On the connection between almost periodic functions and Blazhko light curves

TL;DR

This paper links the Blazhko effect in RR Lyrae stars to almost periodic functions, predicting a harmonic detuning effect (HDE) that explains observed deviations in star light curves, revealing a new aspect of stellar pulsation.

Contribution

It introduces the concept that the Blazhko effect relates to almost periodic functions rather than simple modulation, predicting and explaining the harmonic detuning effect (HDE) in stellar light curves.

Findings

HDE explains deviations in V445 Lyr's harmonics.

HDE observed in V2178 Cyg from Kepler data.

Detectability of HDE depends on phase variation amplitude and observation duration.

Abstract

In this paper it is shown that the mathematical form which most precisely describes the Blazhko RR Lyrae light curves is connected to almost periodic functions and not to the mathematics of modulation. That is, the Blazhko effect is more than a simple external modulation of the pulsation signal. The mathematical framework of almost periodic functions predicts a new observable effect: a shift of the Fourier harmonics of the main pulsation frequency from the exact harmonic position. This phenomenon is called as harmonic detuning effect (HDE).The published deviations of the harmonics of V445 Lyr are explained with this effect. HDE is also found for V2178 Cyg, another Blazhko star observed by the Kepler space telescope. HDE is detectable only if the phase variation part of the Blazhko effect is of large amplitude and non-periodic enough, additionally, the time span of the observed light curve is sufficiently long for obtaining precise frequencies. These three conditions restrict the number of stars showing detectable HDE and explain why this effect has not been discovered up to now.