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 $g_{\mathrm{N}}<{10}^{-9}$ 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 three-dimensional relative velocity $v$ and separation $r$ through a Monte Carlo method, and a statistical relation between the Newtonian acceleration $g_{\mathrm{N}}\equiv GM\mathrm{/}{r}^2$ (where $M$ is the total mass of the binary system) and a kinematic acceleration $g\equiv v^2\mathrm{/}r$ 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 ${\delta }_{\mathrm{o}\mathrm{b}\mathrm{s}-\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{t}}$ between the observed acceleration at $g_{\mathrm{N}}$ and the Newtonian prediction is measured to be: ${\delta }_{\mathrm{o}\mathrm{b}\mathrm{s}-\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{t}}=0.034\pm 0.007$ and $0.109\pm 0.013$ at $g_{\mathrm{N}}\approx {10}^{-8.91}$ 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 $10\sigma$ significance. The deviation represents a direct evidence for the breakdown of standard gravity at weak acceleration. At $g_{\mathrm{N}}={10}^{-10.15}$ m s${}^{-2}$, the observed to Newton predicted acceleration ratio is $g_{\mathrm{o}\mathrm{b}\mathrm{s}}\mathrm{/}{g}_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}={10}^{\sqrt{2}{\delta }_{\mathrm{o}\mathrm{b}\mathrm{s}-\mathrm{n}\mathrm{e}\mathrm{w}\mathrm{t}}}=1.43\pm 0.06$. This systematic deviation agrees with the boost factor that the AQUAL theory predicts for kinematic accelerations in circular orbits under the Galactic external field.