**Publication date:** Aug 2007

**Abstract:**

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.

**Authors:**

Stuchlík, Z.; Slaný, P.; Török, G.;