A Quality Framework for Testing Gravity with Wide Binaries: No Evidence for MOND

Abstract

Wide binaries (WBs) offer a unique opportunity to test gravity in the low-acceleration regime, where modifications such as Milgromian dynamics (MOND) predict measurable deviations from Newtonian gravity. We construct a rigorous framework for conducting the wide binary test (WBT), emphasizing high quality sample selection, filtering of poor astrometric solutions, contamination mitigation, and uncertainty propagation. We show that undetected close binaries, chance alignments, and improper treatment of projection effects can mimic MOND-like signals. We introduce a checklist of best practices to identify and avoid these pitfalls. Applying this framework to Gaia DR3 data, we compile a high-purity sample of WBs within 130 pc with projected separations of 1 - 30 kAU, spanning the transition between the Newtonian and MOND regimes. We find that the scaled relative velocity distribution of wide binaries does not exhibit the 20% enhancement expected from MOND and is consistent with Newtonian gravity across all separations. A meta-analysis of previous WBTs shows that apparent MOND signals diminish as methodological rigour improves. We conclude that when stringent quality controls are applied, there is no observational evidence for MOND-induced velocity boosts in wide binaries. Our results place strong empirical constraints on modified gravity theories operating between a0/10 and 200 a0, where a0 is the MOND acceleration scale. Across this range of internal accelerations, Newtonian gravity is up to 1500x more likely than MOND for our cleanest sample.

Figures (13)

• Figure 1: The $\left( r_{\mathrm{sky}}/r_{\mathrm{M}}, \widetilde{v} \right)$ distribution of WBs within 150 pc, RUWE $< 1.25$ (Section \ref{['RUWE']}), and $\Delta v_{\mathrm{sky}} < 10$$\mathrm{km~s}^{-1}$Cookson_2024. The dashed line is the approximate MOND expectation (Equation \ref{['v_ratio_MOND']}), while the continuous line is the Newtonian prediction normalised to 0.5. The right panel is similar to the left, but imposes an additional filter of $\widetilde{v} < 2.5$. This removes systems with large separations and relative velocities, which are likely chance alignments or flybys.
• Figure 2: The distribution of $r_{\mathrm{sky}}/r_{\mathrm{MOND}}$ and $\widetilde{v}$ for a sample of WBs produced when using an input catalogue with parallax uncertainty below 1% (catalogue C10; left) and 2.5% (catalogue C25; right), following degrouping (Section \ref{['Degrouping']}). We also show the approximate MOND expectation (Equation \ref{['v_ratio_MOND']}) for each sample (dashed line) and the Newtonian expectation (continuous line). Allowing a larger parallax uncertainty leads to a larger sample prior to degrouping, improving the efficiency of the degrouping process and pushing the results closer to the flat Newtonian expectation. The sample totals in each bin are smaller on the right despite the greater number of pairs, because of the more thorough degrouping.
• Figure 3: Colour-magnitude diagram, with stars coloured by RUWE Belokurov_2020 as follows: blue ($<1.25$), yellow ($1.25-1.4$), and red ($>1.4$). Some 20k grey points in the left panel are excluded from the final sample. The right panel restricts to stars with RUWE $<1.25$ truncated into a parallelogram on this diagram, as described in the text. It also implements a few kinematic quality cuts in our checklist, such as $\widetilde{v}$ < 2.5, though these have little effect on the overall appearance, amounting to $\approx 50$ pairs out of $\approx 900$. Notice how the RUWE cut preferentially removes stars which are overluminous for their colour, indicating a possible binary companion. The median colour-magnitude relation for Main Sequence stars used by Hartman_2022 is shown in cyan in the right panel.
• Figure 4: Comparison of Catalogue A with no ipd_frac_multi_peak filter applied, for maximum distances of 130 pc (left) and 150 pc (right).
• Figure 5: The number of WBs in the final sample in each $d_h$ bin. Perfect data should follow the parabolic expectation ($4\pi r^2 \rho_\star \Delta d_h$) shown in cyan, but the actual results flatten out at $d_h \ga 90$ pc, beyond which many of the WBs have insufficiently precise data for the WBT.