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.

Figures (4)

• Figure 1: For several observed QPO X-ray binaries, posterior distributions of the BH parameters $(m, a/m, r/m, b)$ are obtained from the MCMC analysis within the framework of the PR model. The off-diagonal panels display the corresponding two-dimensional confidence contours, while the diagonal panels show the marginalized one-dimensional posterior distributions of each parameter.
• Figure 2: The MCMC analysis within the FR model yields posterior distributions of the BH parameters $(m, a/m, r/m, b)$ for the considered QPO X-ray binaries. The magnetic field parameter $b$ is constrained by an upper limit at the $90\%$ confidence level, whereas the mass $m$, spin parameter $a/m$, and resonance radius $r/m$ are constrained at the $68\%$ confidence level.
• Figure 3: The profiles of the energy flux $F(r)$ (left panel) and temperature $T(r)$ (right panel) of the accretion disk as functions of the dimensionless radius $r/m$ around the considered BH for mass $m=1$, spin parameter $a/m=0.1$, and different values of the dimensionless magnetic field parameter $b$.
• Figure 4: The radial temperature profile for the dimensionless magnetic field parameter $b$ is shown in the left panel, while the corresponding density plot of the temperature distribution on the equatorial $X$--$Y$ plane is presented in the right panel. Here, $X$ and $Y$ denote the Cartesian coordinates.