Peculiar double-periodic pulsation in RR Lyrae stars of the OGLE collection. I. Long-period stars with dominant radial fundamental mode

We present the discovery of a new, peculiar form of double-periodic pulsation in RR Lyrae stars. In four, long-period ($P>0.6$ d) stars observed by the Optical Gravitational Lensing Experiment, and classified as fundamental mode pulsators (RRab), we detect additional, low-amplitude variability, with period shorter than fundamental mode period. The period ratios fall in a range similar to double-mode fundamental and first overtone RR Lyrae stars (RRd), with the exception of one star, in which the period ratio is significantly lower and nearly exactly equals 0.7. Although period ratios are fairly different for the four stars, the light curve shapes corresponding to the dominant, fundamental mode are very similar. The peak-to-peak amplitudes and amplitude ratios (Fourier parameters $R_{21}$ and $R_{31}$) are among the highest observed in RRab stars of similar period, while Fourier phases ($\varphi_{21}$ and $\varphi_{31}$) are among the lowest observed in RRab stars. If the additional variability is interpreted as due to radial first overtone, then, the four stars are the most extreme RRd variables of the longest pulsation periods known. Indeed, the observed period ratios can be well modelled with high metallicity pulsation models. However, at such long pulsation periods, first overtone is typically damped. Five other candidates, with weak signature of additional variability, sharing the same characteristics, were also detected and are briefly discussed.