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Resonant switch model of twin peak HF QPOs applied to the source 4U 1636-53

Resonant Switch (RS) model of twin peak high-frequency quasi-periodic oscillations (HF QPOs) assumes switch of twin oscillations at a resonant point where frequencies of the upper and lower oscillations become commensurable and the twin oscillations change from one pair of the oscillating modes (corresponding to a specific model of HF QPOs) to some other pair due to non-linear resonant phenomena. The RS model is used to determine range of allowed values of spin and mass of the neutron star located at the atoll source 4U 1636-53 where two resonant points are observed at frequency ratios $nu_{U}$ : $nu_{L}$ = 3:2, 5:4. We consider the standard specific models of the twin oscillations based on the orbital and epicyclic geodetical frequencies. The resonant points are determined by the energy switch effect exhibited by the vanishing of the amplitude difference of the upper and lower oscillations. The predicted ranges of the neutron star parameters are strongly dependent on the twin modes applied in the RS model. We demonstrate that for some of the oscillatory modes used in the RS model the predicted parameters of the neutron star are unacceptable. Among acceptable RS models the most promising are those combining the Relativistic Precession and the Total Precession frequency relations or their modifications.