Many Galactic black hole and neutron star sources in low mass X-ray binaries show both chaotic and quasi-periodic variability in their observed X-ray flux. Some of the quasi-periodic oscillations (QPOs) are in the kilohertz range and often come in pairs ν_upp, ν_down of twin peaks in the Fourier power spectra. In four black hole sources with twin peak kHz QPO pairs, ν_upp/ν_down=3/2, and also for neutron star sources the ratio of twin-peak frequencies is mostly close to this value. Based on these and other properties of QPOs, Kluzniak and Abramowicz (2000) concluded that twin peak kHz QPOs are due to a resonance in the accretion disc oscillation modes and they noticed that the specific 3/2 ratio could be a consequence of strong gravity.
   
Using the method of multiple scales, I derive an analytic solution that describes the behaviour of weakly coupled, non-linear oscillations in nearly Keplerian discs close to the 3:2 orbital epicyclic resonance. The solution obtained agrees with the previous numerical simulation. With a particular choice of tunable parameters, the solution fits the observational data for Sco X-1. 
 
 

Vladimir Karas
organizer