Low-Acceleration Gravitational Anomaly from Bayesian 3D Modeling of Wide Binary Orbits: Methodology and Results with Gaia Data Release 3

Abstract

Isolated wide binary stars provide natural laboratories to directly probe gravity for Newtonian acceleration $g_{\mathrm{N}}\lesssim 10^{-9}$ m s${}^{-2}$. Recent statistical analyses of wide binaries have been performed only with sky-projected relative velocities $v_p$ in the pairs. A new method of Bayesian orbit modeling exploiting three relative velocity components including the radial component $v_r$ is developed to measure the gravitational anomaly parameter $\hat{I}“\equiv {\log }_{10}\sqrt{{\hat{I}}_g^3}\equiv {\log }_{10}\sqrt{G_{\mathrm{eff}}/G_{\mathrm{N}}}$ where $G_{\mathrm{eff}}$ is the effective gravitational constant for pseudo-Newtonian elliptical orbits, while $G_{\mathrm{N}}$ is Newton's constant. The method infers individual probability distributions of $\hat{I}“$ and then combines the independent distributions to obtain a consolidated distribution in a specific range of $g_{\mathrm{N}}$. Here the method is described and applied to a sample of 312 wide binaries in a broad dynamic range $10^{-11.0}\lesssim g_{\mathrm{N}}\lesssim 10^{-6.7}$ m s${}^{-2}$ with $v_r$ uncertainties in the range $168<\ddot{I}{ƒ}_{v_r}<380$ m s${}^{-1}$ selected from the Gaia DR3 database. The following results are obtained: $\hat{I}“=0.000\pm 0.011$ ($N_{\mathrm{binary}}=125$) for the high-acceleration regime ($10^{-7.9}\lesssim g_{\mathrm{N}}\lesssim 10^{-6.7}$ m s${}^{-2}$) agreeing well with Newton, but $\hat{I}“=0.085\pm 0.040$ or ${\hat{I}}_g^3=1.48_{-0.23}^{+0.33}$ (35) for a MOND regime ($10^{-11.0}\lesssim g_{\mathrm{N}}\lesssim 10^{-9.5}$ m s${}^{-2}$) and $\hat{I}“=0.063\pm 0.015$ or ${\hat{I}}_g^3=1.34_{-0.08}^{+0.10}$ (111) for a MOND+transition regime ($10^{-11.0}\lesssim g_{\mathrm{N}}\lesssim 10^{-8.5}$ m s${}^{-2}$). These results show that a gravitational anomaly is evident for $g_{\mathrm{N}}\lesssim 10^{-9}$ m s${}^{-2}$ and $\hat{I}“$ in the MOND regime ($\lesssim 10^{-9.5}$ m s${}^{-2}$) agrees with the prediction ($\approx 0.07$) of MOND gravity theories.

28 figures, 3 tables, minor revision to match the version to be published in the Astrophysical Journal