The frequency spectrum of periodically modulated sinusoidal oscillation

TL;DR

This paper presents an analytical Fourier spectrum model of periodically modulated sinusoidal oscillations, explaining key features of the Blazhko effect in RR Lyrae stars and supporting modulation-based physical models.

Contribution

It provides an analytical Fourier spectrum model for amplitude and phase modulated oscillations, elucidating features of the Blazhko effect in RR Lyrae stars.

Findings

The model explains multiplet structures in the spectrum.

It accounts for amplitude asymmetry and frequency doublets.

Results align well with observational data.

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.