Breakdown of the Newton-Einstein Standard Gravity at Low Acceleration in Internal Dynamics of Wide Binary Stars

A gravitational anomaly is found at weak gravitational acceleration g _N ≲ 10^-9 m s^-2 from analyses of the dynamics of wide binary stars selected from the Gaia DR3 database that have accurate distances, proper motions, and reliably inferred stellar masses. Implicit high-order multiplicities are required and the multiplicity fraction is calibrated so that binary internal motions agree statistically with Newtonian dynamics at a high enough acceleration of ≈10^-8 m s^-2. The observed sky-projected motions and separation are deprojected to the 3D relative velocity v and separation r through a Monte Carlo method, and a statistical relation between the Newtonian acceleration g _N ≡ GM/r ² (where M is the total mass of the binary system) and a kinematic acceleration g ≡ v ²/r is compared with the corresponding relation predicted by Newtonian dynamics. The empirical acceleration relation at ≲10^-9 m s^-2 systematically deviates from the Newtonian expectation. A gravitational anomaly parameter δ _obs-newt between the observed acceleration at g _N and the Newtonian prediction is measured to be: δ _obs-newt = 0.034 ± 0.007 and 0.109 ± 0.013 at g _N ≈ 10^-8.91 and 10^-10.15 m s^-2, from the main sample of 26,615 wide binaries within 200 pc. These two deviations in the same direction represent a 10σ significance. The deviation represents a direct evidence for the breakdown of standard gravity at weak acceleration. At g _N = 10^-10.15 m s^-2, the observed to Newton-predicted acceleration ratio is ${g}_{\mathrm{obs}}/{g}_{\mathrm{pred}}={10}^{\sqrt{2}{\delta }_{\mathrm{obs}-\mathrm{newt}}}=1.43\pm 0.06$ . This systematic deviation agrees with the boost factor that the AQUAL theory predicts for kinematic accelerations in circular orbits under the Galactic external field.