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

Abstract 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 10 σ 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 obs / g pred = 10 2 δ obs − newt = 1.43 ± 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.