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

At least four high-frequency quasiperiodic oscillations (QPOs) at frequencies 41Hz, 67Hz, 113Hz, and 167Hz were reported in a binary system GRS 1915+105 hosting near-extreme Kerr black hole with a dimensionless spin a>0.98. 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" f_h, that could excite the radial and vertical epicyclic oscillations with frequencies f_r, f_v. Due to non-linear resonant phenomena the combinational frequencies are allowed as well. Assuming mass M=14.8M_sun and spin a=0.9998 for the GRS 1915+105 Kerr black hole, the model predicts frequencies f_h=41Hz, f_r=67Hz, (f_h+f_r)=108Hz, (f_v-f_r)=170Hz corresponding quite well to the observed ones. 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 GRS 1915+105 within the range of observational errors.