Precessions and parameter constraints from quasiperiodic oscillations in a rotating charged black hole

Abstract We investigate quasi-periodic oscillations (QPOs) as a diagnostic tool for probing frame-dragging effects and accretion disk physics in the spacetime of a rotating regular magnetic black hole (BH). Specifically, we analyze the precession of bound orbits and the epicyclic oscillations of test-particles under small perturbations in the equatorial plane. We demonstrate how the BH’s nonminimal coupling parameter ( $$\lambda /M^4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:mrow> </mml:math> ) and dimensionless magnetic charge ( Q / M ) significantly influence the three fundamental epicyclic frequencies. By applying the relativistic precession model and employing Markov Chain Monte Carlo simulations (MCMC), we constrain the BH’s characteristic parameters, including mass, spin, magnetic charge, and nonminimal coupling, with the use of observational QPO data from five X-ray binaries: $$GRO J1655-40$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mi>R</mml:mi> <mml:mi>O</mml:mi> <mml:mi>J</mml:mi> <mml:mn>1655</mml:mn> <mml:mo>-</mml:mo> <mml:mn>40</mml:mn> </mml:mrow> </mml:math> , $$XTE J1859+226$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>X</mml:mi> <mml:mi>T</mml:mi> <mml:mi>E</mml:mi> <mml:mi>J</mml:mi> <mml:mn>1859</mml:mn> <mml:mo>+</mml:mo> <mml:mn>226</mml:mn> </mml:mrow> </mml:math> , $$H1743-322$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mn>1743</mml:mn> <mml:mo>-</mml:mo> <mml:mn>322</mml:mn> </mml:mrow> </mml:math> , $$XTE J1550-564$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>X</mml:mi> <mml:mi>T</mml:mi> <mml:mi>E</mml:mi> <mml:mi>J</mml:mi> <mml:mn>1550</mml:mn> <mml:mo>-</mml:mo> <mml:mn>564</mml:mn> </mml:mrow> </mml:math> , and $$GRS 1915+105$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mi>R</mml:mi> <mml:mi>S</mml:mi> <mml:mn>1915</mml:mn> <mml:mo>+</mml:mo> <mml:mn>105</mml:mn> </mml:mrow> </mml:math> . Furthermore, we examine the Lense-Thirring, geodetic, and general spin precession frequencies of a test gyroscope attached to a stationary observer around the current BH. Our theoretical results indicate that the regular charged BH suppresses these precession frequencies compared with the Kerr BH case.