Born in a pair (?): Pisces II and Pegasus III

We have used B, V time series photometry collected with the Large Binocular Telescope to undertake the first study of variable stars in the Milky Way ultra-faint dwarf (UFD) satellites, Pisces II and Pegasus III. In Pisces II we have identified a RRab star, one confirmed and a candidate SX Phoenicis star and, a variable with uncertain classification. In Pegasus III we confirmed the variability of two sources: an RRab star and a variable with uncertain classification, similar to the case found in Pisces II. Using the intensity-averaged apparent magnitude of the bona-fide RRab star in each galaxy we estimate distance moduli of (m - M)0= 21.22 \pm 0.14 mag (d= 175 \pm 11 kpc) and 21.21 \pm 0.23 mag (d=174 \pm 18 kpc) for Pisces II and Pegasus III, respectively. Tests performed to disentangle the actual nature of variables with an uncertain classification led us to conclude that they most likely are bright, long period and very metal poor RRab members of their respective hosts. This may indicate that Pisces II and Pegasus III contain a dominant old stellar population (t>12 Gyr) with metallicity -1.8 dex along with, possibly, a minor, more metal-poor component, as supported by the V , B-V color-magnitude diagrams of the two UFDs and their spectroscopically confirmed members. The metallicity spread that we derived from our data sample is 0.4 dex in both systems. Lastly, we built isodensity contour maps which do not reveal any irregular shape, thus making the existence of a physical connection between these UFDs unlikely.