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Close binary systems are the progenitors to both Type Ia supernovae and the compact object mergers that can be detected via gravitational waves. To achieve a binary with a small radial separation, it is believed that the system likely undergoes common envelope (CE) evolution. Despite its importance, CE evolution may be one of the largest uncertainties in binary evolution due to a combination of computational challenges and a lack of observed benchmarks where both the post-CE and pre-CE conditions are known. Identifying post-CE systems in star clusters can partially circumvent this second issue by providing an independent age constraint on the system. For the first time, we conduct a systematic search for white dwarf and main-sequence binary systems in 299 Milky Way open star clusters. Coupling Gaia DR3 photometry and kinematics with multiband photometry from Pan-STARRS1 and the Two Micron All Sky Survey, we apply a machine learning-based approach and find 52 high-probability candidates in 38 open clusters. For a subset of our systems, we present follow-up spectroscopy from the Gemini and Lick Observatories and archival light curves from the Transiting Exoplanet Survey Satellite, Kepler/K2, and the Zwicky Transient Facility. Examples of M dwarfs with hot companions are spectroscopically observed, along with regular system variability. While the kinematics of our candidates are consistent with their host clusters, some systems have spatial positions offset relative to their hosts, potentially indicative of natal kicks. Ultimately, this catalog is a first step to obtaining a set of observational benchmarks to better link post-CE systems to their pre-CE progenitors.

Blue horizontal branch stars (BHBs), excellent distant tracers for probing the Milky Way’s halo density profile, are distinguished in the ${\left(g-r\right)}_{0}$ versus ( i − z ) _0 color space from another class of stars, blue straggler stars. We develop a Bayesian mixture model to classify BHBs using high-precision photometry data from the Dark Energy Survey Data Release 2 (DES DR2). We select ∼2100 highly probable BHBs based on their griz photometry and the associated uncertainties, and we use these stars to map the stellar halo over the Galactocentric radial range 20 kpc ≲ R ≲ 70 kpc. After excluding known stellar overdensities, we find that the number density n _⋆ of BHBs can be represented by a power-law density profile n _⋆ ∝ R ^− ^α with an index of $\alpha ={4.34}_{-0.12}^{+0.13}\pm 0.52$ , consistent with existing literature values. In addition, we examine the impact of systematic errors and the spatial inhomogeneity on the fitted density profile. Our work demonstrates the effectiveness of high-precision griz photometry in selecting BHBs. The upcoming photometric survey from the Rubin Observatory, expected to reach depths 2–3 mag greater than DES during its 10 yr mission, will enable us to investigate the density profile of the Milky Way’s halo out to the virial radius, unraveling the complex processes of formation and evolution in our Galaxy.

Asteroseismic time series data have imprints of stellar oscillation modes, whose detection and characterization through time series analysis allows us to probe stellar interior physics. Such analyses usually occur in the Fourier domain by computing the Lomb–Scargle (LS) periodogram, an estimator of the power spectrum underlying unevenly sampled time series data. However, the LS periodogram suffers from the statistical problems of (1) inconsistency (or noise) and (2) bias due to high spectral leakage. Here, we develop a multitaper power spectrum estimator using the nonuniform fast Fourier transform ( mtNUFFT ) to tackle the inconsistency and bias problems of the LS periodogram. Using a simulated light curve, we show that the mtNUFFT power spectrum estimate of solar-like oscillations has lower variance and bias than the LS estimate. We also apply our method to the Kepler-91 red giant, and combine it with PBjam peakbagging to obtain mode parameters and a derived age estimate of 3.97 ± 0.52 Gyr. PBjam allows the improvement of age precision relative to the 4.27 ± 0.75 Gyr APOKASC-2 (uncorrected) estimate, whereas partnering mtNUFFT with PBjam speeds up peakbagging thrice as much as LS. This increase in efficiency has promising implications for Galactic archaeology, in addition to stellar structure and evolution studies. Our new method generally applies to time-domain astronomy and is implemented in the public Python package tapify , available at https://github.com/aaryapatil/tapify .

The scaling relation between the size of a galaxy’s globular cluster (GC) population ( N _GC ) and the galaxy’s stellar mass ( M _* ) is usually described with a continuous, linear model, but in reality it is a count relationship that should be modeled as such. For massive galaxies, a negative binomial (NB) model has been shown to describe the data well, but it is unclear how the scaling relation behaves at low galaxy masses where a substantial portion of galaxies have N _GC = 0. In this work, we test the utility of Poisson and NB models for describing the low-mass end of the N _GC − M _* scaling relation. We introduce the use of zero-inflated versions of these models, which allow for larger zero populations (e.g., galaxies without GCs) than would otherwise be predicted. We evaluate our models with a variety of predictive model comparison methods, including predictive intervals, the leave-one-out cross-validation criterion, and posterior predictive comparisons. We find that the NB model is consistent with our data, but the naive Poisson is not. Moreover, we find that zero inflation of the models is not necessary to describe the population of low-mass galaxies that lack GCs, suggesting that a single formation and evolutionary process acts over all galaxy masses. Under the NB model, there does not appear to be anything unique about the lack of GCs in many low-mass galaxies; they are simply the low-mass extension of the larger N _GC − M _* scaling relation.

We present Augustus , a catalog of distance, extinction, and stellar parameter estimates for 170 million stars from 14 mag < r < 20 mag and with ∣ b ∣ > 10° drawing on a combination of optical to near-infrared photometry from Pan-STARRS, 2MASS, UKIDSS, and unWISE along with parallax measurements from Gaia DR2 and 3D dust extinction maps. After applying quality cuts, we find 125 million objects have “high-quality” posteriors with statistical distance uncertainties of ≲10% for objects with well-constrained stellar types. This is a substantial improvement over the distance estimates derived from Gaia parallaxes alone and in line with the recent results from Anders et al. We find the fits are able to reproduce the dereddened Gaia color–magnitude diagram accurately, which serves as a useful consistency check of our results. We show that we are able to detect large, kinematically coherent substructures in our data clearly relative to the input priors, including the Monoceros Ring and the Sagittarius Stream, attesting to the quality of the catalog. Our results are publicly available at doi:10.7910/DVN/WYMSXV. An accompanying interactive visualization can be found at http://allsky.s3-website.us-east-2.amazonaws.com .

In almost any study involving optical/near-infrared photometry, understanding the completeness of detection and recovery is an essential part of the work. The recovery fraction is, in general, a function of several variables including magnitude, color, background sky noise, and crowding. We explore how completeness can be modeled, with the use of artificial-star tests, in a way that includes all of these parameters simultaneously within a neural network (NN) framework. The method is able to manage common issues including asymmetric completeness functions and the bilinear dependence of the detection limit on color index. We test the method with two sample Hubble Space Telescope data sets: the first involves photometry of the star cluster population around the giant Perseus galaxy NGC 1275, and the second involves the halo-star population in the nearby elliptical galaxy NGC 3377. The NN-based method achieves a classification accuracy of > 94% and produces results entirely consistent with more traditional techniques for determining completeness. Additional advantages of the method are that none of the issues arising from the binning of the data are present and that a recovery probability can be assigned to every individual star in real photometry. Our data, models, and code (called COINTOSS) can be found online on Zenodo at the following link: https://doi.org/10.5281/zenodo.8306488 .

The physical processes responsible for shaping how galaxies form and quench over time leave imprints on both the spatial (galaxy morphology) and temporal (star formation history; SFH) tracers that we use to study galaxies. While the morphology–SFR connection is well studied, the correlation with past star formation activity is not as well understood. To quantify this, we present Katachi (形), an interpretable convolutional neural network framework that learns the connection between the factors regulating star formation in galaxies on different spatial and temporal scales. Katachi is trained on 9904 galaxies at 0.02 < z < 0.1 in the SDSS-IV MaNGA DR17 sample to predict stellar mass ( M _* ; root mean square error (RSME) 0.22 dex), current star formation rate (SFR; RMSE 0.31 dex), and half-mass time ( t _50 ; RMSE 0.23 dex). This information allows us to reconstruct nonparametric SFHs for each galaxy from gri imaging alone. To quantify the morphological features informing the SFH predictions, we use SHAP (SHapley Additive exPlanations). We recover the expected trends of M _* governed by the growth of galaxy bulges, as well as those of SFR correlating with spiral arms and other star-forming regions. We also find that the SHAP maps of D4000 are more complex than those of M _* and SFR, and that morphology is correlated with t _50 even at fixed mass and SFR. Katachi serves as a scalable public framework to predict galaxy properties from large imaging surveys including Rubin, Roman, and Euclid, with large data sets of high signal-to-noise ratio imaging across limited photometric bands.

Galaxy formation and evolution involve a variety of effectively stochastic processes that operate over different timescales. The extended regulator model provides an analytic framework for the resulting variability (or “burstiness”) in galaxy-wide star formation due to these processes. It does this by relating the variability in Fourier space to the effective timescales of stochastic gas inflow, equilibrium, and dynamical processes influencing giant molecular clouds' creation and destruction using the power spectral density (PSD) formalism. We use the connection between the PSD and autocovariance function for general stochastic processes to reformulate this model as an autocovariance function, which we use to model variability in galaxy star formation histories (SFHs) using physically motivated Gaussian processes in log star formation rate (SFR) space. Using stellar population synthesis models, we then explore how changes in model stochasticity can affect spectral signatures across galaxy populations with properties similar to the Milky Way and present-day dwarfs, as well as at higher redshifts. We find that, even at fixed scatter, perturbations to the stochasticity model (changing timescales vs. overall variability) leave unique spectral signatures across both idealized and more realistic galaxy populations. Distributions of spectral features including H α and UV-based SFR indicators, H δ and Ca H and K absorption-line strengths, D _n (4000), and broadband colors provide testable predictions for galaxy populations from present and upcoming surveys with the Hubble Space Telescope, James Webb Space Telescope, and Nancy Grace Roman Space Telescope. The Gaussian process SFH framework provides a fast, flexible implementation of physical covariance models for the next generation of spectral energy distribution modeling tools. Code to reproduce our results can be found at https://github.com/kartheikiyer/GP-SFH .

Flagship near-future surveys targeting 10 ^8 –10 ^9 galaxies across cosmic time will soon reveal the processes of galaxy assembly in unprecedented resolution. This creates an immediate computational challenge on effective analyses of the full data set. With simulation-based inference (SBI), it is possible to attain complex posterior distributions with the accuracy of traditional methods but with a >10 ^4 increase in speed. However, it comes with a major limitation. Standard SBI requires the simulated data to have characteristics identical to those of the observed data, which is often violated in astronomical surveys due to inhomogeneous coverage and/or fluctuating sky and telescope conditions. In this work, we present a complete SBI-based methodology, SBI ^++ , for treating out-of-distribution measurement errors and missing data. We show that out-of-distribution errors can be approximated by using standard SBI evaluations and that missing data can be marginalized over using SBI evaluations over nearby data realizations in the training set. In addition to the validation set, we apply SBI ^++ to galaxies identified in extragalactic images acquired by the James Webb Space Telescope, and show that SBI ^++ can infer photometric redshifts at least as accurately as traditional sampling methods—and crucially, better than the original SBI algorithm using training data with a wide range of observational errors. SBI ^++ retains the fast inference speed of ∼1 s for objects in the observational training set distribution, and additionally permits parameter inference outside of the trained noise and data at ∼1 minute per object. This expanded regime has broad implications for future applications to astronomical surveys. (Code and a Jupyter tutorial are made publicly available at https://github.com/wangbingjie/sbi_pp .)

With just a month of data, JWST is already transforming our view of the universe, revealing and resolving starlight in unprecedented populations of galaxies. Although “HST-dark” galaxies have previously been detected at long wavelengths, these observations generally suffer from a lack of spatial resolution, which limits our ability to characterize their sizes and morphologies. Here we report on a first view of starlight from a subset of the HST-dark population that is bright with JWST/NIRCam (4.4 μ m < 24.5 mag) and very faint or even invisible with HST (

Stellar ages are key for determining the formation history of the Milky Way, but are difficult to measure precisely. Furthermore, methods that use chemical abundances to infer ages may entangle the intrinsic evolution of stars with the chemodynamical evolution of the Galaxy. In this paper, we present a framework for making probabilistic predictions of stellar ages, and then quantify the contribution of both stellar evolution and Galactic chemical evolution to those predictions using SHapley Additive exPlanations. We apply this interpretable prediction framework to both a simulated Milky Way sample containing stars in a variety of evolutionary stages and an APOGEE-mocked sample of red clump stars. We find that in the former case, stellar evolution is the dominant driver for age estimates, while in the latter case, the more restricted evolutionary information causes the model to proxy ages through the chemical evolution model. We show that as a result of the use of nonintrinsic Galactic chemical information, trends estimated with the predicted ages, such as the age–metallicity relation, can deviate from the truth.

Galaxy stellar mass is known to be monotonically related to the size of the galaxy’s globular cluster (GC) population for Milky Way sized and larger galaxies. However, the relation becomes ambiguous for dwarf galaxies, where there is some evidence for a downturn in GC population size at low galaxy masses. Smaller dwarfs are increasingly likely to have no GCs, and these zeros cannot be easily incorporated into linear models. We introduce the Hierarchical Errors-in-variables ERrors-in-variables BAyesian Lognormal hurdle (HERBAL) model to represent the relationship between dwarf galaxies and their GC populations, and apply it to the sample of Local Group galaxies, where the luminosity range coverage is maximal. This bimodal model accurately represents the two populations of dwarf galaxies: those that have GCs and those that do not. Our model thoroughly accounts for all uncertainties, including measurement uncertainty, uncertainty in luminosity to stellar mass conversions, and intrinsic scatter. The hierarchical nature of our Bayesian model also allows us to estimate galaxy masses and individual mass-to-light ratios from luminosity data within the model. We find that 50% of galaxies are expected to host GC populations at a stellar mass of ${\mathrm{log}}_{10}({M}_{* })=6.996$ , and that the expected mass of GC populations remains linear down to the smallest galaxies. Our hierarchical model recovers an accurate estimate of the Milky Way stellar mass. Under our assumed error model, we find a nonzero intrinsic scatter of ${0.59}_{-0.21}^{+0.3}$ (95% credible interval) that should be accounted for in future models.

Artificial neural network emulators have been demonstrated to be a very computationally efficient method to rapidly generate galaxy spectral energy distributions, for parameter inference or otherwise. Using a highly flexible and fast mathematical structure, they can learn the nontrivial relationship between input galaxy parameters and output observables. However, they do so imperfectly, and small errors in flux prediction can yield large differences in recovered parameters. In this work, we investigate the relationship between an emulator’s execution time, uncertainties, correlated errors, and ability to recover accurate posteriors. We show that emulators can recover consistent results to traditional fits, with a precision of 25%–40% in posterior medians for stellar mass, stellar metallicity, star formation rate, and stellar age. We find that emulation uncertainties scale with an emulator’s width N as ∝ N ^−1 , while execution time scales as ∝ N ^2 , resulting in an inherent tradeoff between execution time and emulation uncertainties. We also find that emulators with uncertainties smaller than observational uncertainties are able to recover accurate posteriors for most parameters without a significant increase in catastrophic outliers. Furthermore, we demonstrate that small architectures can produce flux residuals that have significant correlations, which can create dangerous systematic errors in colors. Finally, we show that the distributions chosen for generating training sets can have a large effect on an emulator’s ability to accurately fit rare objects. Selecting the optimal architecture and training set for an emulator will minimize the computational requirements for fitting near-future large-scale galaxy surveys. We release our emulators on GitHub ( http://github.com/elijahmathews/MathewsEtAl2023 ).

In previous work, we identified a population of 38 cool and luminous variable stars in the Magellanic Clouds and examined 11 in detail in order to classify them as either Thorne–Żytkow objects (TŻOs; red supergiants with a neutron star cores) or super-asymptotic giant branch (sAGB) stars (the most massive stars that will not undergo core collapse). This population includes HV 2112, a peculiar star previously considered in other works to be either a TŻO or high-mass asymptotic giant branch (AGB) star. Here we continue this investigation, using the kinematic and radio environments and local star formation history of these stars to place constraints on the age of the progenitor systems and the presence of past supernovae. These stars are not associated with regions of recent star formation, and we find no evidence of past supernovae at their locations. Finally, we also assess the presence of heavy elements and lithium in their spectra compared to red supergiants. We find strong absorption in Li and s-process elements compared to RSGs in most of the sample, consistent with sAGB nucleosynthesis, while HV 2112 shows additional strong lines associated with TŻO nucleosynthesis. Coupled with our previous mass estimates, the results are consistent with the stars being massive (∼4–6.5 M _⊙ ) or sAGB (∼6.5–12 M _⊙ ) stars in the thermally pulsing phase, providing crucial observations of the transition between low- and high-mass stellar populations. HV 2112 is more ambiguous; it could either be a maximally massive sAGB star, or a TŻO if the minimum mass for stability extends down to ≲13 M _⊙ .

Deep optical and near-infrared imaging of the entire Galactic plane is essential for understanding our Galaxy’s stars, gas, and dust. The second data release of the Dark Energy Camera (DECam) Plane Survey extends the five-band optical and near-infrared survey of the southern Galactic plane to cover 6.5% of the sky, ∣ b ∣ ≤ 10°, and 6° > ℓ > −124°, complementary to coverage by Pan-STARRS1. Typical single-exposure effective depths, including crowding effects and other complications, are 23.5, 22.6, 22.1, 21.6, and 20.8 mag in g , r , i , z , and Y bands, respectively, with around 1″ seeing. The survey comprises 3.32 billion objects built from 34 billion detections in 21,400 exposures, totaling 260 hr open shutter time on the DECam at Cerro Tololo. The data reduction pipeline features several improvements, including the addition of synthetic source injection tests to validate photometric solutions across the entire survey footprint. A convenient functional form for the detection bias in the faint limit was derived and leveraged to characterize the photometric pipeline performance. A new postprocessing technique was applied to every detection to debias and improve uncertainty estimates of the flux in the presence of structured backgrounds, specifically targeting nebulosity. The images and source catalogs are publicly available at http://decaps.skymaps.info/ .

The amount of power contained in the variations in galaxy star-formation histories (SFHs) across a range of time-scales encodes key information about the physical processes which modulate star formation. Modelling the SFHs of galaxies as stochastic processes allows the relative importance of different time-scales to be quantified via the power spectral density (PSD). In this paper, we build upon the PSD framework and develop a physically motivated, 'stochastic' prior for non-parametric SFHs in the spectral energy distribution (SED)-modelling code prospector. We test this prior in two different regimes: (1) massive, |$z = 0.7$| galaxies with both photometry and spectra, analogous to those observed with the LEGA-C survey, and (2) |$z = 8$| galaxies with photometry only, analogous to those observed with NIRCam on JWST. We find that it is able to recover key galaxy parameters (e.g. stellar mass, stellar metallicity) to the same level of fidelity as the commonly used continuity prior. Furthermore, the realistic variability information incorporated by the stochastic SFH model allows it to fit the SFHs of galaxies more accurately and precisely than traditional non-parametric models. In fact, the stochastic prior is |$\gtrsim 2\times$| more accurate than the continuity prior in measuring the recent star-formation rates (log SFR |$_{100}$| and log SFR |$_{10}$|⁠) of both the |$z = 0.7$| and |$z = 8$| mock systems. While the PSD parameters of individual galaxies are difficult to constrain, the stochastic prior implementation presented in this work allows for the development of hierarchical models in the future, i.e. simultaneous SED-modelling of an ensemble of galaxies to measure their underlying PSD. [ABSTRACT FROM AUTHOR]

We present the first detailed chemical-abundance analysis of stars from the dwarf-galaxy stellar stream Wukong/LMS-1 covering a wide metallicity range (⁠|$-3.5 \lt \rm [Fe/H] \lesssim -1.3$|⁠). We find abundance patterns that are effectively indistinguishable from the bulk of Indus and Jhelum, a pair of smaller stellar streams proposed to be dynamically associated with Wukong/LMS-1. We confirmed a carbon-enhanced metal-poor star (⁠|$\rm [C/Fe] \gt +0.7$| and |$\rm [Fe/H] \sim -2.9$|⁠) in Wukong/LMS-1 with strong enhancements in Sr, Y, and Zr, which is peculiar given its solar-level [Ba/Fe]. Wukong/LMS-1 stars have high abundances of α elements up to |$\rm [Fe/H] \gtrsim -2$|⁠ , which is expected for relatively massive dwarfs. Towards the high-metallicity end, Wukong/LMS-1 becomes α-poor, revealing that it probably experienced fairly standard chemical evolution. We identified a pair of N- and Na-rich stars in Wukong/LMS-1, reminiscent of multiple stellar populations in globular clusters. This indicates that this dwarf galaxy contained at least one globular cluster that was completely disrupted in addition to two intact ones previously known to be associated with Wukong/LMS-1, which is possibly connected to similar evidence found in Indus. From these ≥3 globular clusters, we estimate the total mass of Wukong/LMS-1 to be |${\approx }10^{10} \, \mathrm{M}_\odot$|⁠ , representing ∼1 per cent of the present-day Milky Way. Finally, the [Eu/Mg] ratio in Wukong/LMS-1 continuously increases with metallicity, making this the first example of a dwarf galaxy where the production of r -process elements is clearly dominated by delayed sources, presumably neutron-star mergers. [ABSTRACT FROM AUTHOR]

We infer the dynamical masses of stars across the Hertzsprung–Russell (H–R) diagram using wide binaries from the Gaia survey. Gaia 's high-precision astrometry measures the wide binaries' orbital motion, which contains the mass information. Using wide binaries as the training sample, we measure the mass of stars across the 2D H–R diagram using the combination of statistical inference and neural networks. Our results provide the dynamical mass measurements for main-sequence stars from 0.1 to 2 M⊙, unresolved binaries, and unresolved triples on the main sequence, and the mean masses of giants and white dwarfs. Two regions in the H–R diagram show interesting behaviours in mass, where one of them is pre-main-sequence stars, and the other one may be related to close compact object companions like M dwarf-white dwarf binaries. These mass measurements depend solely on Newtonian dynamics with minimal assumptions on eccentricities, providing independent constraints on stellar evolutionary models, and the occurrence rate of compact objects. [ABSTRACT FROM AUTHOR]

This work presents the Globular cluster Extra-tidal Mock Star (GEMS) catalogue of extra-tidal stars and binaries created via three-body dynamical encounters in globular cluster cores. Using the particle-spray code Corespray , we sample |$N=50\, 000$| extra-tidal stars and escaped recoil binaries for 159 Galactic globular clusters. Sky positions, kinematics, stellar properties, and escape information are provided for all simulated stars. Stellar orbits are integrated in seven different static and time-varying Milky Way gravitational potential models where the structure of the disc, perturbations from the Large Magellanic Cloud and the mass and sphericity of the Milky Way's dark matter halo are all investigated. We find that the action coordinates of the mock extra-tidal stars are largely Galactic model independent, where minor offsets and broadening of the distributions between models are likely due to interactions with substructure. Importantly, we also report the first evidence for stellar stream contamination by globular cluster core stars and binaries for clusters with pericentre radii larger than five kiloparsecs. Finally, we provide a quantitative tool that uses action coordinates to match field stars to host clusters with probabilities. Ultimately, combining data from the GEMS catalogue with information of observed stars will allow for association of extra-tidal field stars with any Galactic globular cluster; a requisite tool for understanding population-level dynamics and evolution of clusters in the Milky Way. [ABSTRACT FROM AUTHOR]

We model the stellar abundances and ages of two disrupted dwarf galaxies in the Milky Way stellar halo: Gaia -Sausage Enceladus (GSE) and Wukong/LMS-1. Using a statistically robust likelihood function, we fit one-zone models of galactic chemical evolution with exponential infall histories to both systems, deriving e-folding time-scales of τin = 1.01 ± 0.13 Gyr for GSE and |$\tau _\text{in} = 3.08^{+3.19}_{-1.16}$| Gyr for Wukong/LMS-1. GSE formed stars for |$\tau _\text{tot} = 5.40^{+0.32}_{-0.31}$| Gyr, sustaining star formation for ∼1.5–2 Gyr after its first infall into the Milky Way ∼10 Gyr ago. Our fit suggests that star formation lasted for |$\tau _\text{tot} = 3.36^{+0.55}_{-0.47}$| Gyr in Wukong/LMS-1, though our sample does not contain any age measurements. The differences in evolutionary parameters between the two are qualitatively consistent with trends with stellar mass M ⋆ predicted by simulations and semi-analytic models of galaxy formation. Our inferred values of the outflow mass-loading factor reasonably match |$\eta \propto M_\star ^{-1/3}$| as predicted by galactic wind models. Our fitting method is based only on Poisson sampling from an evolutionary track and requires no binning of the data. We demonstrate its accuracy by testing against mock data, showing that it accurately recovers the input model across a broad range of sample sizes (20 ≤ N ≤ 2000) and measurement uncertainties (0.01 ≤ σ[α/Fe], σ[Fe/H] ≤ 0.5; |$0.02 \le \sigma _{\log _{10}(\text{age})} \le 1$|⁠). Due to the generic nature of our derivation, this likelihood function should be applicable to one-zone models of any parametrization and easily extensible to other astrophysical models which predict tracks in some observed space. [ABSTRACT FROM AUTHOR]

Due to the different environments in the Milky Way's disc and halo, comparing wide binaries in the disc and halo is key to understanding wide binary formation and evolution. By using Gaia Early Data Release 3, we search for resolved wide binary companions in the H3 survey, a spectroscopic survey that has compiled ∼150 000 spectra for thick-disc and halo stars to date. We identify 800 high-confidence (a contamination rate of 4 per cent) wide binaries and two resolved triples, with binary separations mostly between 103 and 105 au and a lowest [Fe/H] of −2.7. Based on their Galactic kinematics, 33 of them are halo wide binaries, and most of those are associated with the accreted Gaia -Sausage-Enceladus galaxy. The wide binary fraction in the thick disc decreases toward the low metallicity end, consistent with the previous findings for the thin disc. Our key finding is that the halo wide binary fraction is consistent with the thick-disc stars at a fixed [Fe/H]. There is no significant dependence of the wide binary fraction on the α-captured abundance. Therefore, the wide binary fraction is mainly determined by the iron abundance, not their disc or halo origin nor the α-captured abundance. Our results suggest that the formation environments play a major role for the wide binary fraction, instead of other processes like radial migration that only apply to disc stars. [ABSTRACT FROM AUTHOR]