APO3 - The Origins of Massive Black Holes and Quasars at High Redshifts |
Speaker_ |
Stuchlik, Zdenek |
Talk _ |
Humpy LNRF-velocity profiles in accretion discs orbiting rapidly rotating Kerr black holes |
Abstract _ |
Change of sign of the LNRF-velocity profile gradient has been found for accretion discs orbiting a rapidly rotating black hole with spin a>0.9953 for Keplerian discs and a>0.99979 for marginally stable thick discs. Aschenbach has shown that the rate of change of the orbital velocity with such a ``humpy'' profile introduces a locally defined critical frequency, but it is done in an unphysical, coordinate-dependent form. We define the critical ``humpy'' frequency in general relativistic, coordinate independent form, and relate the frequency defined in the LNRF to the distant observers. At radius of its definition, the ``humpy'' frequency is compared to the radial and vertical epicyclic frequencies and the Keplerian frequency. We have shown that asymptotically (for 1-a < 0.001) the ratio of the epicyclic frequencies and the humpy frequency is constant, i.e., independent of a, being ~ 3:2 for radial epicyclic frequency and ~ 11:2 for vertical epicyclic frequency. On the other hand, the ratio of Keplerian vs. humpy frequency asymptotically slightly grows being ~23. It is quite interesting that 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. |