Real or apparent? -- Period variations of Kepler and TESS RR Lyrae stars based on their O-C diagrams

It has long been suggested that the rapid and intense O-C variation observed in many RR Lyrae stars, which could not be explained by stellar evolution-induced period variation, are in fact caused by random cycle-to-cycle (C2C) variation in the light curve with a constant average period. We fitted alternative statistical models to O-C diagrams from the 4-year Kepler and 1-year TESS observations and tested their validity. We found that the vast majority of the O-C curves can be satisfactorily explained by assuming timing noise and C2C variations without real period variation.  We show that the strength of the C2C variation is strongly dependent on the pulsation period and metallicity. These relationships suggest that turbulent convection may underlie the C2C varation.