2025ApJ...985..210C

Isolated wide binary stars provide natural laboratories to directly probe gravity for Newtonian acceleration of g_N ≲ 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 (line-of-sight) component v_r is developed to measure the gravitational anomaly parameter ${\rm{\Gamma }}\equiv {\mathrm{log}}_{10}\sqrt{{\gamma }_{g}}\equiv {\mathrm{log}}_{10}\sqrt{{G}_{{\rm{eff}}}/{G}_{{\rm{N}}}}$ where G_eff is the effective gravitational constant for pseudo-Newtonian elliptical orbits, while G_N is Newton's constant. The method infers individual probability distributions of Γ and then combines the independent distributions to obtain a consolidated distribution in a specific range of g_N. Here the method is described and applied to a sample of 312 wide binaries in a broad dynamic range of 10^–11.0 ≲ g_N ≲ 10^–6.7 m s^–2 with v_r uncertainties in the range $168\lt {\sigma }_{{v}_{r}}\lt 380$ m s^–1 selected from the Gaia Data Release 3 database. The following results are obtained: Γ = 0.000 ± 0.011 or γ_g = 1.00 ± 0.05 (N_binary = 125) for the high-acceleration regime (10^–7.9 ≲ g_N ≲ 10^–6.7 m s^–2) agreeing well with Newton, but Γ = 0.085 ± 0.040 or ${\gamma }_{g}=1.4{8}_{-0.23}^{+0.33}$ (35) for the modified Newtonian dynamics (MOND) regime (10^–11.0 ≲ g_N ≲ 10^–9.5 m s^–2) and Γ = 0.063 ± 0.015 or ${\gamma }_{g}=1.3{4}_{-0.08}^{+0.10}$ (111) for the MOND + transition regime (10^–11.0 ≲ g_N ≲ 10^–8.5 m s^–2). These results show that a gravitational anomaly is evident for g_N ≲ 10^–9 m s^–2 and Γ in the MOND regime (≲10^–9.5 m s^–2) agrees with the first-tier prediction (Γ ≈ 0.07 or γ_g ≈ 1.4) of MOND gravity theories.