**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 νh = 41 Hz, νr = 67 Hz,

ν_h+νr = 108 Hz, and ν_v-νr = 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.;