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

TL;DR

This paper introduces a Bayesian 3D orbit modeling method using Gaia DR3 data to detect gravitational anomalies in wide binary stars, providing evidence for modified gravity theories at low accelerations.

Contribution

The paper develops and applies a novel Bayesian orbit modeling technique incorporating radial velocity data to measure gravitational anomalies in wide binaries, extending previous sky-projected velocity analyses.

Findings

Gravitational anomaly detected below $10^{-9}$ m s$^{-2}$ acceleration.

Results align with MOND predictions in low-acceleration regimes.

Newtonian gravity confirmed at higher accelerations.

Abstract

Isolated wide binary stars provide natural laboratories to directly probe gravity for Newtonian acceleration $g_{\rm{N}}\lesssim 10^{-9}$ 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 $\Gamma\equiv\log_{10}\sqrt{\gamma_g}\equiv\log_{10}\sqrt{G_{\rm{eff}}/G_{\rm{N}}}$ where $G_{\rm{eff}}$ is the effective gravitational constant for pseudo-Newtonian elliptical orbits, while $G_{\rm{N}}$ is Newton's constant. The method infers individual probability distributions of $\Gamma$ and then combines the independent distributions to obtain a consolidated distribution in a specific range of $g_{\rm{N}}$. Here the method is described and applied to a sample of 312 wide binaries in a broad dynamic range $10^{-11.0}\lesssim g_{\rm{N}}\lesssim 10^{-6.7}$ m s$^{-2}$ with $v_r$ uncertainties in the range $168<\sigma_{v_r}<380$ m s$^{-1}$ selected from the Gaia DR3 database. The following results are obtained: $\Gamma = 0.000\pm 0.011$ ($N_{\rm{binary}}=125$) for the high-acceleration regime ($10^{-7.9} \lesssim g_{\rm{N}} \lesssim 10^{-6.7}$ m s$^{-2}$) agreeing well with Newton, but $\Gamma = 0.085\pm 0.040$ or $\gamma_g=1.48_{-0.23}^{+0.33}$ (35) for a MOND regime ($10^{-11.0}\lesssim g_{\rm{N}}\lesssim 10^{-9.5}$ m s$^{-2}$) and $\Gamma = 0.063\pm 0.015$ or $\gamma_g=1.34_{-0.08}^{+0.10}$ (111) for a MOND+transition regime ($10^{-11.0}\lesssim g_{\rm{N}}\lesssim 10^{-8.5}$ m s$^{-2}$). These results show that a gravitational anomaly is evident for $g_{\rm{N}}\lesssim 10^{-9}$ m s$^{-2}$ and $\Gamma$ in the MOND regime ($\lesssim 10^{-9.5}$ m s$^{-2}$) agrees with the prediction ($\approx 0.07$) of MOND gravity theories.