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Abstract

The formation of our Milky Manner can be split upward qualitatively into dissimilar phases that resulted in its structurally different stellar populations: the halo and the disk components^ane,2,iii. Revealing a quantitative overall picture of our Milky way'southward assembly requires a large sample of stars with very precise ages. Here we report an analysis of such a sample using subgiant stars. Nosotros discover that the stellar age–metallicity distribution p(τ, [Fe/H]) splits into two almost disjoint parts, separated at age τ≃ 8 Gyr. The younger part reflects a late phase of dynamically quiescent Galactic disk formation with manifest show for stellar radial orbit migration^4,five,6; the other part reflects the earlier phase, when the stellar halo^vii and the sometime α-process-enhanced (thick) deejay^8,9 formed. Our results indicate that the germination of the Galaxy's sometime (thick) disk started approximately xiii Gyr ago, simply 0.8 Gyr after the Large Bang, and 2 Gyr earlier than the concluding assembly of the inner Galactic halo. Almost of these stars formed around 11 Gyr ago, when the Gaia-Sausage-Enceladus satellite merged with our Galaxy^10,11. Over the next five–6 Gyr, the Galaxy experienced continuous element enrichment, ultimately by a cistron of 10, while the star-forming gas managed to stay well mixed.

Principal

To unravel the assembly history of our Milky way we need to learn how many stars were born when, from what material and on what orbits. This requires precise age determinations for a large sample of stars that extend to the oldest possible ages (effectually fourteen Gyr)^9,12. Subgiant stars, which are stars sustained past hydrogen beat out fusion, can be unique tracers for such purposes, as they exist in the brief stellar evolutionary phase that permits the well-nigh precise and direct historic period determination, because their luminosity is a direct measure of their age. Moreover, the chemical element compositions determined from the spectra of their photosphere surfaces accurately reflect their birth material composition billions of years ago. This makes subgiants the best applied tracers of Galactic archaeology, even compared to master-sequence turn-off stars, whose surface abundances may be contradistinct by atomic improvidence effects¹³. Withal, because of the brusque lifetime of their evolutionary phase, subgiant stars are relatively rare, and large surveys are essential to build a large sample of these objects with good spectra, which have not been available in the past.

With the recent data release (eDR3) of the Gaia mission^14,xv and the recent data release (DR7) of the LAMOST spectroscopic survey^sixteen,17, we identify a set of approximately 250,000 subgiant stars based on their position in the constructive temperatures (T _eff)–absolute magnitude (Grand _K) diagram (Fig. 1a). The ages (τ) of these subgiant stars are estimated by plumbing equipment to the Yonsei–Yale (YY) stellar isochrones¹⁸ with a Bayesian approach, which draws on the astrometric distances (parallaxes), apparent magnitudes (fluxes), spectroscopic chemical abundances ([Fe/H], [α/Fe] whereα refers to α elements Mg, Si, Ca, Ti), T _eff and M ₁₀₀₀. As summarized in Fig. 1b, the sample stars have a median relative age uncertainty of just vii.5% across the age range from 1.5 Gyr to the age of the Universe (13.viii Gyr; ref. ¹⁹). The lower historic period limit of our sample is inherent to our approach: younger and hence more luminous subgiants can exist confused with a different stellar evolutionary phase, the horizontal co-operative phase for far older stars, which would cause serious sample contamination. This sample constitutes a 100-fold leap in sample size for stars with comparably precise and consequent age estimates^20,21. In improver, it is a large sample that covers a large spatial volume across the Milky Way (Fig. 1c) and most of the pertinent range in age and in metallicity (ane.five Gyr <τ < xiii.8 Gyr, and −ii.5 < [Fe/H] < 0.4). The sample too has a straightforward spatial selection part that allows us to estimate the space density of the tracers. These ingredients enable an alternative view of the Milky way's assembly history, especially the early formation history.

**Fig. 1: The subgiant star sample with precise ages.**

Our Galaxy's stellar age–metallicity distribution

The photospheric metallicity of any subgiant star of age τ reflects the element composition of the gas from which information technology formed at the epoch τ Gyr ago. The overall distribution of these stellar metallicities at unlike epochs, p(τ, [Fe/H]), thus encodes the chemical enrichment history of our Galaxy milky way. Figure 2a presents this distribution for our data. It shows that the age–metallicity distribution exhibits a number of prominent and distinct sequences, including at least two age-separated sequences with [Fe/H] > −i, and a sequence of exclusively old stars at low metallicity, [Fe/H] < −1. The density of p(τ, [Fe/H]) may change with stellar orbit or Galactocentric radius, in the range our sample covers (vi–14 kpc; Fig. one). Yet, the 'morphology' of the distribution varies but slightly, enabling u.s.a. to focus on the radially averaged distribution p(τ, [Fe/H]) here.

**Fig. ii: Stellar age–metallicity relation revealed past our subgiant star sample.**

It turns out that the complexity of p(τ, [Fe/H]) (Fig. 2a) can exist unravelled by dividing the sample into two subsamples using stellar quantities that are neither τ nor [Fe/H]: the angular momentum J _ϕ (besides denoted as L _Z) and the 'α-enhancement', [α/Fe]. Extensive observations bespeak that the majority of stars in the Milky way formed from gradually enriched gas on loftier-angular momentum orbits, or the extended ('sparse') disk^iv,22, at high J _ϕ and low [α/Fe]. It is as well well established that the distribution of Galactic stars in the [α/Fe]–[Fe/H] plane is bimodal, with a loftier-α sequence reflecting rapid enrichment and a low-α sequence reflecting gradual enrichment, which indicates a natural way to separate whatsoever sample in the [α/Fe]–[Iron/H] plane^eight. This inspired our approach to split up our sample into two, separating the dominant sample portion of gradually enriched deejay stars with high angular momentum from the remainder. Specifically, nosotros used the cut

$$\{\begin{assortment}{c}\begin{array}{cc}{J}_{\varphi } > 1500\,{\rm{kpc}}.{\rm{km}}/{\rm{s}} & {\rm{and}}\stop{array}\\ \{\begin{array}{cc}[\blastoff /Fe] > 0.sixteen, & {\rm{if}}\,[{\rm{Fe}}/{\rm{H}}]\, > -0.5,\\ \,[\alpha /Atomic number 26] < -0.16[{\rm{Fe}}/{\rm{H}}]\,+0.08, & {\rm{if}}\,[{\rm{Iron}}/{\rm{H}}]\, > -0.5,\end{array}\end{array}$$

(one)

which is illustrated as a yellowish shaded area in Fig. 2b, c. The resulting subsamples in the τ–[Iron/H] plane are shown in Fig. 2d, e, where information technology is crucial to recall that the sample split involved neither of the quantities on the two axes, τ and [Atomic number 26/H]. As nosotros desire to focus showtime on the Milky Way's elemental enrichment history, rather than its star-formation history, we normalize the distribution p(τ, [Iron/H]) at each [Fe/H] to yield p(τ | [Atomic number 26/H]), the age distribution at a given [Fe/H].

Figure 2nd, e shows that this cutting in angular momentum and [α/Atomic number 26] separates the Milky way's enrichment history neatly into two distinct age regimes, with a rather sharp transition at τ≃ eight Gyr. Nosotros will therefore refer to these two portions, non conspicuously apparent in earlier data, every bit $p{(\tau |[{\rm{Fe}}/{\rm{H}}])}_{{\rm{belatedly}}}$ and $p{(\tau |[{\rm{Iron}}/{\rm{H}}])}_{{\rm{early}}}$. The distribution of $p{(\tau |[{\rm{Fe}}/{\rm{H}}])}_{{\rm{late}}}$ clearly exhibits a V-shape²³. This shape is presumably a outcome of the secular evolution of the dynamically quiescent disk; the metal-rich ([Fe/H]≳ −0.1) branch arises from stars that have migrated from the inner disk to near the Solar radius. The gradient of that co-operative in $p{(\tau |[{\rm{Atomic number 26}}/{\rm{H}}])}_{{\rm{late}}}$ so results from the (negative) radial metallicity gradient in the disk^one and the fact that the stars that take migrated more needed more than fourth dimension to practice so, and are hence older. Analogously, we presume the lower branch of $p{(\tau |[{\rm{Fe}}/{\rm{H}}])}_{{\rm{late}}}$ at [Fe/H]≲ −0.i to ascend from stars that were born further out and take migrated inwards⁶. A quantitative comparison with secular evolution models of the Galactic disk^4,22 is role of carve up ongoing work.

The older stars, reflected in $p{(\tau |[{\rm{Fe}}/{\rm{H}}])}_{{\rm{early}}}$, show two prominent sequences with distinct [Atomic number 26/H](τ) relations. The stars with −2.five < [Atomic number 26/H] < −1.0 reflect the well-established stellar halo population of our Milky way, whereas the more metallic-rich sequence ([Fe/H]≳ −1) reflects the Galaxy's inner, high-α (thick) disk²⁴; this designation as an sometime disk component is also justified by the stars' angular momentum, as nosotros will show below.

The morphology of the old disk sequence in $p{(\tau |[{\rm{Iron}}/{\rm{H}}])}_{{\rm{early}}}$ is the most striking feature in Fig. 2e; it reveals an uncommonly articulate, continuous and tight age–metallicity relation from [Iron/H]≲ −1 at 13 Gyr ago all the fashion to [Fe/H]≃ 0.5 at seven Gyr ago. A simple model for p(τ | [Fe/H]) of this sequence (Supplementary Data) finds an intrinsic age dispersion of less than 0.82 Gyr at a given [Iron/H] across this half-dozen Gyr interval (Extended Information Fig. 1). Given the sequence's slope, this implies that the [Iron/H] dispersion at a given age is smaller than 0.22 dex across the i.5 dex range in [Atomic number 26/H].

Both the halo and old disk sequences extend to [Fe/H]≃ −1. However, at that [Fe/H] value, the quondam deejay sequence is approximately 2 Gyr older than the halo sequence, leading to a Z-shaped structure in $p{(\tau |[{\rm{Fe}}/{\rm{H}}])}_{{\rm{early}}}$. This feature is a second attribute of the distribution that has non, to our knowledge, been seen before²¹.

Germination and enrichment of the Milky Manner's quondam disk

Tentative hints for some of these features in p(τ | [Atomic number 26/H]) have been seen in before work^24,25 (run into the discussion in the Supplementary Information) but these studies lacked the sample size or precision for definitive inferences virtually the Galactic formation history. Figure ii shows clearly that the erstwhile, high-α 'thick' disk of our Milky Way started to form approximately 13 Gyr agone, which is only 0.eight Gyr after the Big Bang¹⁹, and extended over 5–6 Gyr, and the interstellar stellar medium (ISM) forming the stars was continually enriched by more than 1 dex, from [Fe/H]≃ −ane to 0.5. The tightness of this [Fe/H]–age sequence implies that the ISM must have remained spatially mixed thoroughly during this unabridged period. Had in that location been any radial (or azimuthal) [Fe/H] variations (or gradients) in excess of 0.ii dex in the star-forming ISM at whatever time, this would accept increased the resulting [Fe/H]–historic period scatter beyond what is seen. Such gradients, along with orbital migration, are the main reason that the later Galactic disk shows a considerably higher [Fe/H] dispersion at a given age^4,26. The results also show that the formation of the Milky way's old, α-enhanced disk overlapped in time with the formation of the halo stars: the primeval deejay stars are 1–2 Gyr older than the major halo populations at [Fe/H]≃ −1 (encounter the Z-shaped structure).

In Fig. 3 nosotros examine the $p{(\tau |[{\rm{Fe}}/{\rm{H}}])}_{{\rm{early on}}}$ distribution more closely by separating stars with at least modest angular momentum, J _ϕ > 500 kpc km south^–ane, from those stars on nearly radial or even retrograde orbits, J _ϕ < 500 kpc km s^–one. This further sample differentiation past angular momentum leads once more to two almost disjoint p(τ | [Fe/H]) distributions. The first (Fig. 3, upper panel), with mostly [Fe/H] > −1, is dominated by the tight p(τ | [Atomic number 26/H]) sequence that we we take already attributed to the old disk. The 2d, predominately [Fe/H] < −1.2, reflects the halo.

Fig. iii: Probability of stellar distribution in the J _ϕ versus [Fe/H] plane, p(τ, [Fe/H]), for stars formed in the early phase.

Annotation that Fig. 3, lower panel shows a singled-out gear up of stars with J _ϕ < 500 kpc km s^–ane, for which the p(τ | [Fe/H]) locus indicates that they are the oldest and most metal-poor role of the old disk sequence (meet also Extended Information Fig. ii). These stars indicate that some of the oldest members of the one-time disk sequence were present during an early merger result, past which they were 'splashed' to depression-athwart-momentum orbits^27,28. This ancient merger event is presumably the merger with the Gaia-Enceladus satellite milky way¹¹ (also known as Gaia Sausage¹⁰; hereafter Gaia-Sausage-Enceladus), which has contributed most of the Galaxy'southward halo stars^7,29. The fact that the splashed erstwhile deejay stars with very footling angular momentum are exclusively seen at τ≳ 11 Gyr constitutes potent evidence that the major merger process between the one-time disk and the Gaia-Sausage-Enceladus satellite galaxy was largely completed 11 Gyr ago. This epoch is one Gyr before than previous estimates that were based on the lower age limit of the halo stars, x Gyr (refs. ^11,21,30).

Figure 3 shows the book-corrected 2-dimensional distribution p(τ, [Fe/H]) (come across the Supplementary Information for the correction of the book selection event), rather than the p(τ | [Fe/H]) of Fig. two. Effigy 3 reveals a remarkable feature, namely that the star-formation charge per unit of the old disk reached a prominent maximum at around xi.ii Gyr agone, plain merely when the merger with the Gaia-Sausage-Enceladus satellite milky way was completed, and then continuously declined with time. The most obvious interpretation of this coincidence is that the perturbation from the Gaia-Sausage-Enceladus satellite galaxy profoundly enhanced the star formation of the onetime disk. Annotation that this star-formation superlative among the quondam disk stars ~eleven Gyr ago is very consistent with earlier indications of such a elevation based on abundances only³¹.

To put our results into the bigger picture of galaxy formation and development, the multiple associates phases are seen to be universal among present-day star-forming galaxies. Using the IllustriesTNG simulation, Wang et al.³² showed that galaxy mergers and interactions have played a crucial role in inducing gas inflow, resulting in multiple star formation episodes, intermitted by quiescent phases. Observationally, the best testbed for this theoretical movie would be here at home within our Galaxy. Our study has demonstrated the power of such tests for galactic associates and enrichment history in the total cosmic timeline, from the very early on epoch (τ≃ 13 Gyr or redshift z > ten) to the electric current time.

Methods

Stellar labels from spectroscopy

Building this sample of subgiant stars with precise ages, abundances and orbits requires a number of steps. The first step is to derive stellar atmospheric parameters from the LAMOST DR7 spectra, which nosotros did using the data-driven Payne (DD-Payne) arroyo, verified in detail using analogous data from LAMOST DR5 (ref. ³³). This leads to a catalogue of constructive temperature T _eff, surface gravity log g, microturbulent velocity v _mic and elemental abundance for 16 elements (C, Due north, O, Na, Mg, Al, Si, Ca, Ti, Cr, Mn, Fe, Co, Ni, Cu, Ba) values for seven million stars. We as well derive an α-chemical element to iron abundance ratio [α/Fe], which volition serve in the age estimation to identify the right set of isochrones for each object. For a spectral betoken-to-dissonance ratio (South/N) higher than 50, the typical measurement uncertainties are virtually 30 M in T _eff and 0.05 dex in the abundances nosotros use here: [Iron/H] and [α/Fe] (ref. ³³).

Absolute magnitude and spectroscopic parallax

Determining authentic and precise absolute magnitudes is crucial for age determination of subgiant stars (Fig. 1a). The Gaia astrometry provides high-precision parallax for stars within approximately 2 kpc, whereas for more distant stars the Gaia parallaxes accept uncertainties in excess of 10%. For these afar stars, spectroscopic estimates of accented magnitude are needed to ensure precise historic period determination. Nosotros derive Chiliad _Yard, the absolute magnitude in the Two Micron All Sky Survey (2MASS) K band, from the LAMOST spectra, using a data-driven method based on neural network modelling (see Supplementary Information for details). Extended Data Figure 3 illustrates that for LAMOST spectra with loftier signal-to-noise ratio (South/N > lxxx), our spectroscopic Grand _K estimates are precise to amend than 0.1 mag at [Iron/H] = 0 (and 0.fifteen magazine at [Fe/H] = −1). Furthermore, a comparison between spectroscopic M _Chiliad and geometric One thousand _G from Gaia parallaxes provides an efficient way of identifying unresolved binaries^33,34 (Extended Data Fig. 3). For the subsequent modelling, nosotros combine these two approaches through a weighted mean algorithm

$${M}_{{\rm{K}}}=\frac{{{M}_{{\rm{K}}}}^{{\rm{geom}}}/{\sigma }_{{\rm{geom}}}^{ii}+{{M}_{{\rm{1000}}}}^{{\rm{spec}}}/{\sigma }_{{\rm{spec}}}^{2}}{{\sigma }_{{\rm{spec}}}^{-2}+{\sigma }_{{\rm{geom}}}^{-2}}.$$

Here Grand _Yard ^geom refers to the geometric G _M, i.eastward., M _K derived using Gaia parallax, M _K ^spec the spectroscopic M _K estimates, andσ the uncertainty in the Yard _M estimates. Nosotros are then in a position to select subgiant stars as lying between the 2 straight lines in the T _eff–M _K diagram. Every bit isochrones depend on [Fe/H], this is done separately for each [Fe/H] bin, with the adopted slopes and intercepts for the boundary lines presented in Extended Data Table 1. As an example, the boundaries for stars with solar metallicity are shown in the Fig. 1a. To ensure the boundaries vary smoothly with [Iron/H], we interpolate the slopes and intercepts listed in Extended Data Table ane to match the measured [Iron/H] for each star.

Cleaning sample cuts

To take a subgiant star sample with high purity, we have applied cleaning criteria to discard stars with poor data quality or stars that are possible contaminations of the subgiant sample.

We discard unresolved binaries that nosotros identify through differences in their spectro-photometric parallax and their geometric parallax from Gaia, by requiring

$$\frac{{\varpi }_{{\rm{spec}}-{\rm{photo}}}-{\varpi }_{{\rm{geom}}}}{\sqrt{{\sigma }_{{\rm{spec}}}^{ii}+{\sigma }_{{\rm{geom}}}^{2}}} > 2$$

(3)

Here ${\varpi }_{s{\rm{pec}}-{\rm{photo}}}$ is the spectro-photometric parallax deduced from the distance modulus using the spectroscopic M _Thou and 2MASS credible magnitudes³⁵.
We discard stars with spurious Gaia astrometry by requiring a Gaia re-normalized unit weight mistake (RUWE) larger than i.2 or an astrometric fidelity less than 0.8 (ref. ³⁶).
We discard stars that evidence significant flux variability according to the variation amplitude of the Gaia magnitudes between dissimilar epochs,

$${\varDelta }_{{\rm{G}}}=\frac{\sqrt{{\rm{PHOT}}\_{\rm{G}}\_{\rm{N}}\_{\rm{OBS}}}}{{\rm{PHOT}}\_{\rm{G}}\_{\rm{MEAN}}\_{\rm{FLUX}}\_{\rm{OVER}}\_{\rm{ERROR}}}$$

(4)

where PHOT_G_N_OBS is the number of epochs, and PHOT_G_MEAN_FLUX_OVER_ERROR is the mean flux over fault ratio for Gaia Yard-band photometry. We summate the ensemble median $(\overline{{\varDelta }_{{\rm{G}}}})$ and dispersion σ(Δ _G) of Δ _{One thousand} as a function of Thou-band magnitude and define whatever i star equally a variable if

$$\frac{{\varDelta }_{{\rm{1000}}}-\overline{{\varDelta }_{{\rm{G}}}}}{\sigma ({\varDelta }_{{\rm{1000}}})} > 3$$

(5)

Most of the variables eliminated by this criterion are found to be pre-main-sequence stars.
We discard stars that are less luminous than the subgiant branch of a 20 Gyr isochrone, which is the purlieus of our isochrone grid. Such stars are mainly contaminations of either pre-principal-sequence stars or main-sequence binary stars that survived elimination by the in a higher place criteria.
Nosotros discard all stars with K _Thou brighter than 0.five magazine to avoid contamination from He-burning horizontal branch stars. This comes at a price: we eliminate essentially all stars younger than about i.5 Gyr.
We require all stars in our sample to have LAMOST spectral S/Due north > 20 and to have good DD-Payne fits, by requiring 'qflag_χ ² = good'³³. We farther restrict our stars to have T _eff < 6,800 K, where DD-Payne abundances are most robust.

After these cleaning cuts, the remaining sample contains 247,104 stars (Fig. 1), all of which are presumed to exist subgiants.

Age estimates by isochrones

The ages of the subgiant sample stars are determined by matching the Gaia astrometric parallax ϖ, the LAMOST spectroscopic stellar parameters T _eff, M _K, [Iron/H] and [α/Atomic number 26], and the Gaia and 2MASS photometry in the Grand, BP, RP, J, H and K bands with the YY stellar isochrones^18,37 using a Bayesian approach (meet Supplementary Information for details). Note that in our Bayesian model we have chosen not to impose a prior that all stars should be younger than the current cognition of the age of the Universe from the catholic microwave background measurements of Planck (13.8 Gyr)¹⁹. This is for two main reasons. Get-go, the upper limit of the stellar historic period is an independent test of the age of the Universe, whereas imposing age priors on the inference from the cosmological model might induce bias into the results. 2nd, imposing an upper age limit may increase the complexity of the statistics.

To catechumen the Gaia parallax to absolute magnitudes, we as well demand to know the extinction. Therefore, we have determined the reddening and extinction for private stars using intrinsic colours empirically inferred from their stellar parameters (see Supplementary Information for details).

Nosotros have also tested the historic period estimation using other public isochrones, such as the MIST^38,39, and find that, in the example of the solar α-mixture, the age estimates based on YY and MIST show expert consistency except for the fact that the MST isochrones predict ages older by 0.5 Gyr (Extended Information Fig. 4). Notwithstanding, the α-element enhancement, which is not available in the current public MIST isochrones, has a large affect on the historic period interpretation, and ignoring the α-element enhancement volition lead to an overestimate of stellar age by upward to 2 Gyr for old stars (Extended Data Fig. 4). Ages from the YY isochrones seem to be reasonable as the ages of the oldest stars are comparable to the age of the Universe (Fig. ii).

Orbital actions

Using the radial velocity from the LAMOST information, proper motions from Gaia and a combination of spectro-photometric distance and geometric altitude (come across Supplementary Information for details), we compute the orbital actions (J _R, J _ϕ, J _Z) and the angles of our sample stars using galpy⁴⁰, assuming the MWPotential2014 potential model. We assume that the Sun is located at R _⊙ = 8.178 kpc (ref. ⁴¹) and Z _⊙ = x pc in a higher place the disk mid-aeroplane⁴². We assume the local standard of residue LSR = 220 km s^–ane, and the solar motility with respect to the LSR to be (U _⊙, V _⊙, W _⊙) = (−7.01 km southward^–1, 10.13 km s^–ane, iv.95 km due south^–1) (ref. ⁴³).

Accounting for selection effects

To verify that our findings are not caused by artefacts due to selection furnishings, we prefer two approaches to accost this issue. First, we employ our target selection to the Gaia mock catalogue of Rybizki et al.⁴⁴ and investigate the age–[Fe/H] relation (Extended Data Fig. 5). 2d, we straight right for the volume selection function of our sample to account for the fact that, for a given line of sight, older subgiant stars probe to a smaller distance than the younger stars as the one-time are fainter. The age distribution of the thick disk stars after applying the choice function correction is illustrated in Fig. 3. Eventually, we concluded that the pick function has a negligible impact on our conclusions (see Supplementary Data for more than details).

In addition, we have compared the stellar historic period–[Fe/H] relation from our sample with literature results for both stars²⁵ and globular clusters^45,46,47 that take robust age estimates (Extended Data Fig. 6). The comparisons are qualitatively consequent, albeit the literature samples are too small to describe a articulate moving picture of the assembly and enrichment history of our Galaxy (see Supplementary Data for a detailed discussion).

Data availability

The Gaia eDR3 data is public available at https://www.cosmos.esa.int/spider web/gaia/earlydr3 The LAMOST DR7 spectra information set is public available at http://dr7.lamost.org. The subgiant star catalogue generated and analysed in this study is provided as Supplementary Table 1, and it can besides be reached through a temporary path https://keeper.mpdl.mpg.de/d/019ec71212934847bfed/. The YY isochrones adopted for age determination in this piece of work is public bachelor at http://www.astro.yale.edu/demarque/yyiso.html.

Code availability

The stellar orbit ciphering tool galpy adopted in this work is public available at http://github.com/jobovy/galpy. The DD-Payne lawmaking adopted for determining stellar labels, the neural network code for determining M _M from the LAMOST spectra and the Bayesian code for stellar age estimation are currently non publicly attainable online, every bit they are a role of ongoing survey data analysis efforts that will be applied to the upcoming LAMOST survey spectrum set. Withal, the codes tin can be shared on asking.

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Acknowledgements

We thank D. Xu and Due north. Frankel for helpful discussion, and J. Rybizki for his kind help with using the Gaia mock catalogues. M.X. acknowledges partial support from NSFC grant no. 11833006 for his bookish visit to NAOC from November 2021 to January 2022. This work has used data products from the Guoshoujing Telescope (LAMOST). LAMOST is a National Major Scientific Project congenital by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Committee. LAMOST is operated and managed past the National Astronomical Observatories, Chinese Academy of Sciences. This work has fabricated utilize of data products from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Understanding. The Gaia mission website is https://www.cosmos.esa.int/gaia. The Gaia archive website is https://archives.esac.esa.int/gaia. This publication has likewise used information products from the 2MASS, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Constitute of Engineering science, funded by the National Aeronautics and Space Administration and the National Science Foundation.

Funding

Open admission funding provided past Max Planck Society.

Author data

Affiliations

Max-Planck Institute for Astronomy, Koenigstuhl 17, Heidelberg, Deutschland

Maosheng Xiang & Hans-Walter Rix

Contributions

Thousand.10. conducted the construction of the subgiant sample and the determination of stellar parameters and ages. M.X. and H.-W.R. jointly executed the data analysis and manuscript writing.

Corresponding authors

Correspondence to Maosheng Xiang or Hans-Walter Rix.

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Competing interests

The authors declare no competing interests.

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Nature thank you Timothy Beers and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended information figures and tables

Extended Information Fig. 1 MCMC determination of the intrinsic scatter of the age distribution of old, high-α ('thick') deejay sequence, $P(\tau |[{\rm{Fe}}/{\rm{H}}])$, shown in panel (e) of Fig. two.

The parameters shown are: σ _τ,int – the intrinsic historic period besprinkle, ${\bar{\tau }}_{0}$ – the mean stellar historic period at solar metallicity ([Iron/H] = 0), and a – the slope of mean age every bit a function of [Iron/H]. Specifically, we presume the historic period distribution for given [Fe/H] is $P(\tau ,\delta \tau |[{\rm{Iron}}/{\rm{H}}],{\bar{\tau }}_{0},a,{\sigma }_{\tau ,{\rm{int}}})=G(\tau -\bar{\tau }([{\rm{Fe}}/{\rm{H}}]),\sqrt{{\sigma }_{\tau ,\,{\rm{int}}}^{two}+\delta {\tau }^{2}})$, where G is the Gaussian function, δτ the measurement error of the age τ, and $\bar{\tau }([{\rm{Iron}}/{\rm{H}}])={\bar{\tau }}_{0}+a\times [{\rm{Fe}}/{\rm{H}}]$ (run into Supplementary Information for details). Vertical solid and dashed lines indicate the hateful and 1σ values of the estimated parameters. The resultant upper limit of the intrinsic age scatter σ _τ,int of the 'thick' disk sequence is ~0.82 ± 0.01 Gyr. This indicates that, at a constant historic period, the upper limit of the 'thick' disk intrinsic [Fe/H] dispersion is 0.22 dex. The upper-right corner shows the historic period distribution for stars formed in the early on phase but with −one.05 < [Iron/H] < −0.95, J _ϕ > 500 kpc.km/s – presumably the oldest thick deejay stars. A Gaussian fit to the distribution (crimson curve) yields a mean age of 13 Gyr.

Extended Data Fig. two Stellar density distribution in the J _ϕ versus [Iron/H] aeroplane.

The vertical line delineates a constant J _ϕ of 500 kpc.km/s, which nosotros prefer to split the kinematic halo from the kinematic 'thick' deejay in Fig. 3. At that place is a tail of low-angular-momentum stars (J _ϕ < 500 kpc.km/s) in the metallicity range of −ane≲ [Fe/H]≲ −0.four (box delineated by ruddy dashed lines), presumably the 'splashed' thick disk stars due to the merger with the Gaia-Sausage-Enceladus satellite milky way.

Extended Data Fig. 3 Validation of spectroscopic M_G estimates.

Left: Spectroscopic M_Grand versus geometric M_Thou for a test prepare of stars with spectral S/Northward > lxxx, $\sigma ({M}_{G}^{{\rm{m}}{\rm{due east}}{\rm{o}}{\rm{m}}}) < 0.two$ mag. Colors bespeak stellar number density. The stars with spectroscopic M_K much larger than geometric Thou_{One thousand} are unresolved binaries, for which the geometric Thousand_K are too luminous due to light contribution of the secondary. The solid line indicates the 1:ane line, and the dashed line indicates an offset of 0.75 mag, which corresponds to the case of equal-mass binaries. The small window in the panel shows a histogram of the difference for spectroscopic M_K minus geometric Thou_{One thousand}. Right: doubt of the spectroscopic M₁₀₀₀ estimates every bit a function of S/N, for subgiant stars of different metallicities.

Extended Data Fig. 4 Illustration of age estimates from dissimilar isochrones.

Left: comparison of age estimates from YY (X-axis) and MIST iscohrones (Y-axis), both with [α/Fe] = 0. MIST isochrones yield almost 0.5 Gyr older ages. Currently, MIST isochrones are publically available just with [α/Fe] = 0, while YY isochrones with different [α/Fe] are bachelor. Right: Comparison of age estimates from YY isochrones with [α/Fe] = 0 and with [α/Atomic number 26] = 0.2. The 0.2 dex α-enhancement volition alter the age estimates by 1–2 Gyr, thus information technology is necessary to consider this effect. We adopt the YY isochrones, and take the weighted-hateful ages from isochrones with [α/Fe] = 0, [α/Atomic number 26] = 0.2, and [α/Iron] = 0.four.

Extended Data Fig. 5 Examination of pick effect through Gaia Mock data.

Left console: Historic period – [Atomic number 26/H] relation for subgiant stars in the Gaia mock itemize of Rybizki et al.⁴⁴. The sample includes about 1,250,000 subgiant stars that in the same footprint and magnitude ranges as for the LAMOST. Right console: Aforementioned every bit the left panel, only for a subset of the Gaia mock subgiant stars that has comparable number of the LAMOST sample (most 250,000 stars) randomly drawn from the sample shown in the left panel. Compared to the left console, there are some artifacts for the younger populations (τ < nine Gyr) due to the smaller sample size, only this volition not change the determination.

Extended Data Fig. half dozen Comparison of the age-metallicity relation with literature.

The 5-point stars in crimson represent field stars from Nissen et al.²⁵, while the dots in scarlet are globular clusters (GCs) compiled from Forbes et al.⁴⁵, VandenBerg et al.⁴⁶, and Cohen et al.⁴⁷.

Extended Data Table 1 Slope and intercept of the linear functions for the upper and lower boundary of the subgiant star sample selection

Full size table

Supplementary information

Supplementary Data

Supplementary Information sections i. The data; 2. The sample'due south selection part; 3. The intrinsic historic period scatter of the thick disk; iv. The one-time deejay stars 'splashed' by the merger with the Gaia-Sausage-Enceladus satellite galaxy; 5. Comparison of the age–metallicity relation with the literature.

Peer Review File

Supplementary Table 1

The stellar catalogue generated for and analysed in the current piece of work, in ascii format

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Xiang, Thou., Rix, HW. A time-resolved flick of our Milky Way's early on formation history. Nature 603, 599–603 (2022). https://doi.org/10.1038/s41586-022-04496-five

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Received: 01 November 2021
Accepted: 01 February 2022
Published: 23 March 2022
Issue Date: 24 March 2022
DOI : https://doi.org/10.1038/s41586-022-04496-5

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