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In the last decade, the Kepler and CoRoT space-photometry missions have demonstrated the potential of asteroseismology as a novel, versatile and powerful tool to perform exquisite tests of stellar physics, and to enable precise and accurate characterisations of stellar properties, with impact on both exoplanetary and Galactic astrophysics. Based on our improved understanding of the strengths and limitations of such a tool, we argue for a new small/medium space mission dedicated to gathering high-precision, high-cadence, long photometric series in dense stellar fields. Such a mission will lead to breakthroughs in stellar astrophysics, especially in the metal poor regime, will elucidate the evolution and formation of open and globular clusters, and aid our understanding of the assembly history and chemodynamics of the Milky Way's bulge and few nearby dwarf galaxies., Comment: White paper submitted in response to Voyage 2050 long-term plan in the ESA Science Programme, now published in Experimental Astronomy, see https://link.springer.com/article/10.1007/s10686-021-09711-1

Context. The CoRoT and Kepler missions have paved the way for synergies between exoplanetology and asteroseismology. The use of seismic data helps providing stringent constraints on the stellar properties which directly impact the results of planetary studies. Amongst the most interesting planetary systems discovered by Kepler, Kepler-444 is unique by the quality of its seismic and classical stellar constraints. Its magnitude, age and the presence of 5 small-sized planets orbiting this target makes it an exceptional testbed for exoplanetology. Aims. We aim at providing a detailed characterization of Kepler-444, focusing on the dependency of the results on variations of key ingredients of the theoretical stellar models. This thorough study will serve as a basis for future investigations of the planetary evolution of the system orbiting Kepler-444. Methods. We use local and global minimization techniques to study the internal structure of the exoplanet-host star Kepler-444. We combine seismic observations from the Kepler mission, Gaia DR2 data and revised spectroscopic parameters to precisely constrain its internal structure and evolution. Results. We provide updated robust and precise determinations of the fundamental parameters of Kepler-444 and demonstrate that this low-mass star bore a convective core during a significant portion of its life on the main-sequence. Using seismic data, we are able to estimate the lifetime of the convective core to approximately 8 Gyr out of the 11 Gyr of the evolution of Kepler-444. The revised stellar parameters found by our thorough study are M = 0.754 +- 0.03M_Sun , R = 0.753 +- 0.01R_Sun , Age = 11 +- 1 Gy., Comment: Accepted for publication in Astronomy and Astrophysics

Since the first observations of solar oscillations, helioseismology has been one of the most successful fields of astrophysics. Data of high quality were obtained through the implementation of networks of ground-based observatories such as the GONG project or the BiSON network, coupled with space-based telescopes such as SOHO and SDO missions. Besides the improvement of observational data, solar seismologists developed sophisticated techniques to infer the internal structure of the Sun. These methods, then already extensively used in the field of Geophysics, are called inversion techniques. They allowed to determine the position of the solar convective envelope, its helium abundance and the internal radial profiles of thermodynamic quantities. Back in 1990s these comparisons showed a very high agreement between solar models and the Sun. However, the downward revision of the CNO surface abundances in the Sun induced a drastic reduction of this agreement leading to the solar modelling problem. More than ten years later, in the era of the space-based photometry missions which have established asteroseismology of solar-like stars as a standard approach to obtain their masses, radii and ages, the solar modelling problem still awaits a solution. We will present the results of new helioseismic inversions, discuss the current uncertainties of solar models as well as some possible solutions to the solar problem. We will show how helioseismology can help us grasp what is amiss in our models. We will also show that, far from being an argument about details of solar models, the solar problem has significant implications for seismology of solar-like stars, on the main sequence and beyond, impacting asteroseismology as a whole as well as the fields requiring precise and accurate knowledge of stellar masses, radii and ages, such as Galactic archaeology and exoplanetology., Comment: Accepted for publication in Front. Astron. Space Sci. - Stellar and Solar Physics

A rate splitting based scheme is proposed to operate a broadcast setting with two antennas at the transmit side and two single-antenna receiving terminals. The transmitter knows the magnitude of the channel coefficients, and it is oblivious to the phase information. Each transmit antenna, with a power constraint, sends a private message and a common message to be decoded by both receivers. An achievable rate region is obtained, which enlarges the capacity region of the vector broadcast channel with vector channel magnitude feedback by means of superposition coding., Comment: \c{opyright} 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

The Sun is the most studied of stars and a laboratory of fundamental physics. However, the understanding of our star is stained by the solar modelling problem which can stem from various causes. We combine inversions of sound speed, an entropy proxy and the Ledoux discriminant with the position of the base of the convective zone and the photospheric helium abundance to test combinations of ingredients such as equation of state, abundance and opacity tables. We study the potential of the inversions to constrain ad-hoc opacity modifications and additional mixing in the Sun. We show that they provide constraints on these modifications to the ingredients and that the solar problem likely occurs from various sources and using phase shifts with our approach is the next step to take., Comment: To appear in the proceedings of the PHOST meeting held in Banyuls, France

A key aspect in the determination of stellar properties is the comparison of observational constraints with predictions from stellar models. Asteroseismic Inference on a Massive Scale (AIMS) is an open source code that uses Bayesian statistics and a Markov Chain Monte Carlo approach to find a representative set of models that reproduce a given set of classical and asteroseismic constraints. These models are obtained by interpolation on a pre-calculated grid, thereby increasing computational efficiency. We test the accuracy of the different operational modes within AIMS for grids of stellar models computed with the Li\`ege stellar evolution code (main sequence and red giants) and compare the results to those from another asteroseismic analysis pipeline, PARAM. Moreover, using artificial inputs generated from models within the grid (assuming the models to be correct), we focus on the impact on the precision of the code when considering different combinations of observational constraints (individual mode frequencies, period spacings, parallaxes, photospheric constraints,...). Our tests show the absolute limitations of precision on parameter inferences using synthetic data with AIMS, and the consistency of the code with expected parameter uncertainty distributions. Interpolation testing highlights the significance of the underlying physics to the analysis performance of AIMS and provides caution as to the upper limits in parameter step size. All tests demonstrate the flexibility and capability of AIMS as an analysis tool and its potential to perform accurate ensemble analysis with current and future asteroseismic data yields., Comment: Accepted for publication in MNRAS. 17 pages, 17 figures

Aims: We develop a method that provides a comprehensive analysis of the oscillation spectra of solar-like pulsators. We define new seismic indicators that should be as uncorrelated and as precise as possible and should hold detailed information about stellar interiors. This is essential to improve the quality of the results obtained from asteroseismology as it will provide better stellar models which in turn can be used to refine inferences made in exoplanetology and galactic archaeology. Methods: The presented method - WhoSGlAd - relies on Gram-Schmidt's orthogonalisation process. A Euclidean vector subspace of functions is defined and the oscillation frequencies are projected over an orthonormal basis in a specific order. This allows the obtention of independent coefficients that we combine to define independent seismic indicators. Results: The developed method has been shown to be stable and to converge efficiently for solar-like pulsators. Thus, detailed and precise inferences can be obtained on the mass, the age, the chemical composition and the undershooting in the interior of the studied stars. However, attention has to be paid when studying the helium glitch as there seems to be a degeneracy between the influence of the helium abundance and that of the heavy elements on the glitch amplitude. As an example, we analyse the 16CygA (HD 186408) oscillation spectrum to provide an illustration of the capabilities of the method., Comment: Accepted for publication in Astronomy and Astrophysics, 20 pages

The Sun is the most studied of all stars. It is a reference for all other observed stars and a laboratory of fundamental physics helping us understand processes occuring in conditions irreproducible on Earth. However, our understanding of the Sun is currently stained by the solar modelling problem which can stem from various causes, such as the opacities, the equation of state and the mixing of chemical elements. We combine inversions of sound speed, an entropy proxy and the Ledoux discriminant with constraints such as the position of the base of the convective zone and the photospheric helium abundance. We test various combinations of standard ingredients for solar modelling such as abundance tables, equation of state, formalism for convection and diffusion and opacity tables and study the diagnostic potential of the inversions to constrain ad-hoc modifications of the opacity profile and additional mixing below the convective envelope. Combining inversions provides stringent constraints on the modifications on the models, far beyond what is achievable only from sound speed inversions. We constrain the form and amplitude of the opacity increase required and show that a 15% increase at log T=6.35 provides a significant improvement but that a more global increase of the opacity, within the uncertainties of current tables, coupled with an additional mixing at the bottom of the convective zone gives the best agreement for low metallicity models. We show that high metallicity models do not satisfy all the inversion results. We conclude that the solar problem likely occurs from various small sources, as ingredients such as the equation of state or the formalism of convection can induce small but significant changes and that using phase shift analyses combined with our approach is the next step for a better understanding of the inaccuracies of solar models just below the convective envelope., Comment: Accepted for publication in Astronomy and Astrophysics

Since the CoRoT and Kepler missions, the availability of high quality seismic spectra for red giants has made them the standard clocks and rulers for Galactic Archeology. With the expected excellent data from the TESS and PLATO missions, red giants will again play a key role in Galactic studies and stellar physics, thanks to the precise masses and radii determined by asteroseismology. The determination of these quantities is often based on so-called scaling laws, which have been used extensively for main-sequence stars. We show how the SOLA inversion technique can provide robust determinations of the mean density of red giants within 1 per cent of the real value, using only radial oscillations. Combined with radii determinations from Gaia of around 2 per cent precision, this approach provides robust, less model-dependent masses with an error lower than 10 per cent. It will improve age determinations, helping to accurately dissect the Galactic structure and history. We present results on artificial data of standard models, models including an extended atmosphere from averaged 3D simulations and non-adiabatic frequency calculations to test surface effects, and on eclipsing binaries. We show that the inversions provide very robust mean density estimates, using at best seismic information. However, we also show that a distinction between red-giant branch and red-clump stars is required to determine a reliable estimate of the mean density. The stability of the inversion enables an implementation in automated pipelines, making it suitable for large samples of stars., Comment: Accepted for publication in MNRAS

Modelling the base of the solar convective envelope is a tedious problem. Since the first rotation inversions, solar modellers are confronted with the fact that a region of very limited extent has an enormous physical impact on the Sun. Indeed, it is the transition region from differential to solid body rotation, the tachocline, which furthermore is influenced by turbulence and is also supposed to be the seat of the solar magnetic dynamo. Moreover, solar models show significant disagreement with the sound speed profile in this region. In this paper, we show how helioseismology can provide further constraints on this region by carrying out an inversion of the Ledoux discriminant. We compare these inversions for Standard Solar Models built using various opacity tables and chemical abundances and discuss the origins of the discrepancies between Solar Models and the Sun., Comment: Accepted for publication as a letter in MNRAS

The solar metallicity issue is a long-lasting problem of astrophysics, impacting multi- ple fields and still subject to debate and uncertainties. While spectroscopy has mostly been used to determine the solar heavy elements abundance, helioseismologists at- tempted providing a seismic determination of the metallicity in the solar convective enveloppe. However, the puzzle remains since two independent groups prodived two radically different values for this crucial astrophysical parameter. We aim at provid- ing an independent seismic measurement of the solar metallicity in the convective enveloppe. Our main goal is to help provide new information to break the current stalemate amongst seismic determinations of the solar heavy element abundance. We start by presenting the kernels, the inversion technique and the target function of the inversion we have developed. We then test our approach in multiple hare-and-hounds exercises to assess its reliability and accuracy. We then apply our technique to solar data using calibrated solar models and determine an interval of seismic measurements for the solar metallicity. We show that our inversion can indeed be used to estimate the solar metallicity thanks to our hare-and-hounds exercises. However, we also show that further dependencies in the physical ingredients of solar models lead to a low accuracy. Nevertheless, using various physical ingredients for our solar models, we determine metallicity values between 0.008 and 0.014., Comment: Accepted for publication in MNRAS

The Sun is the most constrained and well-studied of all stars. As a consequence, the physical ingredients entering solar models are used as a reference to study all other stars observed in the Universe. However, our understanding of the solar structure is still imperfect, as illustrated by the current debate on the heavy element abundances in the Sun. We wish to provide additional information on the solar structure by carrying out structural inversions of a new physical quantity, a proxy of the entropy of the solar plasma which properties are very sensitive to the temperature gradient below the convective zone. We use new structural kernels to carry out direct inversions of an entropy proxy of the solar plasma and compare the solar structure to various standard solar models built using various opacity tables and chemical abundances. We also link our results to classical tests commonly found in the literature. Our analysis allows us to probe more efficiently the uncertain regions of the solar models, just below the convective zone, paving the way for new in-depth analyses of the Sun taking into account additional physical uncertainties of solar models beyond the specific question of chemical abundances., Comment: Accepted for publication in Astronomy & Astrophysics

Deciphering the assembly history of the Milky Way is a formidable task, which becomes possible only if one can produce high-resolution chrono-chemo-kinematical maps of the Galaxy. Data from large-scale astrometric and spectroscopic surveys will soon provide us with a well-defined view of the current chemo-kinematical structure of the Milky Way, but will only enable a blurred view on the temporal sequence that led to the present-day Galaxy. As demonstrated by the (ongoing) exploitation of data from the pioneering photometric missions CoRoT, Kepler, and K2, asteroseismology provides the way forward: solar-like oscillating giants are excellent evolutionary clocks thanks to the availability of seismic constraints on their mass and to the tight age-initial-mass relation they adhere to. In this paper we identify five key outstanding questions relating to the formation and evolution of the Milky Way that will need precise and accurate ages for large samples of stars to be addressed, and we identify the requirements in terms of number of targets and the precision on the stellar properties that are needed to tackle such questions. By quantifying the asteroseismic yields expected from PLATO for red-giant stars, we demonstrate that these requirements are within the capabilities of the current instrument design, provided that observations are sufficiently long to identify the evolutionary state and allow robust and precise determination of acoustic-mode frequencies. This will allow us to harvest data of sufficient quality to reach a 10% precision in age. This is a fundamental pre-requisite to then reach the more ambitious goal of a similar level of accuracy, which will only be possible if we have to hand a careful appraisal of systematic uncertainties on age deriving from our limited understanding of stellar physics, a goal which conveniently falls within the main aims of PLATO's core science., Comment: 17 pages, 9 figures, accepted for publication in Astronomical Notes

Convective mixing in Helium-core-burning (HeCB) stars is one of the outstanding issues in stellar modelling. The precise asteroseismic measurements of gravity-modes period spacing ($\Delta\Pi_1$) has opened the door to detailed studies of the near-core structure of such stars, which had not been possible before. Here we provide stringent tests of various core-mixing scenarios against the largely unbiased population of red-clump stars belonging to the old open clusters monitored by Kepler, and by coupling the updated precise inference on $\Delta\Pi_1$ in thousands field stars with spectroscopic constraints. We find that models with moderate overshooting successfully reproduce the range observed of $\Delta\Pi_1$ in clusters. In particular we show that there is no evidence for the need to extend the size of the adiabatically stratified core, at least at the beginning of the HeCB phase. This conclusion is based primarily on ensemble studies of $\Delta\Pi_1$ as a function of mass and metallicity. While $\Delta\Pi_1$ shows no appreciable dependence on the mass, we have found a clear dependence of $\Delta\Pi_1$ on metallicity, which is also supported by predictions from models., Comment: 8 pages, 4 figures, accepted for publication in MNRAS

Asteroseismic parameters allow us to measure the basic stellar properties of field giants observed far across the Galaxy. Most of such determinations are, up to now, based on simple scaling relations involving the large frequency separation, \Delta\nu, and the frequency of maximum power, \nu$_{max}$. In this work, we implement \Delta\nu\ and the period spacing, {\Delta}P, computed along detailed grids of stellar evolutionary tracks, into stellar isochrones and hence in a Bayesian method of parameter estimation. Tests with synthetic data reveal that masses and ages can be determined with typical precision of 5 and 19 per cent, respectively, provided precise seismic parameters are available. Adding independent information on the stellar luminosity, these values can decrease down to 3 and 10 per cent respectively. The application of these methods to NGC 6819 giants produces a mean age in agreement with those derived from isochrone fitting, and no evidence of systematic differences between RGB and RC stars. The age dispersion of NGC 6819 stars, however, is larger than expected, with at least part of the spread ascribable to stars that underwent mass-transfer events., Comment: 17 pages, 13 figures, accepted for publication in MNRAS

Drawing from Self-Determination Theory and diverse theories of language learning motivation, we present a framework that (1) represents a range of orientations that students may take towards learning German, and (2) explains how these orientations are connected to language learning engagement and diverse linguistic and non-linguistic outcomes. We maintain that students who invest in learning because it is meaningful to them personally (that is, those who have a self-determined orientation) are more likely to actively engage with the language academically and with its associated community, and in turn they are more likely to become communicatively and culturally competent. We further claim that a self-determined orientation can be fostered in a social environment that is responsive to learners' need to be active, competent agents who have mutually satisfying relationships with others. We conclude with some alternative avenues of study that would complement the research done to date.