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We introduce the SAPP (Stellar Abundances and atmospheric Parameters Pipeline), the prototype of the code that will be used to determine parameters of stars observed within the core program of the PLATO space mission. The pipeline is based on the Bayesian inference and provides effective temperature, surface gravity, metallicity, chemical abundances, and luminosity. The code in its more general version has a much wider range of potential applications. It can also provide masses, ages, and radii of stars and can be used with stellar types not targeted by the PLATO core program, such as red giants. We validate the code on a set of 27 benchmark stars that includes 19 FGK-type dwarfs, 6 GK-type subgiants, and 2 red giants. Our results suggest that combining various observables is the optimal approach, as this allows the degeneracies between different parameters to be broken and yields more accurate values of stellar parameters and more realistic uncertainties. For the PLATO core sample, we obtain a typical uncertainty of 27 (syst.) ± 37 (stat.) K for Teff, 0.00 ± 0.01 dex for log g, 0.02 ± 0.02 dex for metallicity [Fe/H], −0.01 ± 0.03 R⊙ for radii, −0.01 ± 0.05 M⊙ for stellar masses, and −0.14 ± 0.63 Gyr for ages. We also show that the best results are obtained by combining the νmax scaling relation with stellar spectra. This resolves the notorious problem of degeneracies, which is particularly important for F-type stars., This work presents results from the European Space Agency (ESA) space mission PLATO. The PLATO payload, the PLATO Ground Segment and PLATO data processing are joint developments of ESA and the PLATO Mission Consortium (PMC). Funding for the PMC is provided at national levels, in particular by countries participating in the PLATO Multilateral Agreement (Austria, Belgium, Czech Republic, Denmark, France, Germany, Italy, Netherlands, Portugal, Spain, Sweden, Switzerland, Norway, and United Kingdom) and institutions from Brazil. Members of the PLATO Consortium can be found at https://platomission.com. The ESA PLATO mission website is https://www.cosmos.esa.int/plato. We thank the teams working for PLATO for all their work. We thank P.E. Nissen for providing the reduced spectra of the Kepler legacy stars. M.R.G., M.B., J.G., and M.K. are supported by the Lise Meitner grant from the Max Planck Society. B.P. is partially supported by CNES, the Centre National d’Études Spatiales. We acknowledge support by the Collaborative Research centre SFB 881 (projects A5, A10), Heidelberg University, of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). We thank C. Aerts for providing helpful comments to this study. 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. A.S. acknowledges support from MICINN grant PID2019-108709GB-I00. T.M. acknowledges financial support from Belspo for contract PRODEX PLATO mission development. U.H. acknowledges support from the Swedish National Space Agency (SNSA/Rymdstyrelsen). S.M. has been supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-20-5 New National Excellence Program of the Ministry for Innovation and Technology. N.N. acknowledges Anthony Salsi for useful discussions. V.A. is supported by FCT – Fundação para a Ciência e Tecnologia (FCT) through national grants: UID/FIS/04434/2019; UIDB/04434/2020; UIDP/04434/2020. V.A. also acknowledges the support from FCT through Investigador FCT contract nr. IF/00650/2015/CP1273/CT0001. M.T. acknowledges the funding from MIUR Premiale 2016: MITIC. L.C. is the recipient of the ARC Future Fellowship FT160100402. M.B. is supported through the Lise Meitner grant from the Max Planck Society. We acknowledge support by the Collaborative Research centre SFB 881 (projects A5, A10), Heidelberg University, of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 949173).

The first paper of this series established a linear stochastic wave equation for solar-like p-modes, correctly taking the effect of turbulence thereon into account. In this second paper, we aim at deriving simultaneous expressions for the excitation rate, damping rate, and modal surface effect associated with any given p-mode, as an explicit function of the statistical properties of the turbulent velocity field. We reduce the stochastic wave equation to complex amplitude equations for the normal oscillating modes of the system. We then derive the equivalent Fokker-Planck equation for the real amplitudes and phases of all the oscillating modes of the system simultaneously. The effect of the finite-memory time of the turbulent fluctuations (comparable to the period of the modes) on the modes themselves is consistently and rigorously accounted for, by means of the simplified amplitude equation formalism. This formalism accounts for mutual linear mode coupling in full, and we then turn to the special single-mode case. This allows us to derive evolution equations for the mean energy and mean phase of each mode, from which the excitation rate, the damping rate, and the modal surface effect naturally arise. We show that the expression for the excitation rate of the modes is identical to previous results obtained through a different modelling approach, thus supporting the validity of the formalism presented here. We also recover the fact that the damping rate and modal surface effect correspond to the real and imaginary part of the same single complex quantity. We explicitly separate the different physical contributions to these observables, in particular the turbulent pressure contribution and the joint effect of the pressure-rate-of-strain correlation and the turbulent dissipation. We show that the former dominates for high-frequency modes and the latter for low-frequency modes., Accepted for publication in A&A. 23 pages, 2 figures

Aims. This series of papers aims at building a new formalism specifically tailored to study the impact of turbulence on the global modes of oscillation in solar-like stars. This first paper aims at deriving a linear wave equation that directly and consistently contains the turbulence as an input to the model, and therefore naturally contains the information on the coupling between the turbulence and the modes, through the stochasticity of the equations. Methods. We use a Lagrangian stochastic model of turbulence based on Probability Density Function methods to describe the evolution of the properties of individual fluid particles through stochastic differential equations. We then transcribe these stochastic differential equations from a Lagrangian frame to an Eulerian frame, more adapted to the analysis of stellar oscillations. We combine this method with Smoothed Particle Hydrodynamics, where all the mean fields appearing in the Lagrangian stochastic model are estimated directly from the set of fluid particles themselves, through the use of a weighting kernel function allowing to filter the particles present in any given vicinity. The resulting stochastic differential equations on Eulerian variables are then linearised. Results. We obtain a stochastic, linear wave equation governing the time evolution of the relevant wave variables, while at the same time containing the effect of turbulence. The wave equation generalises the classical, unperturbed propagation of acoustic waves in a stratified medium to a form that, by construction, accounts for the impact of turbulence on the mode in a consistent way. The effect of turbulence consists in a non-homogeneous forcing term, responsible for the stochastic driving of the mode, and a stochastic perturbation to the homogeneous part of the wave equation, responsible for both the damping of the mode and the modal surface effects., Paper accepted for publication in A&A. 18 pages (12 without Appendices), 1 figure. Typos corrected

The space-borne missions CoRoT and Kepler have already brought stringent constraints on the internal structure of low-mass evolved stars, a large part of which results from the detection of mixed modes. However, all the potential of these oscillation modes as a diagnosis of the stellar interior has not been fully exploited yet. In particular, the coupling factor or the gravity-offset of mixed modes, $q$ and $\varepsilon_{\rm g}$, are expected to provide additional constraints on the mid-layers of red giants, which are located between the hydrogen-burning shell and the neighborhood of the base of the convective zone. In the present paper, we investigate the potential of the coupling factor in probing the mid-layer structure of evolved stars. Guided by typical stellar models and general physical considerations, we modeled the coupling region along with evolution. We subsequently obtained an analytical expression of $q$ based on the asymptotic theory of mixed modes and compared it to observations. We show that the value of $q$ is degenerate with respect to the thickness of the coupling evanescent region and the local density scale height. A structural interpretation of the global variations in $q$ observed on the subgiant and the red giant branches, as well as on the red clump, was obtained in the light of this model. We demonstrate that $q$ has the promising potential to probe the migration of the base of the convective region as well as convective extra-mixing in evolved red giant stars with typically $\nu_{\rm max} \lesssim 100~\mu$Hz. We also show that the frequency-dependence of $q$ cannot be neglected in the oscillation spectra of such stars, which is in contrast with what is assumed in the current measurement methods. This analytical study paves the way for a more quantitative exploration of the link of $q$ with the internal properties of evolved stars using stellar models., Comment: 27 pages, accepted in A\&A

Accurate and precise stellar ages are best determined for stars which are strongly observationally constrained, that is which are intrinsically oscillating. We review here the seismic diagnostics which are sensitive to stellar ages and provide some illustrating examples of seismically age-dated stars., 49 pages, 20 figures, contribution to the proceedings of the 13rd Evry Schatzman School on Stellar Astrophysics, "The Ages of Stars", Roscoff 2013, EAS Publications Series, eds. Y. Lebreton, D. Valls-Gabaud, C. Charbonnel

When modelling stars with masses larger than 1.2Msun with no observed chemical peculiarity, atomic diffusion is often neglected because, on its own, it causes unrealistic surface abundances compared with those observed. The reality is that atomic diffusion is in competition with other transport processes. The purpose of this study is to quantify the opposite or conjugated effects of atomic diffusion and rotationally induced mixing in stellar models of low mass stars. Our second goal is to estimate the impact of neglecting both rotational mixing and atomic diffusion in stellar parameter inferences for stars with masses larger than 1.3Msun. Using the AIMS code, we infer the masses and ages of a set of representative artificial stars for which models were computed with the CESTAM evolution code, taking into account rotationally induced mixing and atomic diffusion, including radiative accelerations. We show that for masses lower than 1.3Msun, rotation dominates the transport of chemical elements, and strongly reduces the effect of atomic diffusion, with net surface abundance modifications similar to solar ones. At larger mass, atomic diffusion and rotation are competing equally. Above 1.44Msun, atomic diffusion dominates in stellar models with initial rotation smaller than 80km.s-1 producing a chemical peculiarity which is not observed in Kepler-legacy stars. This indicates that a transport process of chemical elements is missing. Importantly, neglecting rotation and atomic diffusion (including radiative accelerations) in the models, when inferring the parameters of F-type stars, may lead to errors of 5%, 2.5% and 25% respectively for stellar masses, radii and ages. Atomic diffusion (including radiative accelerations) and rotational mixing should be taken into account in stellar models in order to determine accurate stellar parameters., Comment: 15 pages, 7 figures, accepted for publication in A&A

The GIII red giant star epsilon Oph has been found to exhibit several modes of oscillation by the MOST mission. We interpret the observed frequencies of oscillation in terms of theoretical radial p-mode frequencies of stellar models. Evolutionary models of this star, in both shell H-burning and core He-burning phases of evolution, are constructed using as constraints a combination of measurements from classical ground-based observations (for luminosity, temperature, and chemical composition) and seismic observations from MOST. Radial frequencies of models in either evolutionary phase can reproduce the observed frequency spectrum of epsilon Oph almost equally well. The best-fit models indicate a mass in the range of 1.85 +/- 0.05 Msun with radius of 10.55 +/- 0.15 Rsun. We also obtain an independent estimate of the radius of epsilon Oph using high accuracy interferometric observations in the infrared K' band, using the CHARA/FLUOR instrument. The measured limb darkened disk angular diameter of epsilon Oph is 2.961 +/- 0.007 mas. Together with the Hipparcos parallax, this translates into a photospheric radius of 10.39 +/- 0.07 Rsun. The radius obtained from the asteroseismic analysis matches the interferometric value quite closely even though the radius was not constrained during the modelling., Comment: 11 pages, accepted for publication in Astronomy & Astrophysics

We infer from different seismic observations the energy supplied per unit of time by turbulent convection to the acoustic modes of Alpha Cen A (HD 128620), a star which is similar but not identical to the Sun. The inferred rates of energy supplied to the modes (i.e. mode excitation rates) are found to be significantly larger than in the Sun. They are compared with those computed with an excitation model that includes two sources of driving, the Reynolds stress contribution and the advection of entropy fluctuations. The model also uses a closure model, the Closure Model with Plumes (CMP hereafter), that takes the asymmetry between the up- and down-flows (i.e. the granules and plumes, respectively) into account. Different prescriptions for the eddy-time correlation function are also confronted to observational data. Calculations based on a Gaussian eddy-time correlation underestimate excitation rates compared with the values derived from observations for Alpha Cen A. On the other hand, calculations based on a Lorentzian eddy-time correlation lie within the observational error bars. This confirms results obtained in the solar case. With respect to the helioseismic data, those obtained for Alpha Cen A constitute an additional support for our model of excitation. We show that mode masses must be computed taking turbulent pressure into account. Finally, we emphasize the need for more accurate seismic measurements in order to discriminate, in the case of Alpha Cen A, between the CMP closure model and the quasi-Normal Approximation as well as to confirm or not the need to include the excitation by the entropy fluctuations.

Turbulent motions in stellar convection zones generate acoustic energy, part of which is then supplied to normal modes of the star. Their amplitudes result from a balance between the efficiencies of excitation and damping processes in the convection zones. We develop a formalism that provides the excitation rates of non-radial global modes excited by turbulent convection. As a first application, we estimate the impact of non-radial effects on excitation rates and amplitudes of high-angular-degree modes which are observed on the Sun. A model of stochastic excitation by turbulent convection has been developed to compute the excitation rates, and it has been successfully applied to solar radial modes (Samadi & Goupil 2001, Belkacem et al. 2006b). We generalize this approach to the case of non-radial global modes. This enables us to estimate the energy supplied to high-($\ell$) acoustic modes. Qualitative arguments as well as numerical calculations are used to illustrate the results. We find that non-radial effects for $p$ modes are non-negligible: - for high-$n$ modes (i.e. typically $n > 3$) and for high values of $\ell$; the power supplied to the oscillations depends on the mode inertia. - for low-$n$ modes, independent of the value of $\ell$, the excitation is dominated by the non-diagonal components of the Reynolds stress term. We carried out a numerical investigation of high-$\ell$ $p$ modes and we find that the validity of the present formalism is limited to $\ell < 500$ due to the spatial separation of scale assumption. Thus, a model for very high-$\ell$ $p$-mode excitation rates calls for further theoretical developments, however the formalism is valid for solar $g$ modes, which will be investigated in a paper in preparation., 12 pages, accepted for publication in A&A

International audience; Context: The calibration of binary systems with accurately known masses and/or radii provides powerful tools to test stellar structure and evolution theory and to determine the age and helium content of stars. We study the eclipsing double-lined spectroscopic binary system RS Cha, for which we have accurate observations of the parameters of both stars (masses, radii, luminosities, effective temperatures and metallicity). Aims: We have calculated several sets of stellar models for the components of the RS Cha system, with the aim of reproducing simultaneously the available observational constraints and to estimate the age and initial helium abundance of the system. Methods: Using the CESAM stellar evolution code, we model both components starting from the initial mass and metallicity and adjusting the input parameters and physics in order to satisfy the observational constraints. Results: We find that the observations cannot be reproduced if we assume that the abundance ratios are solar but they are satisfied if carbon and nitrogen are depleted in the RS Cha system with respect to the Sun. This is in accordance with the abundances observed in other young stars. The RS Cha system is in an evolutionary stage at the end of the PMS phase where models are not strongly sensitive to various physical uncertainties. However we show that the oscillations of these two stars, which have been detected, would be able to discriminate between different options in the physical description of this evolutionary phase.

In order to prepare the theoretical interpretation of the oscillation frequencies detected by CoRoT, comparisons of results from standard stellar models by the ESTA group have proven to be very useful. The next issue which is briefly addressed here is “what are the additional physical processes that must be included in stellar models computed with different evolutionary codes for the next comparison exercises?” We therefore discuss the impact on oscillation frequencies of several physical processes which are still poorly understood and/or poorly modelled but cannot be fully discarded.

The present work explores the theoretical effects of rotation in calculating the period ratios of double-mode radial pulsating stars with special emphasis on high-amplitude delta Scuti stars (HADS). Diagrams showing these period ratios vs. periods of the fundamental radial mode have been employed as a good tracer of non-solar metallicities and are known as Petersen diagrams (PD).In this paper we consider the effect of moderate rotation on both evolutionary models and oscillation frequencies and we show that such effects cannot be completely neglected as it has been done until now. In particular it is found that even for low-to-moderate rotational velocities (15-50 km/s), differences in period ratios of some hundredths can be found. The main consequence is therefore the confusion scenario generated when trying to fit the metallicity of a given star using this diagram without a previous knowledge of its rotational velocity.

We compute the rates P at which acoustic energy is injected into the solar radial p modes for several solar models. The solar models are computed with two different local treatments of convection: the classical mixing-length theory (MLT hereafter) and Canuto et al (1996)'s formulation (CGM hereafter). Among the models investigated here, our best models reproduce both the solar radius and the solar luminosity at solar age and the observed Balmer line profiles. For the MLT treatment, the rates P do depend significantly on the properties of the atmosphere whereas for the CGM's treatment the dependence of P on the properties of the atmosphere is found smaller than the error bars attached to the seismic measurements. The excitation rates P for modes associated with the MLT models are significantly underestimated compared with the solar seismic constraints. The CGM models yield values for P closer to the seismic data than the MLT models. We conclude that the solar p-mode excitation rates provide valuable constraints and according to the present investigation clearly favor the CGM treatment with respect to the MLT, although neither of them yields values of P as close to the observations as recently found for 3D numerical simulations., 11 pages, 7 figures, accepted for publication in Astronomy & Astrophysics

International audience; We present new spectroscopic observations of the pre-main sequence eclipsing spectroscopic binary RS Cha. A sample of 174 spectra were obtained with the GIRAFFE spectrograph at the SAAO at 32 000 resolution. The radial velocity curves derived from these spectra were combined with previous observations spanning a period of about 30 years to correct the ephemeris of the system, and the result indicates that the orbital period is not constant. Residuals of the binary radial velocity curve for both components with amplitudes up to a few km s-1 and periods on the order of 1 h are clearly seen in our data, which we interpret as the signatures of delta-Scuti type pulsations. We revisited the masses of both components and determined the surface metallicity Z of both components of the RS Cha system by fitting synthetic spectra to observed spectra in a set of selected spectral regions. The synthetic spectra are calculated with the SYNTH code using stellar atmosphere models computed with the Kurucz ATLAS 9 code, along with a list of lines obtained from the VALD database. A selection of the best spectra and the most relevant spectral regions allowed us to determine Z = 0.028 ± 0.005. We also derived new values of v sin i: 64 ± 6 km s-1 and 70 ± 6 km s-1 for the primary and the secondary star, respectively. Finally, we observationally confirm that the RS Cha system is a synchronized and circularized system.

International audience; Acoustic rates of excitation of solar p modes can be estimated from observations in order to place constraints on the modelling of the excitation process and the layers where it occurs in the star. For several reasons (including a poor signal to noise ratio and mode overlap), this estimation is difficult. In this work, we use three completely independent datasets to obtain robust estimates in the solar case for l=1 modes. We also show that the height in the solar atmosphere where the modes are observed must be taken into account. Our three sets of results are shown to be consistent, particularly in the lower part of the p-mode spectrum (from 1.8 mHz to 2.8 mHz). At higher frequencies, the agreement is not as good, because of a larger dispersion of the measurements and also because of some systematic differences which might be due to observation height estimation or to a systematic influence of the noise.

Using up-to-date model atmospheres (Heiter et al. 2002) with the turbulent convection approach developed by Canuto et al. (1996, CGM), quadratic, cubic and square root limb darkening coecients (LDC) are calculated with a least square fit method for the Stromgren photometric system. This is done for a sample of solar metallicity models with eective temperatures between 6000 and 8500 K and with logg between 2.5 and 4.5. A comparison is made between these LDC and the ones computed from model atmospheres using the classical mixing length prescription with a mixing length parameter = 1:25 and= 0:5. For CGM model atmospheres, the law which reproduces better the model intensity is found to be the square root one for the u band and the cubic law for thev band. The results are more complex for the b andy bands depending on the temperature and gravity of the model. Similar conclusions are reached for MLT = 0:5 models. As expected much larger dierences are found between CGM and MLT with= 1:25. In a second part, the weighted limb-darkening integrals, b', and their derivatives with respect to temperature and gravity, are then computed using the best limb-darkening law. These integrals are known to be very important in the context of photometric mode identification of non-radial pulsating stars. The eect of convection treatment on these quantities is discussed and as expected dierences in the b' coecients and derivatives computed with CGM and MLT= 0:5 are much smaller than dierences obtained between computations with CGM and MLT = 1:25.

Model computations of δ Scuti stars, located in the vicinity of the red edge of the classical instability strip, suggest amplitudes of solar-like oscillations larger than in cooler models located outside the instability strip. Solar-like amplitudes in our δ Scuti models are found to be large enough to be detectable with ground-based instruments provided they can be distinguished from the opacity-driven large-amplitude pulsations. There would be advantages in observing simultaneously opacity-driven and stochastically excited modes in the same star. We anticipate their possible detection in the context of the planned asteroseismic space missions, such as the French mission COROT (COnvection ROtation and planetary Transits). We propose known δ Scuti stars as potential candidates for the target selection of these upcoming space missions.

We present several new sets of grids of model stellar atmospheres computed with modified versions of the ATLAS9 code. Each individual set consists of several grids of models with different metallicities ranging from [M/H] = -2.0 to +1.0 dex. The grids range from 4000 to 10000 K in T_eff and from 2.0 to 5.0 dex in logg. The individual sets differ from each other and from previous ones essentially in the physics used for the treatment of the convective energy transport, in the higher vertical resolution of the atmospheres and in a finer grid in the (T_eff, logg) plane. These improvements enable the computation of derivatives of color indices accurate enough for pulsation mode identification. In addition, we show that the chosen vertical resolution is necessary and sufficient for the purpose of stellar interior modelling. To explain the physical differences between the model grids we provide a description of the currently available modifications of ATLAS9 according to their treatment of convection. Our critical analysis of the dependence of the atmospheric structure and observable quantities on convection treatment, vertical resolution and metallicity reveals that spectroscopic and photometric observations are best represented when using an inefficient convection treatment. This conclusion holds whatever convection formulation investigated here is used, i.e. MLT(alpha=0.5), CM and CGM are equivalent. We also find that changing the convection treatment can lead to a change in the effective temperature estimated from Stroemgren color indices from 200 to 400 K., Comment: 20 pages, 10 figures, accepted by A&A

The seismic data provided by the satellites CoRoT and Kepler enabled us to probe the internal rotation of thousands of evolved low-mass stars. Subsequently, several studies showed that current stellar evolution codes are unable to reproduce the low core rotation rates observed in these stars. These results indicate that an additional angular momentum transport process is necessary to counteract the spin up due to the core contraction during the post-main sequence evolution. For several candidates, the transport induced by internal gravity waves (IGW) could play a non-negligible role. In this work, we investigate the effect of IGW generated by penetrative convection on the internal rotation of low-mass stars from the subgiant branch to the beginning of the red giant branch. We show that IGW can efficiently counteract the contraction-driven spin up of the core of subgiant stars if the amplitude of the radial-differential rotation (between the center of the star and the top of the radiative zone) is higher than a threshold value. This threshold depends on the evolutionary stage and is comparable to the differential rotation rates inferred for a sample of subgiant stars observed by the satellite Kepler. Such an agreement can therefore be interpreted as the consequence of a regulation mechanism driven by IGW. This result is obtained under the assumption of a smooth rotation profile and holds true even if a wide range of values is considered for the parameters of the generation model. In contrast, on the red giant branch, we find that IGW remain insufficient, on their own, to explain the observations. We conclude that plume-induced IGW are able to efficiently extract angular momentum from the core of subgiant stars and accordingly have to be taken into account. On the red giant branch, another transport mechanism must likely be invoked., Accepted for publication in A&A, 22 pages

The PLATO (PLAnetary Transits and Oscillations of star) space project will observe about fifty percents of the sky with the main purpose of detecting, confirming and characterizing transiting exoplanets of (super)Earth sizes in the habitable zone of solar-like stars. Determining masses, radii and ages of exoplanets require the knowledge the masses, radii and ages of the host stars. We give a brief presentation of the main features of the mission. We then discuss some expected seismic performances of PLATO for characterizing bright solar-like stars, focusing on the challenging determination of accurate/precise stellar ages.