We analyze the relation between the emission radii of twin kilohertz quasi-periodic oscillations ( kHz QPOs ) and the co-rotation radii of the 12 neutron star low mass X-ray binaries ( NS-LMXBs ) which are simultaneously detected with the twin kHz QPOs and NS spins .
We find that the average co-rotation radius of these sources is \langle r _ { co } \rangle \sim 32 km , and all the emission positions of twin kHz QPOs lie inside the co-rotation radii , indicating that the twin kHz QPOs are formed in the spin-up process .
It is noticed that the upper frequency of twin kHz QPOs is higher than NS spin frequency by \geq 10 % , which may account for a critical velocity difference between the Keplerian motion of accretion matter and NS spin that is corresponding to the production of twin kHz QPOs .
In addition , we also find that \sim 83 % of twin kHz QPOs cluster around the radius range of 15 - 20 km , which may be affected by the hard surface or the local strong magnetic field of NS .
As a special case , SAX J1808.4-3658 shows the larger emission radii of twin kHz QPOs of r \sim 21 - 24 km , which may be due to its low accretion rate or small measured NS mass ( < 1.4 { M _ { \odot } } ) .