Connections between the cycle-to-cycle light curve and O−C variations of non-Blazhko RR Lyrae stars

Context. It is widely known that if the durations of the consecutive cycles of a pulsating star vary in a random fashion, the O−C diagram could show quasi-periodic or irregular variations, even when the actual average period is constant. It has been hypothesised that the period variation observed in many RR Lyrae stars, which are much faster and stronger than would otherwise be explained by an evolutionary origin, could actually be caused by this cycle-to-cycle (C2C) variation effect. So far, quantitative studies have been scarce and space data have not been used to investigate this topic. Aims. Our primary goal is to quantitatively analyse the O−C diagrams of RR Lyrae stars obtained from space photometry and explained by quasi-periodic or irregular periodic variations to see whether they can be explained by random fluctuations in pulsation cycle length, without assuming real period variations. Methods. We fit statistical models to the O−C diagrams and tested their validity and fit. The necessary analysis of the light curves was performed using standard Fourier methods. Results. We found that the vast majority of the O–C curves can be satisfactorily explained by assuming timing noise and the C2C variation without a real mean period variation. We have shown that the strength of the C2C variation is strongly dependent on the pulsation period and metallicity. These correlations suggest that turbulent convection may be behind the C2C variation. The additional frequencies of some RR Lyrae stars and their variation over time play only a marginal role in O−Cs. We have established new arguments to support the idea that the phase jump phenomenon in RRc stars is, in fact, a continuous change; moreover, we find it could also be caused by the C2C variation.