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 $g_{\mathrm{N}}<10^{-9}$ 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 $g_{\mathrm{N}}\equiv GM/r^2$ (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 ${\delta }_{\mathrm{obs}-\mathrm{newt}}$ between the observed acceleration at $g_{\mathrm{N}}$ and the Newtonian prediction is measured to be: ${\delta }_{\mathrm{obs}-\mathrm{newt}}=0.034\pm 0.007$ 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 $g_{\mathrm{obs}}/g_{\mathrm{pred}}=10^{\sqrt{2}{\delta }_{\mathrm{obs}-\mathrm{newt}}}=1.43\pm 0.06$. This systematic deviation agrees with the boost factor that the AQUAL theory predicts for kinematic accelerations in circular orbits under the Galactic external field.

A revised version of the published ApJ paper (2023, 952, 128) including corrections of Figures 12, 18, 20, and Equation (4) to be published in an erratum in press: all corrections are minor and have no impact on the contents or conclusion of the paper

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