Probing the nature of gravity in the low-acceleration limit: wide binaries of extreme separations with perspective effects

TL;DR

The paper tests gravity in the deep low-acceleration regime by analyzing extremely wide, isolated binaries (up to $50~\mathrm{kau}$) using Gaia DR3 data with stringent quality and isolation criteria. It accounts for perspective effects and uses two MC-based methods—the acceleration-plane approach and a $\tilde{v}$-based analysis—to infer the gravity boost factor $\gamma_g$ as a function of Newtonian acceleration $g_N$, finding $\gamma_g\approx1.61^{+0.37}_{-0.29}$ at $g_N\approx10^{-11}$ m s$^{-2}$ and $\gamma_g\approx1.26^{+0.12}_{-0.10}$ at $g_N\approx10^{-10.3}$ m s$^{-2}$, with $\gamma_g\approx1.32^{+0.12}_{-0.11}$ for $g_N\lesssim10^{-10}$ m s$^{-2}$. The results are broadly consistent with MOND-type gravity (AQUAL/QUMOND) and are robust against perspective corrections, eccentricity treatment, and mass estimator (Gaia DR3 vs FLAME) uncertainties. However, the low number of extremely wide binaries limits precision, and a Bayesian 3D approach with high-precision radial velocities is proposed for a more decisive test. Overall, the study strengthens the case for a low-acceleration gravity deviation from Newtonian predictions, challenging standard gravity interpretations relying on dark matter, and highlights the potential MOND-like behavior in stellar binaries at the largest separations.

Abstract

Recent statistical analyses of wide binaries have revealed a boost in gravitational acceleration with respect to the prediction by Newtonian gravity at low internal accelerations $\lesssim 10^{-9}$ m\,s$^{-2}$. This phenomenon is important because it does not permit the dark matter interpretation, unlike galaxy rotation curves. We extend previous analyses by increasing the maximum sky-projected separation from 30 to 50 kilo astronomical units (kau). We show that the so-called ``perspective effects'' are not negligible at this extended separation and, thus, incorporate it in our analysis. With wide binaries selected with very stringent criteria, we find that the gravitational acceleration boost factor, $γ_g \equiv g_{\rm obs}/g_{\mathrm N}$, is $1.61^{+0.37}_{-0.29}$ (from $δ_{\rm obs-newt}\equiv (\log_{10}γ_g)/\sqrt{2}=0.147\pm0.062$) at Newtonian accelerations $g_{\mathrm N} = 10^{-11.0}$ m\,s$^{-2}$, corresponding to separations of tens of kau for solar-mass binaries. At Newtonian accelerations $g_{\mathrm N} = 10^{-10.3}$ m\,s$^{-2}$, we find $γ_g=1.26^{+0.12}_{-0.10}$ ($δ_{\rm obs-newt}=0.072\pm0.027$). For all binaries with $g_{\rm N}\lesssim10^{-10}$ m\,$s^{-2}$ from our sample, we find $γ_g=1.32^{+0.12}_{-0.11}$ ($δ_{\rm obs-newt}=0.085\pm0.027$). These results are consistent with the generic prediction of MOND-type modified gravity, although the current data are not sufficient to pin down the low-acceleration limiting behavior. Finally, we emphasize that the observed deviation from Newtonian gravity cannot be explained by the perspective effects or any separation-dependent eccentricity variation which we have taken into account.

Figures (15)

• Figure 1: Color--magnitude diagrams for the primary (component A, left panel) and secondary (component B, right panel) stars in our wide binary sample. Each point represents a star, plotted in absolute $G$-band magnitude ($M_G$) versus Gaia color ($BP-RP$). The shaded blue region denotes the selection window applied to ensure that both components are main-sequence stars and to exclude evolved objects and outliers. The dashed red lines indicate the magnitude and color boundaries: $3.8 < M_G < 13.4$ and $M_G - 3.2(BP-RP) < 3.8$. Only binaries in which both components fall within the shaded region are retained for subsequent analysis.
• Figure 2: Summary of key error terms and the perspective effects for the wide binary sample, with each panel illustrating a different aspect of the analysis. Top-left: Assessment of line-of-sight distance uncertainties in the context of the perspective effects. The distribution of $\sigma_{\Delta d}/s=\sqrt{\sigma_{d_A}^2+\sigma_{d_B}^2}/s$ is shown; its large value (typically $\mathcal{O}(100)$) makes it impossible to correctly estimate the $\Delta d/d$ term in the perspective effects because the true value of $\Delta d$ is on the order of $s$. Our nominal choice is to assume that the $\Delta d/d$ term is zero. Bottom-left: Distribution of $s/d$, representing the expected distribution of $\sqrt{2}|\Delta d|/d$. Top-center: Distribution of the relative error in the relative PM due to radial velocity uncertainty (perspective effects). The fractional error is generally small for most wide binaries. Bottom-center: Same as the top-center panel, but only for systems with sky-projected separation $s > 30$ kau. In this regime, the impact of perspective effects becomes most significant. Top-right: Distribution of $\ln \left( v_{p(\mathrm{pers})}/v_{p(\mathrm{w/o~pers})} \right)$ for binaries with $s < 30~\mathrm{kau}$, quantifying the typical change in projected relative velocity due to the perspective effects at smaller separations. Bottom-right: Same as the top-right panel, but for binaries with $s > 30~\mathrm{kau}$. The perspective effects become significant only at the largest separations.
• Figure 3: perspective effects as a function of three variables: $s$, $v^2_{\rm pers}/s$ and $s/r_M$. The dots represent $v_{\rm pers}/v$ and the solid red lines denote the median for each bin. For all three graphs, the perspective effects are important only for the last bin.
• Figure 4: Left: Scaling relation for $v_M\equiv v_p/\sqrt{M_{\mathrm{tot}}}$ and $s$. For larger separation, $v_M$ deviates more from the Newtonian scaling relation $v_M\propto s^{-1/2}$. Right: Scaling relation for $\tilde{v}\equiv v/v_c$ and $s/r_M$. For Newtonian gravity, $\tilde{v}$ is expected to remain roughly constant if the dependence of eccentricity on $s$ is not considered.
• Figure 5: The main panel shows the relation between $v_p/v_c$ and $\log_{10}(s/r_M)$ for wide binaries, with running medians indicated for subsamples selected by different projected velocity error ($\sigma_{v_p}$) thresholds. The inset displays the histogram of $\sigma_{v_p}$. The scaling relation is robust to the $\sigma_{v_p}$ selection, with only minor variations due to statistical fluctuations.