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.

arXiv commentA 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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