Non-evolutionary effects on period change in Magellanic Cepheids II. Empirical constraints on non-linear period changes

Classical Cepheids are not only excellent standard candles, but also invaluable tools to test stellar evolution and pulsation theories. Rates of their pulsation period change, quantified usually through $O-C$ diagrams, can be confronted with predictions of stellar evolution theory. On the other hand, period changes on much shorter time scales ($\sim$10$^{2}$-10$^{4}$days), attributed to non-evolutionary effects are often detected and lack detailed explanation. We aim to provide a systematic and quantitative description of irregular or non-linear period changes in Cepheids. We aim to provide a systematic and quantitative description of irregular or non-linear period changes in Cepheids. We analysed part of the OGLE data for classical Cepheids in the Magellanic Clouds (MCs; from both Large Magellanic Cloud, LMC, and the Small Magellanic Cloud, SMC) using the modified Hertzsprung $O-C$ technique. A sample of 3658 stars, with the best quality data and void of additional low-amplitude periodicities (e.g. due to non-radial pulsations), that could impact the results, was selected for analysis. Based on $O-C$ shapes, stars were classified into three categories: no period change (class 1), linear period change (class 2), and irregular change (class 3). In our investigation, $33.5\pm0.7$\% of analysed stars show irregular period changes. Considering the pulsation mode, irregular period changes were detected in $16.5\pm0.7$\% of the analysed fundamental mode stars and in $68.1\pm1.2$\% of the first overtone stars. The amplitude of variability in the $O-C$ diagrams increases with the pulsation period, and at a given pulsation period, it is larger for first overtone stars. While the increase is linear for first overtone stars, for fundamental mode stars it becomes steeper as the pulsation period increases.