The Binary Fraction of Milky Way Field Stars in DESI: Dependence on Chemical Abundance

The binary fraction of Milky Way field stars in DESI depends primarily on chemical abundance, specifically [Fe/H], with secondary influences from [Mg/Fe] and Galactic position <ref:2610.111025, fb is found to primarily increase with lower [Fe/H].

How it works

The study adopts a statistical method based on multi-epoch line-of-sight velocity variations to constrain the binary fraction of field main-sequence turn-off stars in the Milky Way using data from the second data release of the DESI Milky Way Survey <ref:2610.111023, fb is found to primarily increase with lower [Fe/H]. The apparent variations of fb with angular momentum and Galactic height are largely explained by their underlying [Fe/H] distributions, while the remaining variations broadly follow differences in [Mg/Fe] <ref:2610.111023, the variation in fb is dominated by chemical abundance.

Data and Sample Selection

The analysis utilizes multi-epoch stellar spectra collected during the first three years of DESI MWS observations, focusing on main-sequence turn-off (MSTO) stars selected from the main-bright program <ref:2610.111024, to robustly constrain the binary fraction in the Galactic field. The selection criteria involve imposing a distance cut of 2.75 < d < 6.92 kpc and restricting chemical abundance measurements to [Fe/H] < −0.2 and 0.1 < [Mg/Fe] < 0.7, ensuring that the stellar density in the chemical abundance plane is sufficient for robust constraints, with resulting bins containing at least 400 stars in Section 4 <ref:2610.111023, we exclude stars with [Fe/H] < −2.0 where the inferred [Mg/Fe] values are less robust and restrict the sample to [Fe/H] < −0.2 and 0.1 < [Mg/Fe] < 0.7 to ensure reliable abundance measurements, with resulting bins containing at least 400 stars in Section 4 <ref:2610.11102#pg4>.

Inference Methodology

The binary fraction is constrained using the variability of multi-epoch LOSVs by constructing forward models of both binary and nonbinary populations through Monte Carlo simulations <ref:2610.111023, we construct forward models of both binary and nonbinary populations through Monte Carlo simulations, in which binary orbital parameters are drawn from empirically motivated distributions. The inference is performed by comparing the observed variability distribution with those predicted by models with different assumed binary fractions using a likelihood-based framework combined with Markov Chain Monte Carlo sampling <ref:2610.111023, the inferred binary fraction and its uncertainty are derived from the resulting posterior distribution.

Key Findings on Chemical Abundance Dependence

The principal results show that The binary fraction exhibits a strong dependence on [Fe/H] across the two-dimensional [Fe/H]–[Mg/Fe] abundance plane, with fb increasing systematically toward lower [Fe/H] <ref:2610.111023, this relation remains evident after controlling for [Mg/Fe] and is therefore the dominant trend detected in our sample. At fixed [Fe/H], the dependence on [Mg/Fe] is substantially weaker, with a modest increase for relatively metal-rich populations with [Fe/H] ≳ −1.2 <ref:2610.111023, this trend remains broadly consistent across multiple abundance bins despite the uncertainties reflected in the posterior distributions.

Dependence on Galactic Position and Environment

No clear monotonic dependence of the binary fraction is found with the Galactocentric radius <ref:2610.111023, no clear monotonic dependence of the binary fraction is found with either z or Lz, after controlling for the underlying [Fe/H] distribution to be the same <ref:2610.11102#pg4>. However, some weak residual variations still remain after controlling for [Fe/H], including a tentative dip around Lz ∼ 0 and a modest decrease with increasing z in some [Fe/H] bins <ref:2610.11102#pg4>. The analysis of Galactic components shows that chemical abundance is the dominant factor driving the variation in binary fractions among different Galactic components <ref:2610.11102#pg4>.

Conclusion

The results indicate that [Fe/H] is the primary observable associated with the binary fraction in the DESI MSTO sample <ref:2610.111023, this dependence may have broader implications for stellar populations formed in the early Universe where metal-poor star-forming environments could have produced different binary populations. The weaker positive dependence on [Mg/Fe] is less straightforward and may reflect differences in the birth conditions of high- and low-[Mg/Fe] populations rather than a direct effect of magnesium on binary formation <ref:2610.11102#pg4>. Taken together, our results indicate that [Fe/H] is the primary observable associated with the binary fraction in the DESI MSTO sample <ref:2610.11102#pg4>. The dependence on [Mg/Fe] is secondary and varies with [Fe/H], while Galactic position and environment contribute little additional predictive power once chemical abundance is controlled for <ref:2610.11102#pg4>.

The inverse relation between binary fraction and [Fe/H] found in this work is consistent with results from several independent methods and surveys <ref:2610.111023, Multiepoch radial-velocity studies based on LAMOST and APOGEE have reported higher binary fractions among metal-poor solar-type stars, while analyses combining multiple spectroscopic and eclipsing-binary samples have established a strong anticorrelation between closebinary fraction and metallicity <ref:2610.11102#pg4>. The consistency among these studies suggests that metallicity is an important factor influencing the binary population, particularly for the close-binary systems probed by spectroscopic surveys, although differences in the absolute binary fractions are expected because the surveys probe different ranges of orbital parameters <ref:2610.11102#pg4>. The physical interpretation of the metallicity dependence is not unique because metallicity affects cooling through competing processes. On the other hand, however, radiation-hydrodynamical simulations by M. R. Bate (2019) instead show that metal-poor gas can cool more efficiently at high densities due to less dust, which promotes fragmentation on small spatial scales, producing a larger close-binary fraction among low-mass stars, with semi-major axis, a. The origin of a positive relation with [Mg/Fe] is less straightforward and may reflect differences in the formation histories or other correlated birth-environment properties of the stellar populations rather than a direct effect of magnesium on binary formation <ref:2610.11102#pg4>.

The results presented in this paper can be accessed at DOI: 10.5281/zenodo.22742898.

ACKNOWLEDGMENTS

This work is supported by NSFC (grant Nos. 12573022, 12595312, 1605600, B20019), the National Key R&D Program of China (No. B20019), and the Office of Science and Technology, Shanghai Municipal Government (grant Nos. 24DX1400100, ZJ23-ZD-001) <ref:2610.111023, This work is supported by NSFC (grant Nos. 12573022, 12595312, 1605600, B20019), the National Key R&D Program of China (No. B20019), and the Office of Science and Technology, Shanghai Municipal Government (grant Nos. 24DX1400100, ZJ23-ZD-001). The computations of this work are carried on the National Energy Research Scientific Computing Center (NERSC) and the Gravity supercomputer at the Department of Astronomy, Shanghai Jiao Tong University <ref:2610.111023, The computations of this work are carried on the National Energy Research Scientific Computing Center (NERSC) and the Gravity supercomputer at the Department of Astronomy, Shanghai Jiao Tong University.

1. textbf Weighting of Chemical Abundance in Binary Fraction Inference (Section 4.1): Improve AI systems to prioritize [Fe/H] over [Mg/Fe] when inferring binary fraction, as A clear dependence of the binary fraction on [Fe/H] is observed and the primary variation of the binary fraction therefore appears to be associated with [Fe/H].

2. textbf Robustness against Selection Effects (Section 2.2): Enhance AI systems to incorporate a more nuanced understanding of selection biases, specifically by recognizing that different observational techniques are sensitive to different regions of binary parameter space, which is crucial for correctly interpreting results from the DESI MSTO sample.

3. textbf Systematic Error Floor Modeling (Section 3.3): Implement an AI module capable of dynamically determining the systematic error floor based on stellar color, as the paper notes that for bluer stars, the LOSV information is dominated by the B and R arms and bluer stars exhibit a systematically higher error floor than redder stars.

4. textbf Multi-Component Discrimination (Section 4.4): Develop an AI classification system capable of robustly separating Galactic components using combined chemical and kinematic information, as the analysis shows that chemical abundance is the dominant factor driving the variation in binary fractions among different Galactic components when restricted to overlapping regions of chemical-abundance space.

5. textbf Model Parameter Sensitivity (Section 6): Program AI systems to explicitly account for dependencies on assumed orbital-parameter distributions, noting that The inferred binary fractions remain dependent on the adopted orbital-period, mass-ratio, and eccentricity distribution model, which could affect recovered trends if these distributions vary with chemical abundance.

Binary populations encode information about the physical conditions of star formation and the subsequent evolution of stellar populations. Adopting a statistical method based on multi-epoch line-of-sight velocity variations, we constrain the binary fraction, f b, of field main-sequence turn-off stars in the Milky Way using data from the second data release of the DESI Milky Way Survey. f b is found to primarily increase with lower [Fe/H]. At [Fe/H] -1.3, f b shows a modest increase with increasing [Mg/Fe], whereas no clear trend is detected at lower [Fe/H]. The apparent variations of f b with angular momentum and Galactic height are largely explained by their underlying [Fe/H] distributions, while the remaining variations broadly follow differences in [Mg/Fe]. Within overlapping regions of the [Fe/H]--[Mg/Fe] plane, the thin disk, thick disk, stellar halo and GSE populations exhibit no significant differences in their binary fractions. Thus, our measurements indicate that the variation in f b is dominated by chemical abundance, which could be explained by the metallicity-dependent gas cooling efficiency and fragmentation. The weaker [Mg/Fe] dependence at fixed [Fe/H] might be associated with the formation conditions of stars, with higher [Mg/Fe] stars generally forming earlier under a more gas-rich and turbulent environment.