In the Galactic micro-quasars with double peak kHz <br />
quasi-periodic oscillations (QPOs) observed in X-ray fluxes, <br />
the ratio of the twin peak frequencies is exactly, <br />
or almost exactly, 2:3. This rather strongly supports the fact that <br />
they originate a few gravitational radii away from its centre <br />
due to two modes of accretion disk oscillations.<br />
Numerical investigation suggest that post-shock matter, <br />
before it settle down in sub-sonic branch,<br />
execute oscillation in the neighbourhood region of `shock transition\/.<br />
We consider the radial and vertical modes <br />
of oscillating matter to explain twin peaks pair correlation in<br />
high frequency QPOs.<br />
<br />
In fully general relativistic transonic flows, we explicitly present <br />
the possible range of parameters responsible for shocks.<br />
We also demonstrate a simplistic approach to study the effect of <br />
viscosity during accretion around a rotating black hole with a <br />
suitably modified effective potential (pseudo-Kerr potential)<br />
We show shocks can form very close to the horizon <br />
for highly spinning Kerr black holes but move further away when<br />
viscosity is included. The extreme possibilities of the shocks locations<br />
give the upper limits of the QPO frequencies <br />
and hence fixes lower limit of the spin. <br />
We estimate spin of the micro-quasars exhibit twin peak QPOs. <br />
Our major conclusion is that 2:3 ratio exactly occur for minimum <br />
spin(a) parameters a=0.87 and almost exactly, for wide range of spin parameter. <br />
We show that spin must has a lower cut off in observed ratios, <br />
for instance, XTE 1550-564, & GRO 1655-40 indicate a>0.87, for<br />
GRS 1915+105 a>0.83, XTE J1650-500 a>0.78 and H 1743-322 a>0.68.