Asteroseismology with low-amplitude modes in RR Lyrae and classical Cepheid stars

RR Lyrae and Cepheid stars have been long believed to pulsate purely in radial modes and thus we are limited to estimating physical parameters photometrically from those modes only. This picture has changed with the discovery of additional periodicities with amplitudes many orders of magnitude lower than the dominant pulsation. With this, an entirely new research field has opened for these classical pulsators that focuses on the search and characterization of the low-amplitude signals. Massive detection is achievable only with high-quality photometric surveys, such as the OGLE, as well as the Kepler/K2 and TESS missions. While we still lack theoretical explanation for the majority of these periodicities, there is growing evidence that the so-called 0.61 group might be a game changer. This is the only group forming multiple clear sequences in the Petersen diagram, located at period ratios between 0.6 and 0.65 with the overtone pulsation, and has the best chance to have proper mode identification in the future. In this talk, I will review the different types of additional signals in RR Lyrae and classical Cepheids, also mentioning their connection to the mysterious Blazhko effect. I will discuss the latest developments on the derivation of metallicity and mass, and present the modeling efforts and the first steps that have been made recently to perform real asteroseismology of RR Lyrae and classical Cepheids.