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 to improve the reliability of the test by using velocity differences and positions in three dimensions. We use the HARPS spectra to determine accurate RV difference between the WB components, correcting the observed velocities for gravitational redshift and convective shift. We exploit the Gaia distance distributions to determine the projected and intrinsic separations s and r and the 3-dimensional velocity differences of the binaries. Of the 44 pairs observed with HARPS, 27% show sign of multiplicity or are not suitable for the test, and 32 bona-fide WBs survive our selection. Their projected separation s is up to 14 kAU, or 0.06 parsec. We determine distances, eccentricities and position angles to reproduce the velocity differences according to Newton's law, finding reasonable solutions for all WBs but one, and with some systems possibly too near pericenter and/or at too high inclination. Our (limited) number of WBs does not show obvious trends with separation or acceleration and is consistent with Newtonian dynamics. We are collecting a larger sample of this kind to robustly assess these results.