The elusive chase for the first RR Lyr star in a binary system: the case of KIC 2831097

Context. The lack of RR Lyr stars in binary systems is an atypical fact when we consider other classes of variables. Therefore, it has become a challenge for observers to detect an RR Lyr variable in a binary system. Aims. The RR Lyr variable KIC 2831097 was one of the most promising candidates. The phases of maximum brightness in the Kepler photometry showed a regular variation superimposed on a parabolic trend. These variations in the times of maximum brightness (T max s) were interpreted as a possible light-time travel effect (LTTE) in a wide binary and a fast evolutionary change in the period. Methods. We planned two spectroscopic runs with the FIES instrument mounted at the Nordic Optical Telescope to test the hypothesis of binarity. The observations were programmed at the predicted quadratures of the orbit, when the two mean radial velocities are expected to differ by about 100 km s −1 . The GEOS collaboration complemented the spectroscopic survey by a photometric one. We also analysed Gaia time series and intensive TESS photometry. Results. The radial velocity curves obtained at the quadratures show the same mean radial velocity (-203 km s −1 ), which rules the possibility of an LTTE out. The constant mean radial velocity, the [Fe/H] content determined from ground-based CCD observations, and the astrometric parameters supplied by Gaia allow us to infer that KIC 2831097 is a single high-velocity metal-poor RRc star belonging to the Galactic halo. We revisited Kepler photometry and detected a weak Blazhko effect consisting of an oscillation of only 1.1% of the period in about 50 d. We also analysed the TESS photometry of Kepler -1601, whose photometry is contaminated by KIC 2831097. We collected 116 T max s, from the ground-based campaign, 103 T max s from TESS, and 4 T max s from Gaia . In total, we have 3624 T max s. Linear ephemerides cannot fit the whole dataset, but only parts of them. The period shows a tendency to decrease in value, as if it were an evolutionary effect, but not at a constant rate. Conclusions. The spectroscopic and photometric campaigns performed in the framework of a professional-amateur project failed to confirm that KIC 2831097 belongs to a binary system: the chase remains open. As an RR Lyr variable, KIC 2831097 shows an intriguing evolution of the period.