Variable Stars in Local Group Galaxies. IV. RR Lyrae stars in the central regions of the low-density galaxy Crater II

We present a search and analysis of variable stars in the recently discovered Crater~II dwarf galaxy. Based on $B$, $V$, $I$ data collected with the Isaac Newton Telescope (FoV$\sim$0.44 square degrees) we detected 37 variable stars, of which 34 are bone-fide RR Lyrae stars of Crater~II (28 RRab, 4 RRc, 2 RRd). We applied the metal-independent ($V$, $B-V$) Period--Wesenheit relation and derived a true distance modulus ($\mu$ = 20.30$\pm$0.08 mag ($\sigma$=0.16 mag). Individual metallicities for RR Lyrae stars were derived by inversion of the predicted $I$-band Period-Luminosity relation. We find a mean metallicity of [Fe/H]=-1.64 and a standard deviation of $\sigma_{[Fe/H]}$ =0.21 dex, compatible with either negligible or vanishing intrinsic metallicity dispersion. The analysis of the Colour-Magnitude Diagram reveals a stark paucity of blue horizontal branch stars, at odds with other Galactic dwarfs, and globular clusters with similar metal abundances.