Humpy LNRF-velocity profiles in accretion discs orbiting rapidly rotating Kerr black holes: a possible relation to epicyclic oscillations
Change of sign of the LNRF-velocity radial gradient has been found for accretion discs orbiting a rapidly rotating Kerr black hole with spin a > 0.9953 (Keplerian discs) and a > 0.99979 (marginally stable thick discs). The maximal positive rate of change of the orbital velocity in terms of the proper radial distance introduces a locally defined critical frequency characterizing any processes in the disc capable to excite possible oscillations connected with the velocity hump. Comparing the "humpy frequency" related to distant observers with the epicyclic frequencies, we shall show that in Keplerian discs orbiting extremely rapid Kerr holes (1-a < 10-4) the ratio of the epicyclic frequencies and the humpy frequency is constant, i.e., independent of spin, being ∼3:2 for the radial epicyclic frequency and ∼11:2 for the vertical epicyclic frequency. For black holes with a ≈ 0.996, i.e., when the resonant phenomena with ratio 3:1 between the vertical and radial epicyclic oscillations occur near the radius of the critical humpy frequency, there is ratio of the radial epicyclic and the humpy frequency ∼1:12, i.e., the critical frequency is close to the low-frequency QPOs related to the high-frequency QPOs in such spacetimes. For a > 0.996 the resonant orbit with the ratio 4:1 between the vertical and radial epicyclic oscillations occurs in the region of the hump. In the case of thick discs, the situation is more complex due to the dependence on the distribution of the specific angular momentum L characterizing the disc rotation. For L = const tori and (1-a) < 10-6 the frequency ratios of the humpy frequency and the epicyclic frequencies are again constant and independent of both the spin and the specific angular momentum.