Detection of Gravitational Anomaly at Low Acceleration from a Highest-quality Sample of 36 Wide Binaries with Accurate 3D Velocities

We set out to accurately measure gravity in the low-acceleration range $(10^{-11},10^{-9})$ m s$^{-2}$ from 3D motions of isolated wide binary stars. Gaia DR3 provides precise measurements of the four sky-plane components of the 3D relative displacement and velocity ($\mathbf{r}, \mathbf{v}$) for a wide binary, but not comparably precise line-of-sight (radial) separation and relative velocity $v_{r}$. Based on our new observations and the public databases/publications, we assemble a sample of 36 nearby (distance $<150$pc) wide binaries in the low-acceleration regime with accurate values of $v_{r}$ (uncertainty $< 100$ m s$^{-1}$). Kinematic contaminants such as undetected stellar companions are well under control using various observational diagnostics such as Gaia’s ruwe parameter, the color-magnitude diagram, multi-epoch observations of radial velocities, Speckle interferometric follow-up observations, and requiring Hipparcos-Gaia proper motion consistency. For the parameter $Γ\equiv \log_{10}\sqrtγ$ with $γ\equiv G/G_{\rm N}$ (where $G$ is a parameter generalizing Newton’s constant $G_{\rm N}$ in elliptical orbits), we find $Γ=0.102_{-0.021}^{+0.023}$, inconsistent with standard gravity at $4.9σ$, giving a gravity boost factor of $γ=1.600_{-0.141}^{+0.171}$. Four wide binaries have 3D relative velocities exceeding their estimated Newtonian escape velocities with $1<v_{\rm obs}/v_{\rm escN}\le1.2$. These systems are unlikely to be chance associations and are expected in a nonstandard paradigm such as Milgromian dynamics (MOND). The hypothesis that Newtonian gravity can be extrapolated to the low-acceleration limit is falsified by this independent study with accurate 3D velocities. Future radial velocity monitoring and Speckle interferometric imaging for larger samples will be useful to refine the present result.

💡 Research Summary

The authors present a direct test of gravity in the ultra‑low‑acceleration regime (10⁻¹¹–10⁻⁹ m s⁻²) by exploiting the three‑dimensional (3D) relative motions of wide binary (WB) stars in the solar neighbourhood. Using Gaia DR3 they obtain precise sky‑plane positions and proper motions (x′, y′, vₓ′, v_y′) for each pair, and complement these data with high‑precision radial velocities (v_r) from a combination of new observations (LCO‑NRES, Gemini‑North MAROON‑X) and archival spectroscopic surveys (HARPS, APOGEE, etc.). All selected binaries have radial‑velocity uncertainties below 100 m s⁻¹, ensuring that the full 3D velocity vector is known to better than a few percent.

From an initial pool of nearby (d < 150 pc) binaries whose Newtonian acceleration g_N = G_N M_tot/r² lies in the target range, the authors apply a stringent contamination filter: (i) Gaia RUWE < 1.4 and colour‑magnitude diagram cuts to reject non‑main‑sequence or unresolved multiples; (ii) multi‑epoch radial‑velocity monitoring to identify hidden spectroscopic companions; (iii) speckle interferometry at the 2.1 m SPM telescope to flag close visual companions down to tens of AU; and (iv) Hipparcos–Gaia proper‑motion consistency to eliminate chance alignments. After these cuts, 36 “pure” wide binaries remain, representing the highest‑quality low‑acceleration sample to date (≈ four times larger than previous 3D studies).

The theoretical framework compares Newtonian gravity with Modified Newtonian Dynamics (MOND). In MOND the effective gravitational constant becomes G = γ G_N, where γ > 1 in the low‑acceleration regime, and the exact value depends on the external field effect (EFE) from the Milky Way. For an isolated binary the boost could approach γ ≈ 2, but for the Solar‑neighbourhood EFE (≈ 1.8 a₀) numerical studies predict γ ≈ 1.3–1.4.

To infer γ the authors adopt a Bayesian 3D orbital model (Chae 2025a,b). Each binary is described by six free parameters: eccentricity e, inclination i, pericentre phase φ₀, true anomaly Δφ, a mass‑ratio factor log f_M, and the gravity‑boost parameter Γ ≡ log₁₀√γ. Priors enforce isotropic orientations (sin i), uniform pericentre phases, and a phase‑occupancy distribution proportional to instantaneous orbital speed (Eq. 3). The likelihood connects the free parameters to the observed (r, v) vector, accounting for the much larger uncertainties in the line‑of‑sight separation (z′) than in the transverse components. Markov‑Chain Monte‑Carlo sampling yields posterior PDFs p_i(Γ) for each system; the joint posterior for the whole sample is the product of the individual PDFs.

The combined analysis yields Γ = 0.102 +0.023/‑0.021, corresponding to a gravity‑boost factor γ = 10^{2Γ} ≈ 1.60 ± 0.16. This deviates from the Newtonian expectation (γ = 1) at 4.9σ significance, providing strong evidence for a systematic excess in the effective gravitational strength at the examined accelerations. Moreover, four binaries exhibit observed 3D relative speeds exceeding their Newtonian escape velocities by 0–20 %, a configuration that is highly unlikely for unbound chance pairs but is naturally accommodated in MOND‑type theories with an external field.

The paper discusses several caveats. The sample size, while unprecedented for 3D studies, remains modest, and the external field strength is treated with a simplified model rather than a full Galactic potential reconstruction. Systematic errors in radial velocities and the detection limits of speckle imaging could leave undetected low‑mass companions, potentially biasing the inferred γ upward. Nevertheless, the authors argue that their multi‑diagnostic contamination control makes such biases sub‑dominant.

Future work outlined includes (i) expanding the sample to > 100 binaries with continued high‑precision RV monitoring and speckle imaging, (ii) exploiting forthcoming Gaia data releases (DR4) that will improve radial‑velocity precision and provide better parallaxes for the line‑of‑sight separation, and (iii) incorporating more realistic external‑field models based on up‑to‑date Galactic mass models. Achieving these goals would sharpen the test of low‑acceleration gravity and could decisively confirm or refute MOND‑like modifications, with profound implications for the need for dark matter on galactic scales.