Probing Kerr black hole in a uniform Bertotti-Robinson magnetic field through astrophysical quasi-periodic oscillations

Abstract: In this study, the behavior of high-frequency quasi-periodic oscillations (QPOs) is investigated around a Kerr black hole immersed in a uniform Bertotti-Robinson magnetic field. The motion of the test particle is analyzed by determining the geodesic equations and evaluating the corresponding orbital, radial, and vertical epicyclic frequencies. These fundamental frequencies are used to construct the theoretical framework of QPO models based on parametric and forced resonance mechanisms. Observational data obtained from several black hole X-ray binaries (GRO J1655-40, XTE J1550-564, XTE J1859+226, GRS 1915+105, H1743-322, M82~X-1, and Sgr~A$^{*}$) are used to constrain the black hole parameters through Bayesian inference and Markov Chain Monte Carlo (MCMC) analyses. For the X-ray binaries GRO J1655-40, GRS 1915+105, H1743-322, and M82~X-1, nonzero values of the dimensionless parameter $b=Bm$ are obtained at the $68\%$ confidence level within the framework of the parametric resonance model, while only upper bounds at the $90\%$ confidence level are obtained for the remaining sources. In contrast, in the case of the forced resonance model, only an upper bound at the $90\%$ confidence interval is obtained for the magnetic field parameter for all considered X-ray binary sources. The analysis indicates that the value of the magnetic field parameter is small but not negligible, producing minor modifications to particle dynamics and epicyclic frequencies. The influence of the magnetic field is further examined through the properties of the innermost stable circular orbit and the radiative properties of the thin accretion disk, including the energy flux and temperature profiles, within the allowed parameter range inferred from the MCMC analysis.