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

Context. Recent studies have shown that the irregular O−C variations observed in many non-Blazhko RR Lyrae stars may result from random, cycle-to-cycle (C2C) variations in their light curves. However, centuries-long data series reveal that the O−C diagrams of Blazhko stars exhibit particularly large-amplitude, irregular variations. Aims. In this letter, we extend the previous investigation of non-Blazhko stars to Kepler Blazhko stars to explore the role of C2C variations in the O−C diagrams. Methods. We derived the O−C diagrams from Kepler space telescope light curves using a precise template-fitting method. Based on their Fourier analyses, we also constructed residual O−C diagrams that were pre-whitened for frequencies associated with the Blazhko effect. We then fitted the same statistical models to both types of O−Cs that we had previously applied to non-Blazhko stars. Results. The optimal statistical model includes the C2C variation for 74% of the O−C curves in our Blazhko sample, and the parameter describing the strength of the C2C variation is significantly larger than that obtained for non-Blazhko stars. This may explain the strong irregular O−C variations previously observed in Blazhko stars. Furthermore, we found a strong positive correlation between the C2C variation strength and the amplitude of the frequency-modulation component of the Blazhko effect, indicating a connection between the two phenomena.