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Distributions of wide binary stars in theory and in Gaia data: III. Orbital momenta, masses, and manifestations of MOND

Valeri V. Makarov

TL;DR

This study introduces the projected orbital momentum $\nu$ as a per-pair observable for 103,169 Gaia DR3 wide binaries to probe mass distributions and test gravity in the weak-acceleration regime. Through Monte Carlo population synthesis informed by empirical distributions of eccentricity and semimajor axis, the authors infer a subsolar total-mass distribution with a median near $0.85\,M_{\odot}$ and show the observed $\nu$–$s$ and $\nu$–$a$ relations align with Newtonian dynamics. A dedicated MOND test predicts sizeable deviations at large separations, but the data show no excess momentum, arguing against MOND in this regime. The results imply a dynamical-age effect linking mass to orbit size and demonstrate that wide Gaia binaries are a powerful, data-driven probe of gravity theories beyond the Solar System.

Abstract

Using the censored catalog of 103,169 resolved Gaia DR3 binary stars with accurate astrometric data for each component, a new observable, object-specific parameter is computed for each pair: the projected orbital momentum. This parameter is the product of four functions of physical characteristics: total mass, semimajor axis, eccentricity, and inclination angle. Using the previously estimated marginal probability densities of eccentricity and semimajor axis, and assuming an isotropic orientation of binary systems, the sample distribution of mass was adjusted using a concordance metric of the observed and synthetic distributions of orbital momenta and an ad hoc functional model. The best-fitting mass density model is found to faithfully reproduce the observed dependence of orbital momenta on apparent separation, although the absolute luminosity distributions indicate a tendency of the widest systems to more frequently include solar-type primaries. The anticipated manifestation of MOND is computed in the investigated parameter space \{separation, momentum\}. This effect is absent in the given data. The median total mass of the widest Gaia binaries is found to be somewhat higher than that of the tighter pairs, which is interpreted as a dynamical age effect.

Distributions of wide binary stars in theory and in Gaia data: III. Orbital momenta, masses, and manifestations of MOND

TL;DR

This study introduces the projected orbital momentum as a per-pair observable for 103,169 Gaia DR3 wide binaries to probe mass distributions and test gravity in the weak-acceleration regime. Through Monte Carlo population synthesis informed by empirical distributions of eccentricity and semimajor axis, the authors infer a subsolar total-mass distribution with a median near and show the observed – and – relations align with Newtonian dynamics. A dedicated MOND test predicts sizeable deviations at large separations, but the data show no excess momentum, arguing against MOND in this regime. The results imply a dynamical-age effect linking mass to orbit size and demonstrate that wide Gaia binaries are a powerful, data-driven probe of gravity theories beyond the Solar System.

Abstract

Using the censored catalog of 103,169 resolved Gaia DR3 binary stars with accurate astrometric data for each component, a new observable, object-specific parameter is computed for each pair: the projected orbital momentum. This parameter is the product of four functions of physical characteristics: total mass, semimajor axis, eccentricity, and inclination angle. Using the previously estimated marginal probability densities of eccentricity and semimajor axis, and assuming an isotropic orientation of binary systems, the sample distribution of mass was adjusted using a concordance metric of the observed and synthetic distributions of orbital momenta and an ad hoc functional model. The best-fitting mass density model is found to faithfully reproduce the observed dependence of orbital momenta on apparent separation, although the absolute luminosity distributions indicate a tendency of the widest systems to more frequently include solar-type primaries. The anticipated manifestation of MOND is computed in the investigated parameter space \{separation, momentum\}. This effect is absent in the given data. The median total mass of the widest Gaia binaries is found to be somewhat higher than that of the tighter pairs, which is interpreted as a dynamical age effect.
Paper Structure (10 sections, 14 equations, 8 figures)

This paper contains 10 sections, 14 equations, 8 figures.

Table of Contents

  1. Introduction
  2. The cleaned data sample
  3. Specific orbital momentum
  4. Median orbital momentum versus separation
  5. Implementation of MC simulations
  6. Total mass models
  7. Generation of random noise in orbital momenta
  8. Results
  9. A search for manifestations of MOND in the widest binaries
  10. Conclusions

Figures (8)

  • Figure 1: The histogram of projected specific orbital momenta of 103,169 binary systems.
  • Figure 2: Distribution concordance metric L1F of Monte Carlo random samples of orbital configurations with the empirical sample from Gaia GR3 data in the projected orbital momentum parameter $\nu$ versus the assumed shape $h$ of the total mass modeled with the Gamma distribution in Eq. \ref{['Gamma.eq']}. The small L1F value indicates the best match of the distributions.
  • Figure 3: HR diagrams of absolute $G$ magnitudes versus BP$-$RP colors for primary and secondary components of the investigated sample of resolved binaries in Gaia DR3.
  • Figure 4: The histograms of observed projected specific momenta (light gray) and simulated projected specific orbital momenta (cyan) of Gaia DR3 binary stars.
  • Figure 5: Binned median logarithm of orbital momentum $\nu$ (black dots) and the $\{0.16,0.84\}$ quantiles (red dots) versus the (left panel) the logarithm of observed projected separation $s$ in AU and (right panel) the logarithm of simulated physical semimajor axis $a$ in AU. The yellow and cyan thick lines are the fits presented in Eqs. \ref{['1fit.eq']} and \ref{['2fit.eq']}, respectively.
  • ...and 3 more figures