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

TL;DR

This work tests whether spin-aligned acceleration in accelerating Kerr (Kerr-C) black holes leaves measurable imprints on QPOs in X-ray binaries. It derives fundamental geodesic frequencies in the accelerating spacetime and maps them to QPOs via three models—RP, PR, and FR—using seven diverse sources, with Bayesian MCMC (dynesty) to constrain BH parameters and the acceleration parameter $A m$. Across all models, the acceleration parameter remains consistent with zero within 90% confidence, indicating the spacetime is effectively Kerr-like for the observed systems. The results reinforce the Kerr metric as a robust description of strong-field gravity in these binaries while establishing upper bounds on possible environmental accelerations that would perturb QPOs at current sensitivities.

Abstract

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$^{*}$). 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.

Figures (3)

• Figure 1: The posterior distributions of the BH mass $M$, spin parameter $a/M$, orbital radius $r/M$, and dimensionless acceleration parameter $m\cdot A$, obtained within the RP model using the observed QPOs of X-ray binaries, are given in Table \ref{['tab: I']}. The corner plots display the marginalized posterior distributions, with the shaded regions corresponding to the 68% and 90% confidence intervals for each source.
• Figure 2: The posterior distributions of the BH mass $M$, spin parameter $a/M$, orbital radius $r/M$, and dimensionless accelerating parameter $m\cdot A$, obtained within the PR model using the observed QPOs of X-ray binaries, are given in Table \ref{['tab: I']}. The corner plots represent the marginalized posterior distributions, with the shaded regions corresponding to the 68% and 90% confidence intervals for each source.
• Figure 3: The posterior distributions of the BH mass $M$, spin parameter $a/M$, orbital radius $r/M$, and dimensionless acceleration parameter $m\cdot A$, obtained within the forced resonance model using the observed QPOs of X-ray binaries, are provided in Table \ref{['tab: I']}. The corner plots display the marginalized posterior distributions, with the shaded regions corresponding to the 68% and 90% confidence intervals for each source.