The global normal disk oscillations and the persistent low-frequency quasi-periodic oscillations in X-ray binaries

We suggest that persistent low-frequency quasi-periodic oscillations (QPOs) detected in the black hole (BH) sources XTE J1118+480, GRO J1655-40, and LMC X-l at similar to0.1 Hz, in HZ Her/Her X-l at similar to0.05 Hz, and in neutron star (NS) binaries 4U 1323-62, 4U 1746-31, and EXO 0748--76 at similar to1 Hz are caused by the global disk oscillations in the direction normal to the disk (normal mode). We argue that these disk oscillations are a result of the gravitational interaction between the central compact object and the disk. A small displacement of the disk from the equatorial plane results in a linear gravitational restoring force opposite to this displacement. Our analysis shows chat the frequency of this mode is a function of the mass of the central object and that it also depends on the inner and outer radii of the disk, which in turn are related to the orbital period of the binary system. We derive an analytical formula for the frequency of the normal disk mode and show that these frequencies can be related to the persistent lower QPO frequencies observed in the NS and BH sources. We offer a new independent approach to the BH mass determination by interpreting this low QPO frequency as the global disk oscillation frequency. The implementation of this method combined with the independent method recently developed by Shrader & Titarchuk that uses the X-ray energy spectra results in stringent constraints for the BH masses.