Similar additional frequency patterns on fundamental and overtone mode RR Lyrae stars showing $f_{68}$ frequencies

Abstract

Up to now, it seemed that the additional frequencies in the fundamental mode (RRab) and in the overtone mode pulsating (RRc and RRd) RR Lyrae stars have different nature. RRab stars show frequencies associated with periodic doubling, as well as frequencies at the first and second radial overtones, and linear combinations of these. RRc stars show frequencies with specific ratios ($f_1/f_x\sim$0.61, or $\sim$0.63) which are explained by non-radial modes and frequencies with $f_x/f_1\sim0.68$ ratio which have no currently accepted explanation. To search for similarities in spectral content, we compared the Fourier spectra of the recently published TESS and K2 data of RRc stars with the spectra of Kepler RRab stars that do not show the Blazhko effect but contain additional frequencies. The time series data have been analysed using standard Fourier methods, and the possibility of the excitation of the second radial overtone mode in RRab stars has also been tested using numerical hydrodynamical codes. We show that the additional frequencies appear in non-Blazhko RRab stars at the position of the second radial overtone mode, and the pattern they create, is very similar to that caused by the additional frequencies with the period ratio $\sim0.68$ in RRc stars. The former explanation of the additional frequencies of these RRab stars by a second radial overtone is unlikely.