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The standard cosmological model ($\Lambda$-CDM) predicts that galaxies are built through hierarchical assembly on cosmological timescales$^{1,2}$. The Milky Way, like other disc galaxies, underwent violent mergers and accretion of small satellite galaxies in its early history. Thanks to Gaia-DR2$^3$ and spectroscopic surveys$^4$, the stellar remnants of such mergers have been identified$^{5-7}$. 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 owing 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 ($\sim$ 11%) for a sample of stars observed by the $\mathit{Kepler}$ space mission$^8$. 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 disc) before the in-fall of the satellite galaxy Gaia-Enceladus/Sausage$^{5,6}$ around 10 billions years ago, Comment: Updated with the final version accepted for publication as a Letter in Nature Astronomy (29 pages, 10 figures, 2 tables, including main article and methods section). Improved presentation of results, which have not changed from the previous version

State-of-the-art stellar structure and evolution codes fail to adequately describe turbulent convection. For stars with convective envelopes, such as red giants, this leads to an incomplete depiction of the surface layers. As a result, the predicted stellar oscillation frequencies are haunted by systematic errors, the so-called surface effect. Different empirically and theoretically motivated correction relations have been proposed to deal with this issue. In this paper, we compare the performance of these surface correction relations for red giant branch stars. For this purpose, we apply the different surface correction relations in asteroseismic analyses of eclipsing binaries and open clusters. In accordance with previous studies of main-sequence stars, we find that the use of different surface correction relations biases the derived global stellar properties, including stellar age, mass, and distance estimates. We furthermore demonstrate that the different relations lead to the same systematic errors for two different open clusters. Our results overall discourage from the use of surface correction relations that rely on reference stars to calibrate free parameters. Due to the demonstrated systematic biasing of the results, the use of appropriate surface correction relations is imperative to any asteroseismic analysis of red giants. Accurate mass, age, and distance estimates for red giants are fundamental when addressing questions that deal with the chemo-dynamical evolution of the Milky Way galaxy. In this way, our results also have implications for fields, such as galactic archaeology, that draw on findings from stellar physics.

Over the course of its history, the Milky Way has ingested multiple smaller satellite galaxies. While these accreted stellar populations can be forensically identified as kinematically distinct structures within the Galaxy, it is difficult in general to precisely date the age at which any one merger occurred. Recent results have revealed a population of stars that were accreted via the collision of a dwarf galaxy, called \textit{Gaia}-Enceladus, leading to a substantial pollution of the chemical and dynamical properties of the Milky Way. Here, we identify the very bright, naked-eye star $\nu$\,Indi as a probe of the age of the early in situ population of the Galaxy. We combine asteroseismic, spectroscopic, astrometric, and kinematic observations to show that this metal-poor, alpha-element-rich star was an indigenous member of the halo, and we measure its age to be $11.0 \pm 0.7$ (stat) $\pm 0.8$ (sys)$\,\rm Gyr$. The star bears hallmarks consistent with it having been kinematically heated by the \textit{Gaia}-Enceladus collision. Its age implies that the earliest the merger could have begun was 11.6 and 13.2 Gyr ago at 68 and 95% confidence, respectively. Input from computations based on hierarchical cosmological models tightens (i.e. reduces) slightly the above limits., Comment: Accepted for publication as a Letter in Nature Astronomy (26 pages, 7 figures, including main article and methods section)

The importance of studying the Gaia DR2 parallax zero-point by external means was underlined by Lindegren et al. (2018), and initiated by several works making use of Cepheids, eclipsing binaries, and asteroseismology. Despite a very efficient elimination of basic-angle variations, a small fluctuation remains and shows up as a small offset in the Gaia DR2 parallaxes. By combining astrometric, asteroseismic, spectroscopic, and photometric constraints, we undertake a new analysis of the Gaia parallax offset for nearly 3000 red-giant branch (RGB) and 2200 red clump (RC) stars observed by Kepler, as well as about 500 and 700 red giants (both RGB and RC) selected by the K2 Galactic Archaeology Program in campaigns 3 and 6. Engaging into a thorough comparison of the astrometric and asteroseismic parallaxes, we are able to highlight the influence of the asteroseismic method, and measure parallax offsets in the Kepler field that are compatible with independent estimates from literature and open clusters. Moreover, adding the K2 fields to our investigation allows us to retrieve a clear illustration of the positional dependence of the zero-point, in general agreement with the information provided by quasars. Lastly, we initiate a two-step methodology to make progress in the simultaneous calibration of the asteroseismic scaling relations and of the Gaia DR2 parallax offset, which will greatly benefit from the gain in precision with the third Data Release of Gaia., Comment: 15 pages, 17 figures, Accepted for publication in A&A

Using asteroseismic data from the Kepler satellite, we explore the systematic uncertainties arising from changes in the input physics used when constructing evolution models of solar-type stars. We assess the impact of including atomic diffusion and of varying the metallicity mixture on the determination of global stellar parameters (i.e., radius, mass, and age). We find significant systematic uncertainties on global stellar parameters when diffusion is included in stellar grids. Furthermore, we find the systematic uncertainties on the global stellar parameters to be comparable to the statistical uncertainties when a different metallicity mixture is employed in stellar grids., Comment: 3 pages, 3 figures, proceeding of PHOST (Physics of Oscillating Stars) - a conference in honour of Prof. H. Shibahashi, 2-7 Sept. 2018, Banyuls-sur-mer (France)