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# Chronologically dating the early assembly of the Milky Way

## Abstract

The standard cosmological model predicts that galaxies are built through hierarchical assembly on cosmological timescales1,2. The Milky Way, like other disk galaxies, underwent violent mergers and accretion of small satellite galaxies in its early history. Owing to Gaia Data Release 23 and spectroscopic surveys4, the stellar remnants of such mergers have been identified5,6,7. The chronological dating of such events is crucial to uncover the formation and evolution of the Galaxy at high redshift, but it has so far been challenging due to difficulties in obtaining precise ages for these oldest stars. Here we combine asteroseismology—the study of stellar oscillations—with kinematics and chemical abundances to estimate precise stellar ages (~11%) for a sample of stars observed by the Kepler space mission8. Crucially, this sample includes not only some of the oldest stars that were formed inside the Galaxy but also stars formed externally and subsequently accreted onto the Milky Way. Leveraging this resolution in age, we provide compelling evidence in favour of models in which the Galaxy had already formed a substantial population of its stars (which now reside mainly in its thick disk) before the infall of the satellite galaxy Gaia-Enceladus/Sausage5,6 around 10 billion years ago.

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## Data availability

All raw observational data are publicly available: Kepler light curves at https://archive.stsci.edu/kepler/publiclightcurves.html; Gaia DR2 at https://gea.esac.esa.int/archive and APOGEE DR14 may be accessed via https://www.sdss.org/dr14/. APOGEE DR14 raw data have been used in the top panels of Fig. 2. Processed data such as individual frequencies, orbital and stellar parameters are available in Supplementary Table 1 or on request. Evolutionary tracks are publicly available at https://doi.org/10.5281/zenodo.4032320 and theoretical stellar models and oscillation frequencies are available on request.

## Code availability

The asteroseismic modelling results were provided by the code AIMS, available at https://lesia.obspm.fr/perso/daniel-reese/spaceinn/aims/version1.3, and cross-checked using the code PARAM (http://stev.oapd.inaf.it/cgi-bin/param). The peak bagging was performed using the pipeline PBJam (https://github.com/grd349/PBjam) and the orbital parameter determination with galpy (https://www.galpy.org). The codes CLES and LOSC used for stellar evolution and adiabatic oscillation computations are not publicly available, but evolutionary tracks, structure models and oscillation files are available on reasonable request.

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## Acknowledgements

J.M., J.T.M., A.M., F.V. and E.W. acknowledge support from the ERC Consolidator Grant funding scheme (project ASTEROCHRONOMETRY, G.A. no. 772293). F.V. acknowledges the support of a Fellowship from the Center for Cosmology and AstroParticle Physics at The Ohio State University. M.V. is supported by FEDER - Fundo Europeu de Desenvolvimento Regional through COMPETE2020 - Programa Operacional Competitividade e Internacionalização by grants PTDC/FIS-AST/30389/2017 and POCI-01-0145-FEDER-030389. C.C. acknowledges partial support from DFG Grant CH1188/2-1 and from the ChETEC COST Action (CA16117), supported by COST (European Cooperation in Science and Technology). G.B. acknowledges fundings from the SNF AMBIZIONE grant no. 185805 (Seismic inversions and modelling of transport processes in stars) and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 833925, project STAREX). G.R.D. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (CartographY GA 804752). M.B.N. acknowledges support from the UK Space Agency. O.J.H. acknowledges the support of the UK Science and Technology Facilities Council (STFC). This article made use of AIMS, a software for fitting stellar pulsation data, developed in the context of the SPACEINN network, funded by the European Commission’s Seventh Framework Programme. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular, the institutions participating in the Gaia Multilateral Agreement. The computations described in this paper were performed using the University of Birmingham’s BlueBEAR HPC service, which provides a high-performance computing service to the university’s research community. See http://www.birmingham.ac.uk/bear for more details. We thank S. McGee for reading and commenting on the manuscript.

## Author information

Authors

### Contributions

J.M. led the project, with help from J.T.M., A.M., F.V., C.C. and W.J.C. G.R.D. designed the pipeline for the light-curve analysis. J.M., J.T.M., A.M., F.V., G.R.D., O.J.H., M.B.N., S.K. and W.E.v.R. worked on extracting mode parameters from the Kepler light curves. J.M., A.N. and R.S. performed the stellar modelling and theoretical oscillation frequency computations. J.M., G.B. and B.M.R. worked on the stellar parameter determination from individual frequencies using Bayesian inference code AIMS. A.M. estimated stellar parameters from global observational constraints using the code PARAM. B.M. and M.V. provided global seismic parameters. J.T.M. and F.V. performed the kinematics and chemical composition analysis from Gaia DR2 and APOGEE DR14 datasets. E.W. derived absolute stellar luminosity from Gaia DR2. J.W.F. provided radiative opacity data at low temperature for the alpha-enhanced chemical mixture used in the stellar evolution code. All authors have contributed to the interpretation of the data and the results, and discussion and giving comments on the paper.

### Corresponding author

Correspondence to Josefina Montalbán.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks David Soderblom and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Data samples.

a, Diagram [α/Fe] versus [Fe/H] for all the Kepler-APOGEE-DR14 sample (grey dots). Orange symbols are the targets in our sub-sample: red giant stars with [Fe/H] < − 0.5, and blue ones are the first ascending red giant branch targets selected for characterization in this paper. b, Teff versus $${\nu }_{\max }$$ diagram (equivalent to Kiel diagram) of our target sample (color-coded by metallicity), overlying the complete Kepler-APOGEE-DR14 one (grey empty and full symbols). The dashed lines corresponds to two [α/Fe]=0.2 evolutionary tracks: blue M=0.9 M, [Fe/H]=-1.0; orange, same mass but [Fe/H]=-0.5.

### Extended Data Fig. 2 Posterior probability distributions for KIC 4143467 stellar properties as inferred by AIMS.

a-f: age, mass, radius, mean density, luminosity and frequency at maximun power, respectively. The oscillation spectra of this target is shown in first panel of Fig. 1. The vertical dash-dotted lines indicate the value of the corresponding parameter in the best-fitting model from the MCMC sampling.

### Extended Data Fig. 3 Posterior probability distributions for KIC 12111110 stellar properties as inferred by AIMS.

a-f: age, mass, radius, mean density, luminosity and frequency at maximun power, respectively. The vertical dash-dotted lines indicate the value of the corresponding parameter in the best-fitting model from the MCMC sampling.

### Extended Data Fig. 4 Age distribution using PARAM for the APOGEE-Kepler sample with stellar radius limited to 14 R⊙.

a-b, [α/Fe] vs. [Fe/H] distribution of the sample coloured by age (a) and eccentricity (b). The symbol size scales with $${\nu }_{\max }$$. c, Age distributions of accreted and in-situ stars, so classified from their [α/Fe] and eccentricity values; d, Kiel diagram of the sample coloured by metallicity. Notice that the ‘very old’ (yellow dots Teff > 5400 K) suggest that we have underestimated the mass loss for those stars.

### Extended Data Fig. 5 Age distribution using PARAM for the APOGEE-Kepler sample with stellar radius limited to 8 R⊙.

a-b, [α/Fe] vs. [Fe/H] distribution of the sample coloured by age (a) and eccentricity (b). The symbol size scales with $${\nu }_{\max }$$. c, Age distributions of accreted and in-situ stars, so classified from their [α/Fe] and eccentricity values; d, Kiel diagram of the sample coloured by metallicity. Notice that the ‘very old’ (yellow dots Teff > 5400 K) suggest that we have underestimated the mass loss for those stars.

### Extended Data Fig. 6 Age and eccentricity distributions for different selection criteria for in-situ and accreted populations.

Age against eccentricity (e) for the stars in the sample coloured by [Fe/H]}. Circles represent age values of the best fitting models, and horizontal lines their uncertainties ([16%-84%] C.I. from full posterior distributions). Uncertainties on e are smaller than the symbol size. The diamond represents ν Indi25 (not included in the distributions). The histogram above reflects the combined posterior distributions for the stars in each selection. a,c, division line [Mg/Fe] = -0.5 [Fe/H]-0.3 (ref. 14). b,d, division line [Mg/Fe] = -0.2 [Fe/H] (ref. 26). Top and bottom panels correspond to eccentricity threshold 0.7 and 0.6 respectively.

### Extended Data Fig. 7 Probabilistic graphical model of that used to fit the mean age and intrinsic age spread of the in- and ex-situ populations defined on the basis of element abundances and orbital parameters.

We assume the measured ages are drawn from an underlying true age θ distribution that is Gaussian with a mean μ with a standard deviation τ. We assume that the true age distribution is contaminated by stars whose mass is higher than expected (and therefore appear younger), likely due to some poorly understood process such as binary interactions. We model these contaminants as also being drawn from another normal distribution with a mean μc and spread τc which has a fractional contribution ε to the total age distribution (hence the main population contributes 1 − ε).

## Supplementary information

### Supplementary Information

Supplementary Table 1 with the stellar parameters for the final sample of 95 targets.

### Supplementary Data

Machine-readable version of Supplementary Table 1.

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Montalbán, J., Mackereth, J.T., Miglio, A. et al. Chronologically dating the early assembly of the Milky Way. Nat Astron 5, 640–647 (2021). https://doi.org/10.1038/s41550-021-01347-7

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