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 $g_{\rm{N}} < 10^{-9}$ m s$^{-2}$ from analyses of the dynamics of wide binary stars selected from the Gaia EDR3 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 three-dimensional relative velocity $v$ and separation $r$ through a Monte Carlo method, and a statistical relation between the Newtonian acceleration $g_{\rm{N}} \equiv GM/r^2$ (where $M$ is the total mass of the binary system) and a kinematic acceleration $g \equiv v^2/r$ 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 $\delta_{\rm{obs-newt}}$ between the observed acceleration at $g_{\rm{N}}$ and the Newtonian prediction is measured to be: $\delta_{\rm{obs-newt}}= 0.034\pm 0.007$ and $0.109\pm 0.013$ at $g_{\rm{N}}\approx10^{-8.91}$ 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 $10\sigma$ significance. The deviation represents a direct evidence for the breakdown of standard gravity at weak acceleration. At $g_{\rm{N}}=10^{-10.15}$ m s$^{-2}$, the observed to Newton predicted acceleration ratio is $g_{\rm{obs}}/g_{\rm{pred}}=10^{\sqrt{2}\delta_{\rm{obs-newt}}}=1.43\pm 0.06$. This systematic deviation agrees with the boost factor that the AQUAL theory predicts for kinematic accelerations in circular orbits under the Galactic external field.