LNRF-velocity hump-induced oscillations of a Keplerian disc orbiting near-extreme Kerr black hole: a possible explanation of high-frequency QPOs in GRS 1915+105

Context: At least four high-frequency quasiperiodic oscillations (QPOs) at frequencies 41 Hz, 67 Hz, 113 Hz, and 167 Hz were reported in a binary system GRS 1915+105 hosting near-extreme Kerr black hole with a dimensionless spin a > 0.98.
Aims: We attempt to explain all four observed frequencies by an extension of the standard resonant model of epicyclic oscillations.
Methods: We use the idea of oscillations induced by the hump of the orbital velocity profile (related to locally non-rotating frames-LNRF) in discs orbiting near-extreme Kerr black holes, which are characterized by a “humpy frequency” ν_h, that could excite the radial and vertical epicyclic oscillations with frequencies ν_r, ν_v. Due to non-linear resonant phenomena, the combinational frequencies are allowed as well.
Results: Assuming mass M = 14.8 M_⊙ and spin a = 0.9998 for the GRS 1915+105 Kerr black hole, the model predicts frequencies ν_h = 41 Hz, ν_r = 67 Hz, ν_h+ν_r = 108 Hz, and ν_v-ν_r = 170 Hz corresponding quite well to the observed ones.
Conclusions: For black-hole parameters being in good agreement with those given observationally, the forced resonant phenomena in non-linear oscillations, excited by the “hump-induced” oscillations in a Keplerian disc, can explain high-frequency QPOs in near-extreme Kerr black-hole binary system GRS 1915+105 within the range of observational errors.