Quasi-periodic oscillations from charged-particle motion around a Kerr black hole with a current-loop magnetic field

We study the orbital and epicyclic frequencies of a charged particle around a Kerr black hole in the electromagnetic field of an equatorial current loop. The field is treated as a test field. We apply the relativistic precession model to the three simultaneous quasi-periodic oscillations (QPOs) of GRO J1655-40. Neutral Kerr motion reproduces the QPO frequencies and the black-hole mass measured from the companion-star orbit, but it gives a spin lower than the value obtained from fitting the thermal X-ray spectrum. In the outer dipole approximation, the three QPO frequencies can be reproduced with a mass consistent with the companion-star measurement and a spin consistent with that inferred from fitting the thermal X-ray spectrum. At leading order, the result already depends on whether the particle orbit lies inside or outside the loop; higher multipoles introduce an additional strong dependence on the loop radius. For the sampled solutions, the fitted mass remains closest to the dynamical estimate when the particle orbit lies outside a compact loop, whereas an orbit inside the loop gives larger masses.