The origin of the most probable 3:2 twin-peak quasi-periodic oscillations (QPOs) frequency ratio in the micro-quasars

In the present study, we notice that within a few gravitational radii, where the X-ray emission originates, the perturbations in the accretion disk may excite high frequency quasi-periodic oscillations (QPOs). The vertical and the radial disk oscillations frequencies due to the perturbation exhibit a 3:2 twin-peak ratio which is most commonly detected in the X-ray fluxes in many Galactic micro-quasars. The high frequency QPOs happen most likely if the oscillations occur very close to the center. We further notice that the perturbations originate in the neighborhood of the shock transition or from a discontinuity in the disk, and could be the possible mechanism to excite the high frequency QPOs. The shocks are more probable in the X-ray emission region and may form very close to the horizon particularly, when the black hole spin is very high. Studying the shock locations as a function of the black hole spin in a fully general relativistic inviscid transonic accretion flows, we calculate the disk oscillation frequencies and their ratios in that perturbed orbit. Further, from the spin dependence, we estimate the 'most probable spin interval' in the micro-quasars by considering the 1/M scaling hypothesis in high frequency QPOs. Finally, we find the spin (a) interval which lies for XTE 1550-564, at a similar to (0.89-0.99), for the GRO 1655-40, at a similar to (0.96-0.99) and for the GRS 1915+105, at a similar to (0.74-0.999). The uncertainty in the mass analysis corresponds to the above spin intervals. (C) 2012 Elsevier B.V. All rights reserved.