Testing gravity with wide binaries. 3D velocities and distances of wide binaries from Gaia and HARPS

Wide binaries (WBs) are interesting systems to test Newton-Einstein gravity in low potentials. The basic concept is to verify whether the difference in velocity between the WB components is compatible with what is expected from the Newton law. Previous attempts, based solely on Gaia proper motion differences scaled to transverse velocity differences using mean parallax distances, do not provide conclusive results. Here we add to the Gaia transverse velocities precise measurements of the third velocity component, the radial velocity (RV), in order to identify multiple stars and improve the reliability of the test by using velocity differences and positions in three dimensions. We mined the ESO archive for observations of WBs with the high precision HARPS spectrograph, and we used these observations to search for RV variations, that indicate the presence of additional stars in the system. We used the HARPS spectra to determine accurate RV differences between the WB components while also correcting the observed velocities for gravitational redshift and convective shift. We exploited the Gaia distance distributions to determine the projected and intrinsic separations s and r and the three-dimensional velocity differences of the binaries. We retrieved 44 pairs observed with HARPS, most of them with numerous observations, spanning time baselines from one week to several years. A considerable fraction (27$%$) of these pairs show signs of multiplicity or are not suitable for the test, and 32 bona fide WBs survived our selection. Their projected separation s is up to 14 kAU, or 0.06 parsec. The median renormalized unit weight error parameter for the final sample is 0.975, highest value 1.24, and the median RV variability is 10 m s^-1 with a standard deviation of 6 m s^-1. Gaia RVs are on average smaller by only 68 m s^-1 from those determined with HARPS, with an RMS dispersion of 311 m s^-1. We determined the distances, eccentricities, and position angles to reproduce the velocity differences according to Newton's law, finding reasonable solutions for all WBs but one, and some systems are possibly too near pericenter and/or at too high inclination. We show that precise (and accurate) multiple RVs of WB candidates are a very powerful tool to make the WBs test of gravity more robust and reliable. These observations allow one to minimize or eliminate one of the major limitations of previous tests, that is, the presence of multiple systems, and make the comparison with theory straightforward, without the need to resort to complex simulations. Our (limited) number of WBs does not show obvious trends with separation or acceleration and is consistent with Newtonian dynamics. We are currently collecting a larger sample of this kind to robustly assess these results.