Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-type Gravitational Anomaly at Low Acceleration

Technical Summary: Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests

Problem Statement
Wide binary stars serve as natural laboratories for testing gravity in the low-acceleration regime ($g \lesssim 10^{-9} \text{ m s}^{-2}$), where the effects of dark matter are negligible. Recent statistical analyses of Gaia DR3 data have reported a gravitational anomaly consistent with Modified Newtonian Dynamics (MOND), characterized by a boost factor $\gamma \approx 1.3-1.6$. However, conflicting studies (e.g., Banik et al. 2024; Pittordis et al. 2025; Cookson et al. 2026) claim that standard Newtonian gravity is preferred or that no deviation exists. These conflicting results hinge on two primary methodological issues: (1) the implementation of data quality control, specifically the "Banik cut" on the normalized velocity error ($\sigma_{\tilde{v}}$), and (2) the realistic modeling of hierarchical multiple-star systems (triples and higher-order multiples) which can mimic gravitational boosts. This paper re-examines these issues to determine if the reported MOND-type anomaly is robust against these specific criticisms.

Methodology
The authors conduct extensive statistical gravity tests using sky-projected 2D velocities ($v_p$) from three distinct samples: K.-H. Chae (2023), I. Banik et al. (2024), and C. Pittordis et al. (2025) (PSS). The study employs three primary testing frameworks:

1. Acceleration-Plane Test: A Monte Carlo deprojection method analyzing the orthogonal deviation ($\Delta_\perp$) of observed acceleration from Newtonian predictions in the logarithmic acceleration plane.
2. $\tilde{v}$-Distribution Test: Comparing the histogram of the normalized 2D velocity ($\tilde{v} = v_p / v_c(r_p)$) against theoretical predictions for pure binaries and those with hidden companions.
3. Median-$\tilde{v}$-Profile Test: Analyzing the scaling of the median $\tilde{v}$ as a function of normalized separation ($r_p/r_M$).

Key methodological steps include:

• Bias Analysis of Quality Cuts: Using mock Newtonian binaries with controlled errors, the authors simulate the effects of the Banik cut ($\sigma_{\tilde{v}} < 0.1 \max(1, \tilde{v}/2)$) and other cuts (e.g., $\sigma_{v_p} < 50 \text{ m s}^{-1}$).
• Triple Modeling Calibration: The authors implement the triple-star modeling algorithm proposed by Pittordis et al. (2025) for samples satisfying $ruwe < 1.2$. Crucially, they calibrate the fraction of triples ($f_{trip}$) using data from the high-acceleration (Newtonian) regime where chance alignments are negligible, rather than fitting $f_{trip}$ simultaneously with gravity models in the transition/MOND regime.
• Comparison with Numerical Solutions: Theoretical predictions are compared against both approximate analytical models and recent realistic numerical QUMOND solutions by J. Pflamm-Altenburg (2025) that account for two-body dynamics and the Galactic external field effect (EFE).
• High-Quality Subsample Analysis: A subsample of nearby binaries ($d < 150 \text{ pc}$) satisfying the strict quality framework of Cookson et al. (2026) is analyzed to address claims of insufficient statistics and data contamination.

Key Contributions and Results

1. The Banik Cut Introduces Bias:
   The study demonstrates that the Banik cut is not a neutral quality control measure. Because the relative error $\sigma_{\tilde{v}}$ increases with separation ($r_p$), the cut selectively removes high-precision data points with higher $\tilde{v}$ values in the low-acceleration regime. This artificially suppresses the rising trend of $\tilde{v}$, biasing the data toward Newtonian predictions. In contrast, a cut based on absolute velocity error ($\sigma_{v_p} < 50 \text{ m s}^{-1}$) removes data uniformly without introducing such a bias.

2. Calibration of Multiple-Star Fractions:
   When the triple fraction ($f_{trip}$) is calibrated using Newtonian-regime data (where binaries must obey Newtonian gravity), the resulting $f_{trip}$ values are significantly lower than those derived by Pittordis et al. (2025), who fitted $f_{trip}$ in the transition/MOND regimes.

   • For the Chae (2023) sample with $ruwe < 1.2$, $f_{trip} \approx 0.10 \pm 0.03$.
   • For the PSS sample, $f_{trip} \approx 0.12 \pm 0.03$ (or $0.07$ depending on flyby assumptions).
     Using these calibrated fractions, the acceleration-plane test reveals a significant gravitational anomaly ($\delta_{obs-newt} > 0$) with statistical significance $> 5\sigma$ in the low-acceleration regime. The previously claimed preference for Newtonian gravity by Pittordis et al. (2025) is attributed to the use of an uncalibrated, overestimated $f_{trip}$ and a limited dynamic range that excluded the pure Newtonian regime.

3. Robustness of the Anomaly with High-Quality Data:
   Analyzing a large sample ($N \approx 480$ in the MOND regime) of nearby binaries ($d < 150 \text{ pc}$) that satisfies the strict quality cuts of Cookson et al. (2026), the authors find:

   • The median $\tilde{v}$ profile rises with separation, deviating from the flat Newtonian prediction.
   • The claim of "no evidence for MOND" by Cookson et al. (2026) is shown to be a consequence of low number statistics ($N=61$ in the MOND regime), which allows random fluctuations to mimic a flat profile, combined with the use of biased stellar masses and an incorrect Newtonian benchmark ($\tilde{v} \approx 0.49$).
   • When corrected for mass biases and using sufficient statistics, the data show a $>3\sigma$ deviation from Newtonian gravity, consistent with a boost factor $\gamma \approx 1.4-1.5$.

4. Agreement with Realistic Numerical Models:
   The observed behavior of the gravitational anomaly in the transition regime ($10^{-10} \lesssim g_N \lesssim 10^{-9} \text{ m s}^{-2}$) aligns more closely with realistic numerical QUMOND solutions (J. Pflamm-Altenburg 2025) than with approximate test-particle models. The distinction between Newtonian gravity and MOND is confirmed to be robust when proper calibration and realistic modeling are applied.

Significance and Claims
The paper concludes that the low-acceleration gravitational anomaly reported in wide binary studies is a robust feature of the data, not an artifact of poor data quality or unmodeled multiple stars. The authors assert that:

• The "Banik cut" is a biased selection criterion that artificially weakens the MOND signal.
• Claims of Newtonian preference in recent literature stem from methodological flaws, specifically the lack of calibration of hierarchical system fractions in the Newtonian regime and the use of insufficient sample sizes in the low-acceleration regime.
• When these issues are corrected, statistical tests on 2D velocities consistently confirm a breakdown of standard gravity at low accelerations, favoring MOND-type theories with a boost factor of $\gamma \approx 1.3-1.6$.
• The results are consistent with recent realistic numerical solutions for wide binary orbits in QUMOND, suggesting that refined statistical analyses are converging with direct 3D orbit modeling results.

The authors emphasize that while 3D orbit modeling will play an increasingly important role with future Gaia data releases, current 2D statistical tests, when properly controlled for bias and hierarchical contamination, provide strong, independent confirmation of the gravitational anomaly.