Fourier analysis of the hydrodynamic limit-cycle models of pulsating stars

The pulsation motions of the limit-cycle model can be described as a superposition of the Fourier harmonics, in the adiabatic layers each harmonics being identified with the corresponding standing wave. Near the resonance II_o/II_l =k the harmonics of orderk is also identified with the overtone of orderl. The spectra of the oscillatory moment of inertia obey to the power dependence on the Fourier harmonics orderk. In cepheids with periods shorter than 9 days the bump is due to the wave packet generated by the second overtone, whereas at periods longer than 10 days the bump feature is due to the traveling pulse reflected off the stellar core.