The frequency spectrum of periodically modulated sinusoidal oscillation

Abstract

The mathematical model of periodically amplitude and phase modulated sinusoidal oscillation is studied, and its Fourier spectrum is given analytically. The Fourier spectrum of the model explains the main features of the frequency spectrum of RR Lyrae stars showing light curve modulation called the Blazhko effect: among others the appearance of multiplets, the rapid decrease of their amplitudes in increasing orders, the asymmetry of the amplitudes of the side frequency pairs, and the possibility of the occurrence of frequency doublets instead of triplets in the spectrum. The good agreement of the results of this mathematical model with observational facts favours those physical models of the Blazhko effect which explain the phenomenon as a modulation of the oscillation with the modulation frequency, f_m.