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

T0 review · 3 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The low-acceleration gravitational anomaly in wide binaries survives both stringent data-quality control and realistic modeling of hidden companion stars, confirming a MOND-type velocity boost at more than 5σ significance.

desk verdict Careful, mostly persuasive re-analysis showing the low-acceleration anomaly survives the Pittordis triple model and Cookson quality cuts; main weaknesses are an untested f_trip constancy assumption and no shipped code/data. read the letter →

arxiv 2607.14450 v1 pith:UVICTTZV submitted 2026-07-16 astro-ph.GA astro-ph.HEastro-ph.SRgr-qchep-th

Kyu-Hyun Chae , Youngsub Yoon This is my paper · ORCID
classification astro-ph.GAastro-ph.HEastro-ph.SRgr-qchep-th
keywords widebinariesMONDmodifiedgravityGaiaDR3hierarchicalsystemslowaccelerationqualitycontrolbiasgalacticdynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper re-examines the two main objections raised against earlier wide-binary evidence for modified gravity: that poor data quality—especially a cut on the uncertainty of the normalized velocity v-tilde—and unseen companion stars in hierarchical systems could fake a low-acceleration anomaly. The authors implement the most realistic triple-star model currently proposed and the full quality-control framework advocated by skeptical studies, then calibrate the hidden-companion fraction in the high-acceleration Newtonian regime before testing low accelerations. They find that neither objection removes the anomaly: the median v-tilde still rises with separation, and the deviation from the Newtonian prediction is positive at internal accelerations below about 10^-9 m/s^2 with combined significance greater than 5σ. The shape of the deviation matches recent realistic QUMOND two-body orbit solutions rather than Newtonian gravity, and studies reporting Newtonian consistency are traced to an uncalibrated triple fraction, a biased velocity-error cut, or too few low-acceleration binaries.

What carries the argument

The central object is the normalized sky-plane velocity v-tilde = v_p / v_c(r_p), the observed 2D relative velocity divided by the Newtonian circular speed at the projected separation; in Newtonian gravity its median should be nearly flat in separation, so a rising v-tilde profile is a gravity signal. Two tools carry the argument: the acceleration-plane test, which projects each binary's logarithmic Newtonian and empirical acceleration onto a diagonal coordinate and measures the orthogonal deviation from Newton, and a forward model of apparent binaries with hidden companion stars, encoded by an effective lower limit on the inner orbit semi-major axis that reproduces the proposed 'realistic'

What would settle it

Measure the hidden-companion fraction directly in the 3–30 kau separation range—for example, by searching each primary for a resolved or astrometric companion via high-resolution imaging and radial-velocity monitoring rather than inferring it statistically—and check whether the fraction equals the Newtonian-calibrated value. If the hidden-companion fraction rises steeply with projected separation, or if the astrometric quality cut admits more short-period inner binaries at large separations, the rising v-tilde profile could be partly spurious; if it stays flat, the anomaly is gravitational.

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Extended reading notes

Core claim

The central claim is that wide binary stars with projected separations larger than a few thousand astronomical units show a relative velocity that rises above the Newtonian prediction as the internal acceleration drops below roughly 10^-9 m/s^2, and that this rise survives the two main challenges raised against it. Implementing the most sophisticated triple-star model currently proposed, the authors calibrate the hidden-companion fraction using high-acceleration Newtonian binaries; with that calibration, the low-acceleration bins still show a positive deviation from Newton, with combined significance exceeding 5σ. Applying the full set of quality cuts advocated by skeptical studies—distance

Load-bearing premise

The fraction of apparent binaries hiding an unseen companion star, measured in the high-acceleration Newtonian regime, is assumed to stay constant as binaries move to larger separations; if it actually grows with separation, some of the rising velocity signal could be contamination rather than gravity.

Editorial extensions

If this is right

  • The low-acceleration anomaly is not an artifact of hidden triples: a nearly pure nearby subsample with a fitted triple fraction of about 0.03 still shows the velocity boost.
  • A quality cut based on the uncertainty of v-tilde is biased: it selectively removes lower-mass and higher-velocity systems at large separations, so future studies should use absolute velocity-error cuts or direct uncertainty propagation.
  • The hidden-companion fraction must be calibrated in the Newtonian regime free of chance alignments; using a value fitted to the low-acceleration region biases the test toward Newtonian gravity.
  • The observed velocity boost, corresponding to γ ≈ 1.3–1.6, agrees with realistic two-body QUMOND predictions under the Galactic external field, while approximate test-particle MOND models overpredict the effect in the transition regime.
  • Reports of no anomaly based on samples with fewer than about 100 MOND-regime binaries are statistically unable to distinguish Newton from a γ = 1.4 boost, so their null result is expected even if modified gravity is correct.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the constancy of the hidden-companion fraction across separations is confirmed, the v-tilde profile versus r_p/r_M could be used to map the MOND interpolation function in the external-field-dominated regime, where current constraints are weakest.
  • Targeted follow-up of wide binaries in the 3–30 kau range—high-resolution imaging and radial-velocity monitoring to find hidden companions directly rather than statistically—would settle whether the calibrated triple fraction truly holds at large separations.
  • The bias analysis suggests a practical prescription for the next generation of astrometric surveys: use absolute proper-motion velocity errors and direct uncertainty propagation, and verify Newtonian predictions in the high-acceleration regime before interpreting low-acceleration bins.
  • A direct 3D orbit analysis of the small d<150 pc sample with radial velocities could independently confirm the statistical result and potentially distinguish AQUAL from QUMOND in the transition regime.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reexamines the wide-binary gravity tests from Gaia DR3 that have yielded conflicting conclusions about a low-acceleration anomaly. It focuses on two challenges raised by null-result studies: data quality cuts (especially the Banik cut on the uncertainty of the normalized velocity) and the modeling of hierarchical systems with hidden companions. The authors implement the Pittordis et al. (2025) 'PSS' triple model via an effective algorithm (Eq. 18), calibrate the hidden-companion fraction f_trip in the Newtonian regime, and then run acceleration-plane, v-tilde-distribution, and median-v-tilde-profile tests on three samples (Chae 2023, Banik et al. 2024, PSS 2025). Their central claim is that the low-acceleration anomaly (δ_obs-newt > 0 at g_N ≲ 1e-9 m/s^2) survives all reasonable choices of data quality cuts and multiple-star modeling, with a combined significance >5σ, and that the observed trend agrees with the realistic QUMOND orbit solutions of Pflamm-Altenburg (2025). They further argue that the Banik cut introduces an r_p-dependent bias, that Cookson et al. (2026) had too few MOND-regime binaries (N=61) to discriminate models, and that the PSS preference for Newton is traceable to an overestimated f_trip and an inaccurate MOND transition-regime model.

Significance. If the main claim holds, the paper is a significant contribution to the wide-binary gravity debate: it addresses the two most prominent criticisms (data quality and hidden companions) with a unified modeling framework and shows that a MOND-type anomaly remains. Its strengths include the calibration of f_trip in the Newtonian regime rather than fitting the low-acceleration signal, the use of external numerical QUMOND solutions rather than a model tuned to the data, and the explicit power calculation in Figure 39 showing that Cookson et al.'s sample is too small to distinguish Newton from boosted gravity. The Pflamm-Altenburg comparison is a genuinely new element that goes beyond earlier approximate MOND treatments. The main caveat, discussed below, is that the r_p-independence of f_trip is asserted rather than directly tested; this is the weakest link in an otherwise well-constructed analysis.

major comments (3)
  1. [§5.2, Eq. (18), Figs. 25, 29, 53] The central assumption that f_trip is independent of the outer projected separation is asserted at the end of §5.2.2, but it is not tested. f_trip is calibrated in one Newtonian bin (x0 ≈ -8.0) and then held fixed across all bins. However, the sample-defining cuts (ruwe<1.2, ipd_frac_multi_peak=0, CMD cut, distance limit) are applied to member stars, and the probability of passing those cuts could correlate with distance and stellar mass distributions that vary with r_p. Figure 9 demonstrates that a different contaminant fraction, f_flyby, changes strongly with r_p, so an r_p-dependent f_trip is not implausible. A per-bin increase of f_trip from ~0.1 to ~0.4 could in principle produce the observed rise in median v-tilde without modified gravity. Figure 53 excludes a single global f_trip=0.41 because it destroys the Newtonian-regime agreement, but it does not exclude a per-bin f_trip(r_p)
  2. [§7 (summary bullets; Figs. 25, 29, 43)] The headline 'combined statistical significance of >5σ' is not defined. Multiple bins, three different tests, and several overlapping samples are used, so the effective number of independent trials is unclear. As written, the >5σ claim is not falsifiable because the reader cannot tell which comparisons are being combined and how. Please specify the exact combination rule — for example, a single pre-specified bin/test, a meta-analysis with a stated correlation model, or a false-discovery-rate control — and provide the resulting p-value. This is particularly important because the paper itself reports different significances in different tests (e.g., 2.3σ in one configuration of Figure 36, 4.6σ in Figure 31, etc.).
  3. [§3, Fig. 13 and §5.4] The paper states that I. Banik et al. (2024) used an erroneous Newtonian benchmark, with their ⟨v⟩=0.64 for α=1 being 0.55 and their 'Newtonian' consequently boosted by ≈1.37 in the effective gravitational constant. This is a serious claim about a published null result and is used in §5.4 to explain why Banik et al. preferred Newton. It is not needed for the internally calibrated measurement of the anomaly, but it is central to the paper's dismissal of one of the main contrary studies. Please provide a step-by-step reproduction of the relevant calculation, or a numerical table with the same inputs, so that the 0.55 value and the boost factor can be independently checked. If this is simply taken from previous papers, the derivation should be restated here.
minor comments (4)
  1. [Title and §5.1] There are typographical issues: 'T ests' in the typeset title and 'f pb' in §5.1 where 'η_phot' is introduced. Please proofread the final PDF version.
  2. [Fig. 13] The figure mixes theoretical prediction bands, sample-specific colored bands, and individual points with several curves. Please separate the Newtonian benchmark comparison into a dedicated panel or expand the legend, as the current figure is difficult to read.
  3. [§5.1 and abstract] The acronyms 'PSS' and 'CMD' are used without expansion at first appearance. The Gaia parameter 'ipd_frac_multi_peak' is typeset inconsistently; define it once and use a uniform notation.
  4. [§7] The paper honestly states that the distinction between realistic and approximate MOND solutions is 'not conclusive from the present studies.' This caveat should also appear in the abstract, where the agreement with Pflamm-Altenburg (2025) is currently presented more strongly than the body supports.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the MOND-regime signal is not fitted but is measured relative to a Newtonian benchmark calibrated in the Newtonian regime, and MOND comparisons use external numerical solutions.

full rationale

The paper's central claim—that the low-acceleration anomaly survives proper data-quality control and multiple-star modeling—is not circular. The hidden-companion fraction f_trip is calibrated in the Newtonian regime (e.g., 'we calibrate f_trip using the high-acceleration bin (≳10^−8.3 m s^−2)' and Figure 25's 'f_trip is determined by matching data with the Newtonian prediction in the rightmost bin'); it is then held fixed when evaluating the MOND-regime residual δ_obs−newt. Thus the MOND-regime excess is an observed residual, not a fitted parameter. The MOND comparison uses independent external numerical solutions (J. Pflamm-Altenburg 2025), not a model tuned to the present data. The paper also applies the triple model of Pittordis et al. (2025) and the quality framework of Cookson et al. (2026), both external benchmarks. Self-citations are numerous—especially to Chae's own acceleration-plane methodology and mass-luminosity relation—but the load-bearing ingredients (samples, eccentricities, external MOND orbit solutions, and the PSS triple model) are independent or re-derived here. The f_trip constancy assumption is a stated modeling assumption, not a definitional identity, and the paper explicitly tests robustness by showing that a single large f_trip cannot simultaneously fit both the Newtonian and MOND regimes (Figure 53). No step reduces by construction to its own inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The analysis is ultimately a calibrated measurement: f_trip is fitted in the Newtonian regime and the anomaly is read off at low acceleration. No new physical entities are introduced. The result depends on the validity of the triple model and the constancy of f_trip across separation, both of which are domain assumptions rather than proven facts.

free parameters (3)
  • f_trip (fraction of triples) = 0.10±0.03 (Chae sample, ruwe<1.2); 0.12±0.03 / 0.07±0.03 (PSS sample); 0.03±0.03 (d<150 pc)
    Calibrated by matching data to the Newtonian prediction in the high-acceleration bin (x0 ≈ -8.0) of the acceleration-plane test. This parameter sets the baseline for the Newtonian prediction at all accelerations; the anomaly is read off afterward.
  • a_inn,min coefficients in Equation (18) = 11.7 − 5.5 log10(r_p/kau)
    Adjusted to reproduce the Pittordis et al. triple-model v-tilde distributions for ruwe<1.2 samples. It is fitted to a simulation, not to the gravity data, but it is still a free parameter of the contamination model.
  • f_flyby (chance-alignment fraction) options = no flyby / PSS-like (remove v-tilde > 5.5) / max flyby (R>0.1 or no R)
    Bracket choices for removing chance-alignment pairs. These are modeling assumptions rather than a single fitted value, and the final significance varies somewhat across the options.
assumptions (5)
  • standard math Random orbital phase and isotropic orientation for wide binary orbits.
    Used in Monte Carlo deprojection (Section 2) to convert 2D projected velocities to 3D acceleration estimates; standard assumption in this field.
  • domain assumption Newtonian gravity is valid at g_N > 10^-8.3 m/s^2, and MOND effects are negligible there.
    Needed to calibrate f_trip from the high-acceleration bin. If the anomaly extended into that regime, the calibration would absorb MOND into the triple fraction.
  • domain assumption The Pittordis et al. triple model, with the effective implementation of Equation (18), fully captures hierarchical-system contamination in ruwe<1.2 samples.
    The whole analysis assumes the triple model correctly describes how hidden companions boost v-tilde; an inaccurate model would bias the inferred f_trip and the Newtonian baseline.
  • domain assumption The external-field-effect QUMOND solution by Pflamm-Altenburg (2025) is the correct MOND benchmark for wide binaries.
    Used to compare the observed anomaly to MOND. The paper explicitly favors this solution over earlier approximate ones; if this solution is wrong, the quantitative match to MOND would change.
  • domain assumption The El-Badry et al. (2021) R parameter reliably separates gravitationally-bound pairs from chance alignments.
    Used in the 'max flyby' option and to define the R<0.1 subsamples. If the R parameter misclassifies real binaries, the flyby corrections would be biased.

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Cite this review

Pith. "Pith review of Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-type Gravitational Anomaly at Low Acceleration." pith.science (2026). https://pith.science/paper/UVICTTZV

@misc{pith2026260714450,
  author       = {Pith},
  title        = {Pith review of: Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-type Gravitational Anomaly at Low Acceleration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UVICTTZV}},
  note         = {Machine review of arXiv:2607.14450}
}
abstract

Wide binary stars provide natural laboratories for directly probing gravity in the low-acceleration regime, as dark matter inferred from any viable gravity has negligible effects on their internal dynamics. Various recent studies including Bayesian 3D analyses have shown that wide binaries with separations greater than several thousand astronomical units experience MOND-type gravity with a boost factor of $\gamma\approx 1.3-1.6$. However, results claiming preference for, or no deviation from, standard gravity have also been published during the same period, particularly highlighting the roles of data quality control and realistic modeling of multiple-star (i.e., triple and higher-order) systems that host hidden companion stars. Here we carefully reexamine the issues of data quality control and modeling multiple-star systems in statistical gravity tests based on sky-projected 2D velocities of wide binary stars. Through extensive tests including the acceleration-plane test, the $\tilde v$-distribution test, and the median-$\tilde v$-profile test (where $\tilde v$ is the sky-plane 2D relative velocity normalized by the Newtonian circular velocity between the two stars), we show that proper data quality control or reasonable variation in multiple-star modeling cannot remove the low-acceleration gravitational anomaly but confirms the MOND-type gravitational anomaly, particularly consistent with recent realistic MOND solutions of wide binary orbits. We find that studies claiming no evidence for the low-acceleration gravitational anomaly are consequences of bypassed calibration of the fraction of multiple-star systems using the Newtonian-regime data, bias-introduction in data quality control that is not taken into account in gravity tests, or insufficient statistics in the low-acceleration regime.

Figures

Figures reproduced from arXiv: 2607.14450 by the authors.

Figure 1
Figure 1. This figure illustrates the statistical properties of mock wide binaries generated assuming Newtonian gravity. For clarity, all wide binaries have the same eccentricity e = 0.75 and similar total masses with Mtot = 1.4 × (1.000 ± 0.068)M⊙. Random scatters of σvp = 35 ± 3 m s−1 are added to Newton-predicted sky-projected velocities vp as described in the text. The top left panel shows the predicted values of vp as a … view at source ↗
Figure 2
Figure 2. Same as [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Same as [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (48 more)
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: This figure shows error properties in three samples from the literature (I. Banik et al. 2024; K.-H. Chae 2023; C. Pittordis et al. 2025). Errors of vp and ˜v as well as their relative errors (i.e., the inverse of their S/N) are shown. The three samples have similar er…
Figure 6
Figure 6. Figure 6: Distributions of the ratio of two estimates of the vp error are shown for the three samples used in this work [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Distributions of vp and ˜v with respect to rp in three samples (introduced in [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: For the samples shown in [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: For the samples by I. Banik et al. (2024) and C. Pittordis et al. (2025) (PSS) shown in [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Scaling of the median of ˜v with respect to rp/rM in the three samples shown in [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: This figure shows the statistical properties of eccentricities for the three samples of wide binaries with R < 0.1 shown in [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 12
Figure 12. Figure 12 [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: This upper panel shows how median ˜v varies with the exponent α of the power-law eccentricity distribu￾tion (Equation (14)) in Newtonian gravity. The black solid and dashed curves represent respectively the results with and without measurement errors as illustrated in…
Figure 14
Figure 14. Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]
Figure 15
Figure 15. Figure 15: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]
Figure 16
Figure 16. Figure 16: The black(blue) curve represents the scaling of the median relative error of ˜v(vp) with respect to rp/rM. The horizontal dashed line represents one half of the relative uncertainty of Mtot used for the Banik cut (see the text). σMtot /Mtot = 0.068. This is the reason…
Figure 17
Figure 17. Figure 17: This figure exhibits the effect of the Banik cut on the scaling of ˜v with respect to rp/rM. In each panel, the displayed curves are based on the medians in the 7 bins of log10(rp/rM) indicated by the vertical gray dotted lines. Black solid curve is for the entire sam…
Figure 18
Figure 18. Figure 18: The upper panel shows the scaling of Mtot (total mass of the binary) for the I. Banik et al. (2024) sample using the same bins of log10(rp/rM) defined in [PITH_FULL_IMAGE:figures/full_fig_p016_18.png]
Figure 19
Figure 19. Figure 19: This figure shows the effect of the cut σvp < 50 m s−1 on the scaling of ˜v using the same bins of log10(rp/rM) defined in [PITH_FULL_IMAGE:figures/full_fig_p017_19.png]
Figure 21
Figure 21. Figure 21: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_21.png]
Figure 22
Figure 22. Figure 22: Various numerical predictions of AQUAL and QUMOND on wide binary kinematics are shown. The nu￾merical results by K.-H. Chae & M. Milgrom (2022) and A. H. Zonoozi et al. (2021) are based on the assumption that two-body dynamics in MOND gravity can be treated as test– p…
Figure 23
Figure 23. Figure 23: This figure investigates how the ˜v distribution in a sample depends on the limit on Gaia’s ruwe parameter using wide binaries from K.-H. Chae (2023). The left and right columns show distributions in two specific ranges of rp. The top row shows all wide binaries that …
Figure 24
Figure 24. Figure 24: Distributions of ˜v from the C. Pittordis et al. (2025) triple modeling in some bins of rp. Red dotted curves are the same as those (‘Post-cuts’ option) shown in [PITH_FULL_IMAGE:figures/full_fig_p022_24.png]
Figure 25
Figure 25. Figure 25: Acceleration-plane test results for the K.-H. Chae (2023) sample with ruwe < 1.2 and PM relative error < 0.005 based on the PSS triple model shown in [PITH_FULL_IMAGE:figures/full_fig_p023_25.png]
Figure 26
Figure 26. Figure 26: The left column is the same as the left column of [PITH_FULL_IMAGE:figures/full_fig_p024_26.png]
Figure 27
Figure 27. Figure 27: Same as the left column of [PITH_FULL_IMAGE:figures/full_fig_p025_27.png]
Figure 28
Figure 28. Figure 28: Each column is similar to the right column (with the perspective effect) of [PITH_FULL_IMAGE:figures/full_fig_p026_28.png]
Figure 29
Figure 29. Figure 29: Same as [PITH_FULL_IMAGE:figures/full_fig_p027_29.png]
Figure 30
Figure 30. Figure 30: The observed distribution of ˜v is compared with the predictions of Newtonian gravity and a boosted gravity model to represent MOND gravity in the MOND (low-acceleration) regime. The left column is for binaries with rp < 0.08rM, most of which must be in the Newtonian …
Figure 31
Figure 31. Figure 31: This figure shows ˜v distributions for the PSS sample in a similar format as [PITH_FULL_IMAGE:figures/full_fig_p029_31.png]
Figure 32
Figure 32. Figure 32: This figure shows ˜v distributions for the I. Banik et al. (2024) sample with the limit ruwe < 1.2. The two panels are in the same format as those in the right column of [PITH_FULL_IMAGE:figures/full_fig_p030_32.png]
Figure 33
Figure 33. Figure 33: For wide binaries in the three ranges of rp considered in Section 5.4, the distributions of rp/rM and gN = GNMtot/r2 are shown. For binaries in the range rp < 0.7 kau, we exclude systems whose angular separation is less than 2 arcseconds (3.7%) to ensure highest possi…
Figure 34
Figure 34. Figure 34: This figure compares Newtonian predictions of the ˜v distribution for pure binaries by this work with those by C. Pittordis et al. (2025). Because observational scatters are added to the theoretical predictions, ˜v > 1.4 occur for wide binaries in the range 10 < rp < …
Figure 35
Figure 35. Figure 35: This figure is similar to [PITH_FULL_IMAGE:figures/full_fig_p033_35.png]
Figure 36
Figure 36. Figure 36: same as [PITH_FULL_IMAGE:figures/full_fig_p034_36.png]
Figure 37
Figure 37. Figure 37: The median of ˜v increases with rp, even for subsamples with ˜v < 1.5, 2, 2.5, and 5. However, as we saw in [PITH_FULL_IMAGE:figures/full_fig_p035_37.png]
Figure 38
Figure 38. Figure 38: This figure shows results of the ˜v-distribution test with the limit ˜v < 1.5 for the PSS sample. Two ranges of rp used in [PITH_FULL_IMAGE:figures/full_fig_p036_38.png]
Figure 40
Figure 40. Figure 40: The profile of median ˜v from [PITH_FULL_IMAGE:figures/full_fig_p037_40.png]
Figure 39
Figure 39. Figure 39: Each histogram represents the distribution of median ˜v in 2×106 random observations of Nbinary mock wide binaries obeying pseudo-Newtonian gravity with a gravity boost factor of γ = 1.4 (so, a velocity boost of √ 1.4). Mock wide binaries are produced using actual wid…
Figure 41
Figure 41. Figure 41: Various mass estimates of stars are compared for a subsample taken from the PSS sample (C. Pittordis et al. 2025). For 36% of the stars, Gaia DR3 FLAME masses are available; they are represented by red dots. The rest (64%) are represented by orange dots that follow th…
Figure 42
Figure 42. Figure 42: This figure shows a color-magnitude diagram for stars using the Gaia DR3 color BP−RP and absolute mag￾nitude MG. The stars with d < 150 pc from the PSS sample follow a narrow diagonal band. Stars with BP − RP > 1.0 are mostly under the arbitrary cut line suggested by …
Figure 43
Figure 43. Figure 43: Profile of median ˜v in the sample satisfying ˜v < 1.5 and d < 150 pc is shown and compared with theoretical predictions of Newton and MOND models. The Newtonian prediction is calculated for all wide binaries in the sample based on individual eccentricities from H.-C.…
Figure 44
Figure 44. Figure 44: Similar to [PITH_FULL_IMAGE:figures/full_fig_p041_44.png]
Figure 45
Figure 45. Figure 45: Same as the upper left panel of [PITH_FULL_IMAGE:figures/full_fig_p041_45.png]
Figure 46
Figure 46. Figure 46: Similar to [PITH_FULL_IMAGE:figures/full_fig_p042_46.png]
Figure 49
Figure 49. Figure 49 [PITH_FULL_IMAGE:figures/full_fig_p043_49.png]
Figure 47
Figure 47. Figure 47: Similar to the right column of [PITH_FULL_IMAGE:figures/full_fig_p043_47.png]
Figure 48
Figure 48. Figure 48: Each panel shows the profile of median ˜v for a subsample belonging to a quadrant in the R.A. space of the sample shown in the upper right panel of [PITH_FULL_IMAGE:figures/full_fig_p043_48.png]
Figure 51
Figure 51. Figure 51: This figure shows the normalized histogram (or, probability distribution) of ˜v in three regimes of the PSS sample with d < 150 pc. The upper limit of ˜v = 1.5 used in this section is indicated by the vertical dashed line, and the fraction outside the limit is indicat…
Figure 52
Figure 52. Figure 52: Similar to [PITH_FULL_IMAGE:figures/full_fig_p045_52.png]
Figure 53
Figure 53. Figure 53: Similar to [PITH_FULL_IMAGE:figures/full_fig_p046_53.png]

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