Abstract:
We study the bound orbit conditions for equatorial and eccentric orbits around a Kerrblack hole both in the parameter space (E,L,a) representing the energy, angular mo-mentum of the test particle, and spin of the black hole, and also (e,μ,a) space rep-resenting the eccentricity, inverse-latus rectum of the orbit, and spin. We apply theseconditions and implement the relativistic precession (RP) model to M82X-1, which is anIntermediate-mass black hole (IMBH) system, where two high-frequency Quasi-PeriodicOscillations (HFQPOs) and a low-frequency QPO were simultaneously observed. As-suming that the QPO frequencies can also be generated by equatorial and eccentrictrajectories, we calculate the probability distributions to infere,a, and periastron dis-tance,rp, of the orbit giving rise to simultaneous QPOs. We find that an eccentric orbitsolution is possible in the region between innermost stable circular orbit (ISCO) and themarginally bound circular orbit (MBCO) fore=0.2768+0.0657−0.0451,a=0.2897±0.0087,andrp=4.6164+0.0694−0.1259
