RRab variables with identical light-curve shapes at different pulsation periods

In this paper, we report on the detection of RRab stars with quasi-identical-shape light curves but period differences as large as \(0.05-0.21\) d using the Galactic bulge data of the OGLE-IV survey. We have examined stars with shorter periods than the Oosterhoff~I ridge of the bulge. These stars generally have smaller amplitudes and larger Fourier phase-differences than the typical bulge RRab stars have at the same period. Many of these "anomalous" stars have good-quality light curves without any sign of the Blazhko modulation. Examining their Fourier parameters revealed that several of these stars show very similar light-curve to the typical bulge RR Lyrae. We found hundreds of quasi-identical-shape light-curve pairs with different periods between the "anomalous"- and the "normal"-position RRab stars based on the OGLE \(I\)-band data. The OGLE \(V\)-band, and the archive VVV and MACHO surveys \(K_s\)-, \(b\)- and \(r\)-band data of these stars were also checked for light-curve-shape similarity. Finally, 149 pairs with identical-shape light curves in each available photometric band were identified. Calculating the physical properties of the variables using empirical formulae, on average, \(-0.5\)~dex, \(-0.13\)~mag, 0.67, and 165~K differences between the [Fe/H], \(M_V\), \(R/R_\odot\), and \(T_{\mathrm{eff}}\) values of the members of the pairs are derived, being the short-period stars less metal-poor, fainter, smaller and hotter than the long-period variables. To explain the existence of variables with different physical properties and pulsation periods but with identical-shape light curves is a challenging task for modelling.