Four 'Peculiar' RRd Stars Observed by K2

Four stars pulsating simultaneously with a dominant period $P_D$$\in$(0.28,0.39) d and an {\it additional} period $P_A$$\in$(0.20,0.27) d have been identified from among the more than 3000 RR Lyrae stars observed by the Kepler space telescope during NASA's K2 Mission. All four stars are located in the direction of the Galactic Bulge and have period ratios, $P_A$/$P_D$, significantly smaller than those of most double-mode RR Lyrae (RRd) stars: $P_A$/$P_D$$\in$(0.694,0.710) vs. $P_1$/$P_0$$\in$(0.726,0.748). Three of the stars are faint ($<$$V$$>$=18--20 mag) and distant and are among the `peculiar' RRd (pRRd) stars discovered by Prudil et al. (2017); the fourth star, EPIC 216764000 (=V1125 Sgr), is a newly discovered pRRd star several magnitudes brighter than the other three stars. In this paper the high-precision long-cadence K2 photometry is analyzed in detail and used to study the cycle-to-cycle light variations. The pulsational characteristics of pRRd stars are compared with those of `classical' and `anomalous' RRd (cRRd, aRRd) stars. The conclusion by Prudil et al. that pRRd stars form a separate group of double-mode pulsators and are not simply very-short-period cRRd stars is confirmed. V1127 Aql and AH Cam are identified as other probable members of the class of pRRd stars.