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We investigate the relation between the parameters of the energy spectrum andthe frequency and amplitude of the kilohertz quasi-periodic oscillations (kHzQPOs) in the low-mass X-ray binary 4U 1636$-$53. We fit the $3-180$-keVspectrum of this source with a model that includes a thermal Comptonisationcomponent. We show that the frequencies of both kHz QPOs follow the samerelation as a function of the parameters of this spectral component, except fora systematic frequency shift, whereas the rms fractional amplitude of each QPOfollows a different relation with respect to those same parameters. Thisimplies that, while the dynamical mechanism that sets the frequencies of theQPO can be the same for both kHz QPOs, the radiative mechanisms that set theamplitudes of the lower and the upper kHz QPO are likely different. We discussthe implications of these results to the modelling of the kHz QPOs and thepossibility that the lower kHz QPO reflects a resonance between theComptonising medium and the photons from the accretion disc and/or the neutronstar surface.

Relation between the properties of the kilohertz quasi-periodic oscillations and spectral parameters in 4U 1636$-$53