On the connection between almost periodic functions and Blazhko light curves

In this paper, it is shown that the mathematical form that 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 the harmonic detuning effect (HDE). The published deviations of the harmonics of V445 Lyr are explained by this effect. The HDE is also found for V2178 Cyg, which is another Blazhko star observed by the Kepler space telescope. The HDE is detectable only if the phase variation part of the Blazhko effect is of large amplitude and non-periodic enough and, additionally, if 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.