Twin Peaks kHz QPOs: Mathematics of the 3:2 Orbital Resonance

Using the method of multiple scales, one can derive an analytic solution that describes the behaviour of weakly coupled, non-linear oscillations in nearly Keplerian discs around neutron stars or black holes close to the $3:2$ orbital epicyclic resonance. The obtained solution agrees with a previous numerical simulation. Such a result may be relevant to the kilohertz quasi-periodic variability in X-ray fluxes observed in many Galactic black hole and neutron star sources. With a particular choice of tunable parameters, the solution fits accurately the observational data for Sco X-1.

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