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

TL;DR

The study tests whether cycle-to-cycle (C2C) light-curve variations explain irregular O-C variations observed in Blazhko RR Lyrae stars using Kepler data. It derives high-precision O-C diagrams via a template-fitting method, constructs residual O-C curves by pre-whitening Blazhko-related Fourier components, and applies four statistical models ($M1$–$M4$) to both original and residual curves. The main finding is that for $20$ of $27$ Blazhko stars, models that include C2C variation ($M2$ or $M4$) best describe the data, with the C2C-strength parameter $σ_η$ consistently larger than in non-Blazhko stars and showing a very strong positive correlation with the Blazhko FM amplitude $R = \sqrt{\sum A_i^2}$ (original curves, $r ≈ 0.973$). The work also identifies two background Kepler stars as new Blazhko candidates and highlights a close but unresolved physical link between C2C variability and Blazhko modulation, underscoring the need for theoretical explanation.

Abstract

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. 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. 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. 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.

Figures (5)

• Figure 1: Phase-noise values for the optimal models based on the original O$-$C curves ($\sigma^{(1)}_e$) and the residuals ($\sigma^{(2)}_e$). The gray line with unit slope illustrates the overall similarity of the two sets. Red symbols correspond to Kepler's original target stars, and blue rectangles to stars found in the background pixels.
• Figure 2: Top: Dependence of the $\sigma_\eta$ parameter characterizing the C2C variation in RRab stars, on the pulsation period for the original O$-$C curves (left) and for the residuals (right). Grey dots represent the sample of non-Blazhko stars from Benko_2025. Bottom: $\sigma_\eta$ as a function of the strength of the FM component of the Blazhko effect for the original O$-$Cs (left) and for the residuals (right). Green lines show linear fits; $r$ denotes the Pearson correlation coefficient. Red dots correspond to Kepler's original targets, and blue rectangles to background stars.
• Figure 3: O$-$C diagrams of Kepler Blazhko RR Lyrae stars prepared using the template fitting method. Red curves: the main target stars of the Kepler mission, for which the light curves were taken from Benko2014; blue curves: stars found by Forro2022 in the background pixels. There can be a difference of four orders of magnitude in the O$-$C values of individual stars (see vertical scales). The light yellow bars show errors estimated based on Monte Carlo simulation.
• Figure 4: continued
• Figure 5: continued. The last panel shows KPP26, in which Forro2022 found uncertain amplitude variations in addition to KPP23.