X-ray binaries reside in isolated environments and therefore experience only small perturbations to the background spacetime geometries.