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The Planetary Transits and Oscillations of stars mission (PLATO) will allow us to measure surface rotation and monitor photometric activity of tens of thousands of main sequence solar-type and subgiant stars. This paper is the first of a series dedicated to the preparation of the analysis of stellar surface rotation and photospheric activity with the near-future PLATO data. We describe in this work the strategy that will be implemented in the PLATO pipeline to measure stellar surface rotation, photometric activity, and long-term modulations. The algorithms are applied on both noise-free and noisy simulations of solar-type stars, which include activity cycles, latitudinal differential rotation, and spot evolution. PLATO simulated systematics are included in the noisy light curves. We show that surface rotation periods can be recovered with confidence for most of the stars with only six months of observations and that the {recovery rate} of the analysis significantly improves as additional observations are collected. This means that the first PLATO data release will already provide a substantial set of measurements for this quantity, with a significant refinement on their quality as the instrument obtains longer light curves. Measuring the Schwabe-like magnetic activity cycle during the mission will require that the same field be observed over a significant timescale (more than four years). Nevertheless, PLATO will provide a vast and robust sample of solar-type stars with constraints on the activity-cycle length. Such a sample is lacking from previous missions dedicated to space photometry., Comment: 19 pages, 16 figures, accepted for publication in A&A

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., Comment: Accepted for publication in A&A. 23 pages, 2 figures

Asteroseismology is a powerful tool to infer fundamental stellar properties. The use of these asteroseismic-inferred properties in a growing number of astrophysical contexts makes it vital to understand their accuracy. Consequently, we performed a hare-and-hounds exercise where the hares simulated data for 6 artificial main-sequence stars and the hounds inferred their properties based on different inference procedures. To mimic a pipeline such as that planned for the PLATO mission, all hounds used the same model grid. Some stars were simulated using the physics adopted in the grid, others a different one. The maximum relative differences found (in absolute value) between the inferred and true values of the mass, radius, and age were 4.32 per cent, 1.33 per cent, and 11.25 per cent, respectively. The largest systematic differences in radius and age were found for a star simulated assuming gravitational settling, not accounted for in the model grid, with biases of -0.88 per cent (radius) and 8.66 per cent (age). For the mass, the most significant bias (-3.16 per cent) was found for a star with a helium enrichment ratio outside the grid range. Moreover, a ~7 per cent dispersion in age was found when adopting different prescriptions for the surface corrections or shifting the classical observations by $\pm 1\sigma$. The choice of the relative weight given to the classical and seismic constraints also impacted significantly the accuracy and precision of the results. Interestingly, only a few frequencies were required to achieve accurate results on the mass and radius. For the age the same was true when at least one $l=2$ mode was considered., Comment: Accepted for publication in the Monthly Notices of the Royal Astronomical Society

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., Comment: Paper accepted for publication in A&A. 18 pages (12 without Appendices), 1 figure. Typos corrected

The use of the full potential of stellar seismology is made difficult by the improper modeling of the upper-most layers of solar-like stars and their influence on the modeled frequencies. Our knowledge on these \emph{surface effects} has improved thanks to the use of 3D hydrodynamical simulations but the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure: the reduced-$\Gamma_1$ model (RGM) and the gas-$\Gamma_1$ model (GGM). Starting from the fully compressible turbulence equations, we derive both the GGM and RGM models using a closure to model the flux of turbulent kinetic energy. It is found that both models originate from two terms: the source of turbulent pressure due to compression produced by the oscillations and the divergence of the flux of turbulent pressure. It is also demonstrated that they are both compatible with the adiabatic approximation but also imply a number of questionable assumptions mainly regarding mode physics. Among others hypothesis, one has to neglect the Lagrangian perturbation of the dissipation of turbulent kinetic energy into heat and the Lagrangian perturbation of buoyancy work., Comment: 7 pages, 1 figure. Accepted as a Letter in Astronomy and Astrophysic

The development of space-borne missions has significantly improved the quality of the measured spectra of solar-like oscillators. Their $p$-mode line profiles can now be resolved, and the asymmetries inferred for a variety of stars other than the Sun. However, it has been known for a long time that the asymmetries of solar $p$-modes are reversed between the velocity and the intensity spectra. Understanding the origin of this reversal is necessary in order to use asymmetries as a tool for seismic diagnosis. For stars other than the Sun, only the intensity power spectrum is sufficiently resolved to allow for an estimation of mode asymmetries. We recently developed an approach designed to model and predict these asymmetries in the velocity power spectrum of the Sun and to successfully compare them to their observationally derived counterparts. In this paper we expand our model and predict the asymmetries featured in the intensity power spectrum. We find that the shape of the mode line profiles in intensity is largely dependent on how the oscillation-induced variations of the radiative flux are treated, and that modelling it realistically is crucial to understanding asymmetry reversal. Perturbing a solar-calibrated grey atmosphere model, and adopting the quasi-adiabatic framework as a first step, we reproduce the asymmetries observed in the solar intensity spectrum for low-frequency modes. We conclude that, unlike previously thought, it is not necessary to invoke an additional mechanism (e.g. non-adiabatic effects, coherent non-resonant background signal) to explain asymmetry reversal. This additional mechanism is necessary, however, to explain asymmetry reversal for higher-order modes., Comment: 9 pages, 4 figures. Accepted for publication in A&A

In this paper, we aim to develop a predictive model for solar radial $p$-mode line profiles in the velocity spectrum. Unlike the approach favoured by prior studies, this model is not described by free parameters and we do not use fitting procedures to match the observations. Instead, we use an analytical turbulence model coupled with constraints extracted from a 3D hydrodynamic simulation of the solar atmosphere. We then compare the resulting asymmetries with their observationally derived counterpart. We find that stochastic excitation localised beneath the mode upper turning point generates negative asymmetry for $\nu < \nu_\text{max}$ and positive asymmetry for $\nu > \nu_\text{max}$. On the other hand, stochastic excitation localised above this limit generates negative asymmetry throughout the $p$-mode spectrum. As a result of the spatial extent of the source of excitation, both cases play a role in the total observed asymmetries. By taking this spatial extent into account and using a realistic description of the spectrum of turbulent kinetic energy, both a qualitative and quantitative agreement can be found with solar observations perfoemed by the GONG network. We also find that the impact of the correlation between acoustic noise and oscillation is negligible for mode asymmetry in the velocity spectrum., Comment: 26 pages (19 without appendices), 14 figures. Accepted for publication in A&A

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

Space-borne missions CoRoT and Kepler have provided a rich harvest of high-quality photometric data for solar-like pulsators. It is now possible to measure damping rates for hundreds of main-sequence and thousands of red-giant. However, among the seismic parameters, mode damping rates remain poorly understood and thus barely used for inferring the physical properties of stars. Previous approaches to model mode damping rates were based on mixing-length theory or a Reynolds-stress approach to model turbulent convection. While able to grasp the main physics of the problem, those approaches are of little help to provide quantitative estimates as well as a definitive answer on the relative contribution of each physical mechanism. Our aim is thus to assess the ability of 3D hydrodynamical simulations to infer the physical mechanisms responsible for damping of solar-like oscillations. To this end, a solar high-spatial resolution and long-duration hydrodynamical 3D simulation computed with the ANTARES code allows probing the coupling between turbulent convection and the normal modes of the simulated box. Indeed, normal modes of the simulation experience realistic driving and damping in the super-adiabatic layers of the simulation. Therefore, investigating the properties of the normal modes in the simulation provides a unique insight into the mode physics. We demonstrate that such an approach provides constraints on the solar damping rates and is able to disentangle the relative contribution related to the perturbation of the turbulent pressure, the gas pressure, the radiative flux, and the convective flux contributions. Finally, we conclude that using the normal modes of a 3D numerical simulation is possible and is potentially able to unveil the respective role of the different physical mechanisms responsible for mode damping provided the time-duration of the simulation is long enough., Comment: Accepted in A&A, 15 pages, and 13 figures

The preparation of science objectives of the ESA's PLATO space mission will require the implementation of hare-and-hound exercises relying on the massive generation of representative simulated light-curves. We developed a light-curve simulator named the PLATO Solar-like Light-curve Simulator (PSLS) in order to generate light-curves representative of typical PLATO targets, i.e. showing simultaneously solar-like oscillations, stellar granulation, and magnetic activity. At the same time, PSLS also aims at mimicking in a realistic way the random noise and the systematic errors representative of the PLATO multi-telescope concept. To quantify the instrumental systematic errors, we performed a series of simulations at pixel level that include various relevant sources of perturbations expected for PLATO. From the simulated pixels, we extract the photometry as planned on-board. The simulated light-curves are then corrected for instrumental effects using the instrument Point Spread Functions reconstructed on the basis of a microscanning technique that will be operated during the in-flight calibration phases. These corrected light-curves are then fitted by a parametric model, which we incorporated in PSLS. We show that the instrumental systematic errors dominate the signal only at frequencies below 20muHz and are found to mainly depend on stellar magnitude and on the detector charge transfer inefficiency. To illustrate how realistic our simulator is, we compared its predictions with observations made by Kepler on three typical targets and found a good qualitative agreement with the observations. PSLS reproduces the main properties of expected PLATO light-curves. Its speed of execution and its inclusion of relevant stellar signals as well as sources of noises representative of the PLATO cameras make it an indispensable tool for the scientific preparation of the PLATO mission., Comment: 19 pages, 16 figures, Astronomy & Astrophysics (in press)

The CoRoT and Kepler missions provided a wealth of high-quality data for solar-like oscillations. To make the best of such data for seismic inferences, we need theoretical models with precise near-surface structure, which has significant influence on solar-like oscillation frequencies. The mixing-length parameter, $\alpha$, is a key factor for the near-surface structure. In the convection formulations used in evolution codes, the $\alpha$ is a free parameter that needs to be properly specified. We calibrated $\alpha$ values by matching entropy profiles of 1D envelope models with those of 3D CO$^5$BOLD models. For such calibration, previous works concentrated on the classical mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence (FST) models. For the atmosphere part in the 1D models, we use the Eddington grey $T(\tau)$ relation and the one with the solar-calibrated Hopf-like function. For both the MLT and FST models with a mixing length $l=\alpha H_p$, calibrated $\alpha$ values increase with increasing $g$ or decreasing $T_{\rm eff}$. For the FST models, we also calibrated values of $\alpha^*$ defined as $l=r_{\rm top}-r+\alpha^*H_{p,{\rm top}}$. $\alpha^*$ is found to increase with $T_{\rm eff}$ and $g$. As for the correspondence to the 3D models, the solar Hopf-like function gives a photospheric-minimum entropy closer to a 3D model than the Eddington $T(\tau)$. The structure below the photosphere depends on the convection model. However, not a single convection model gives the best correspondence since the averaged 3D quantities are not necessarily related via an EOS. Although the FST models with $l=r_{\rm top}-r+\alpha^*H_{p,{\rm top}}$ are found to give the frequencies closest to the solar observed ones, a more appropriate treatment of the top part of the 1D convective envelope is necessary., Comment: 14 pages, 18 figures, accepted to Astronomy and Astrophysics

The CoRoT and Kepler missions have provided high-quality measurements of the frequency spectra of solar-like pulsators, enabling us to probe stellar interiors with a very high degree of accuracy by comparing the observed and modeled frequencies. However, the frequencies computed with 1D models suffer from systematic errors related to the poor modeling of the uppermost layers of stars. These biases are what is commonly named the near surface effect. The dominant effect is related to the turbulent pressure that modifies the hydrostatic equilibrium and thus the frequencies. This has already been investigated using grids of 3D RMHD simulations, which also were used to constrain the parameters of the empirical correction models. However, the effect of metallicity has not been considered so far. We study the impact of metallicity on the surface effect across the HR diagram, and provide a method for accounting for it when using the empirical correction models. We computed a grid of patched 1D stellar models with the stellar evolution code CESTAM in which poorly modeled surface layers have been replaced by averaged stratification computed with the 3D RMHD code CO5BOLD. We found that metallicity has a strong impact on the surface effect: keeping T_eff and log g constant, the frequency residuals can vary by up to a factor two. Therefore, the influence of metallicity cannot be neglected. We found that a correct way of accounting for it is to consider the surface Rosseland mean opacity. It allowed us to give a physically-grounded justification as well as a scaling relation for the frequency differences at nu_max as a function of T_eff, log g and kappa. Finally, we provide prescriptions for the fitting parameters of the correction functions. We show that the impact of metallicity through the Rosseland mean opacity must be taken into account when studying and correcting the surface effect., Comment: 15 pages, 7 figures. Accepted for publication in A&A

First-ascent red giants with masses below about $2\,M_\odot$ ignite helium in their degenerate core as a flash. Stellar evolution codes predict that the He flash consists of a series of consecutive subflashes. The detection of mixed modes in red giants from space missions CoRoT and Kepler has opened new opportunities to search for stars in this evolution stage. During a subflash, the He burning shell is convective, which splits the cavity of gravity modes in two. We here investigate how this additional cavity modifies the oscillation spectrum of the star. We calculate the asymptotic mode frequencies of stellar models going through a He subflash using the JWKB approximation. To predict the detectability of the modes, we estimate their expected heights, taking into account the effects of radiative damping in the core. Our results are then compared to the oscillation spectra obtained by calculating numerically the mode frequencies during a He subflash. We show that during a He subflash, the detectable oscillation spectrum mainly consists of modes trapped in the acoustic cavity and in the outer g-mode cavity. The spectrum should thus resemble that of a core-helium-burning giant. However, we find a list of clear, detectable features that could enable us to identify red giants passing through a He subflash. In particular, during a He subflash, several modes that are trapped in the innermost g-mode cavity are expected to be detectable. We show that these modes could be identified by their frequencies or by their rotational splittings. Other features, such as the measured period spacing of gravity modes or the location of the H-burning shell within the g-mode cavity could also be used to identify stars going through a He subflash. The features derived in this study can now be searched for in the large datasets provided by the CoRoT and Kepler missions., Comment: 25 pages, 20 figures, accepted in A&A

Oscillation modes with a mixed character, as observed in evolved low-mass stars, are highly sensitive to the physical properties of the innermost regions. Measuring their properties is therefore extremely important to probe the core, but requires some care, due to the complexity of the mixed-mode pattern. This work aims at providing a consistent description of the mixed-mode pattern of low-mass stars, based on the asymptotic expansion. We also aim at studying the variation of the gravity offset $\varepsilon_{g}$ with stellar evolution. We revisit previous work about mixed modes in red giants and empirically test how period spacings, rotational splittings, mixed-mode widths and heights can be estimated in a consistent view, based on the properties of the mode inertia ratios. From the asymptotic fit of the mixed-mode pattern of a large set of red giants at various evolutionary stages, we derive unbiased and precise asymptotic parameters. As the asymptotic expansion of gravity modes is verified with a precision close to the frequency resolution for stars on the red giant branch (10$^{-4}$ in relative values), we can derive accurate values of the asymptotic parameters. We decipher the complex pattern in a rapidly rotating star, and explain how asymmetrical splittings can be inferred, as well as the stellar inclinations. This allows us to revisit the stellar inclinations in two open clusters, NGC 6819 and NGC 6791: our results show that the stellar inclinations in these clusters do not have privileged orientation in the sky. The variation of the asymptotic gravity offset along with stellar evolution is investigated in detail. We also derive generic properties that explain under which conditions mixed modes can be observed., Comment: Accepted in A&A, AA/2018/32777

Context: the space-borne missions CoRoT and Kepler have provided photometric observations of unprecedented quality. The study of solar-like oscillations observed in red giant stars by these satellites allows a better understanding of the different physical processes occurring in their interiors. In particular, the study of the mode excitation and damping is a promising way to improve our understanding of stellar physics that has, so far, been performed only on a limited number of targets. Aims: the recent asteroseismic characterization of the evolutionary status for a large number of red giants allows us to study the physical processes acting in the interior of red giants and how they are modify during stellar evolution. In this work, we aim to obtain information on the excitation and damping of pressure modes through the measurement of the stars' pressure mode widths and amplitudes and to analyze how they are modified with stellar evolution. The objective is to bring observational constraints on the modeling of the physical processes behind mode excitation and damping. Methods: we fit the frequency spectra of red giants with well defined evolutionary status using Lorentzians functions to derive the pressure mode widths and amplitudes. To strengthen our conclusions, we used two different fitting techniques. Results: pressure mode widths and amplitudes were determined for more than 5000 red giants. With a stellar sample two orders of magnitude larger than previous results, we confirmed that the mode width depends on stellar evolution and varies with stellar effective temperature. In addition, we discovered that the mode width depends on stellar mass. We also confirmed observationally the influence of the stellar metallicity on the mode amplitudes, as predicted by models., Comment: 13 pages, 21 figures, 4 tables

Oscillation properties are usually measured by fitting symmetric Lorentzian profiles to the power spectra of Sun-like stars. However the line profiles of solar oscillations have been observed to be asymmetrical for the Sun. The physical origin of this line asymmetry is not fully understood, although it should depend on the depth dependence of the source of wave excitation (convective turbulence) and details of the observable (velocity or intensity). For oscillations of the Sun, it has been shown that neglecting the asymmetry leads to systematic errors in the frequency determination. This could subsequently affects the results of seismic inferences of the solar internal structure. Using light curves from the {\it Kepler} spacecraft we have measured mode asymmetries in 43 stars. We confirm that neglecting the asymmetry leads to systematic errors that can exceed the $1\sigma$ confidence intervals for seismic observations longer than one year. Therefore, the application of an asymmetric Lorentzian profile is to be favoured to improve the accuracy of the internal stellar structure and stellar fundamental parameters. We also show that the asymmetry changes sign between cool Sun-like stars and hotter stars. This provides the best constraints to date on the location of the excitation sources across the Hertzsprung-Russel diagram., Comment: 8 pages, 7 Figures, 1 Table, Accepted to ApJ

Turbulent convection is certainly one of the most important and thorny issues in stellar physics. Our deficient knowledge of this crucial physical process introduces a fairly large uncertainty concerning the internal structure and evolution of stars. A striking example is overshoot at the edge of convective cores. Indeed, nearly all stellar evolutionary codes treat the overshooting zones in a very approximative way that considers both its extent and the profile of the temperature gradient as free parameters. There are only a few sophisticated theories of stellar convection such as Reynolds stress approaches, but they also require the adjustment of a non-negligible number of free parameters. We present here a theory, based on the plume theory as well as on the mean-field equations, but without relying on the usual Taylor's closure hypothesis. It leads us to a set of eight differential equations plus a few algebraic ones. Our theory is essentially a non-mixing length theory. It enables us to compute the temperature gradient in a shrinking convective core and its overshooting zone. The case of an expanding convective core is also discussed, though more briefly. Numerical simulations have quickly improved during recent years and enabling us to foresee that they will probably soon provide a model of convection adapted to the computation of 1D stellar models., Comment: Accepted in A&A, 17 pages

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

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., Comment: Accepted for publication in A&A, 22 pages

The space-borne missions have provided a wealth of highly accurate data. However, our inability to properly model the upper-most region of solar-like stars prevents us from making the best of these observations. This problem is called "surface effect" and a key ingredient to solve it is turbulent pressure for the computation of both the equilibrium models and the oscillations. While 3D hydrodynamic simulations help to include properly the turbulent pressure in the equilibrium models, the way this surface effect is included in the computation of stellar oscillations is still subject to uncertainties. We aim at determining how to properly include the effect of turbulent pressure and its Lagrangian perturbation in the adiabatic computation of the oscillations. We also discuss the validity of the gas-gamma model (GGM) and reduced gamma model (RGM) approximations, which have been used to compute adiabatic oscillations of equilibrium models including turbulent pressure. We use a patched model of the Sun with an inner part constructed by a 1D stellar evolution code (CESTAM) and an outer part by the 3D hydrodynamical code (CO$^5$BOLD). Then, the adiabatic oscillations are computed using the ADIPLS code for the GGM and RGM and with the MAD code imposing the adiabatic condition on an existing time-dependent convection (TDC) formalism. We show that the computation of the oscillations using the TDC formalism in the adiabatic limit improves significantly the agreement with the observed frequencies compared to the GGM and RGM. Of the components of the turbulent pressure perturbation, the perturbation of the density and advection term is found to contribute most to the frequency shift. We propose a formalism to evaluate the frequency shift due to the inclusion of the term with the turbulent pressure perturbation in the variational principle in order to extrapolate our result to other stars., Comment: 11 pages, 7 figures, accepted for publication in Astronomy and Astrophysics

The power of asteroseismology relies on the capability of global oscillations to infer the stellar structure. For evolved stars, we benefit from unique information directly carried out by mixed modes that probe their radiative cores. This third article of the series devoted to mixed modes in red giants focuses on their coupling factors that remained largely unexploited up to now. With the measurement of the coupling factors, we intend to give physical constraints on the regions surrounding the radiative core and the hydrogen-burning shell of subgiants and red giants. A new method for measuring the coupling factor of mixed modes is set up. It is derived from the method recently implemented for measuring period spacings. It runs in an automated way so that it can be applied to a large sample of stars. Coupling factors of mixed modes were measured for thousands of red giants. They show specific variation with mass and evolutionary stage. Weak coupling is observed for the most evolved stars on the red giant branch only; large coupling factors are measured at the transition between subgiants and red giants, as well as in the red clump. The measurement of coupling factors in dipole mixed modes provides a new insight into the inner interior structure of evolved stars. While the large frequency separation and the asymptotic period spacings probe the envelope and the core, respectively, the coupling factor is directly sensitive to the intermediate region in between and helps determining its extent. Observationally, the determination of the coupling factor is a prior to precise fits of the mixed-mode pattern, and can now be used to address further properties of the mixed-mode pattern, as the signature of the buoyancy glitches and the core rotation., Comment: Accepted in A&A

Seismic observations have shown that a number of evolved stars exhibit low-amplitude dipole modes, which are referred to as depressed modes. Recently, these low amplitudes have been attributed to the presence of a strong magnetic field in the stellar core of those stars. We intend to study the properties of depressed modes in evolved stars, which is a necessary condition before concluding on the physical nature of the mechanism responsible for the reduction of the dipole mode amplitudes. We perform a thorough characterization of the global seismic parameters of depressed dipole modes and show that these modes have a mixed character. The observation of stars showing dipole mixed modes that are depressed is especially useful for deriving model-independent conclusions on the dipole mode damping. Observations prove that depressed dipole modes in red giants are not pure pressure modes but mixed modes. This result invalidates the hypothesis that the depressed dipole modes result from the suppression of the oscillation in the radiative core of the stars. Observations also show that, except for the visibility, the seismic properties of the stars with depressed modes are equivalent to those of normal stars. The mixed nature of the depressed modes in red giants and their unperturbed global seismic parameters carry strong constraints on the physical mechanism responsible for the damping of the oscillation in the core. This mechanism is able to damp the oscillation in the core but cannot fully suppress it. Moreover, it cannot modify the radiative cavity probed by the gravity component of the mixed modes. The recent mechanism involving high magnetic field proposed for explaining depressed modes is not compliant with the observations and cannot be used to infer the strength and the prevalence of high magnetic fields in red giants., Comment: accepted in A&A

The rich harvest of seismic observations over the past decade provides evidence of angular momentum redistribution in stellar interiors that is not reproduced by current evolution codes. In this context, transport by internal gravity waves can play a role and could explain discrepancies between theory and observations. The efficiency of the transport of angular momentum by waves depends on their driving mechanism. While excitation by turbulence throughout the convective zone has already been investigated, we know that penetrative convection into the stably stratified radiative zone can also generate internal gravity waves. Therefore, we aim at developing a semianalytical model to estimate the generation of IGW by penetrative plumes below an upper convective envelope. We derive the wave amplitude considering the pressure exerted by an ensemble of plumes on the interface between the radiative and convective zones as source term in the equation of momentum. We consider the effect of a thermal transition from a convective gradient to a radiative one on the transmission of the wave into the radiative zone. The plume-induced wave energy flux at the top of the radiative zone is computed for a solar model and is compared to the turbulence-induced one. We show that, for the solar case, penetrative convection generates waves more efficiently than turbulence and that plume-induced waves can modify the internal rotation rate on shorter time scales. We also show that a smooth thermal transition significatively enhances the wave transmission compared to the case of a steep transition. We conclude that driving by penetrative convection must be taken into account as much as turbulence-induced waves for the transport of internal angular momentum., Comment: Accepted for publication in A&A, 21 pages

A leap forward has been performed due to the space-borne missions, MOST, CoRoT and Kepler. They provided a wealth of observational data, and more precisely oscillation spectra, which have been (and are still) exploited to infer the internal structure of stars. While an adiabatic approach is often sufficient to get information on the stellar equilibrium structures it is not sufficient to get a full understanding of the physics of the oscillation. Indeed, it does not permit one to answer some fundamental questions about the oscillations, such as: What are the physical mechanisms responsible for the pulsations inside stars? What determines the amplitudes? To what extent the adiabatic approximation is valid? All these questions can only be addressed by considering the energy exchanges between the oscillations and the surrounding medium. This lecture therefore aims at considering the energetical aspects of stellar pulsations with particular emphasis on the driving and damping mechanisms. To this end, the full non-adiabatic equations are introduced and thoroughly discussed. Two types of pulsation are distinguished, namely the self-excited oscillations that result from an instability and the solar-like oscillations that result from a balance between driving and damping by turbulent convection. For each type, the main physical principles are presented and illustrated using recent observations obtained with the ultra-high precision photometry space-borne missions (MOST, CoRoT and Kepler). Finally, we consider in detail the physics of scaling relations, which relates the seismic global indices with the global stellar parameters and gave birth to the development of statistical (or ensemble) asteroseismology. Indeed, several of these relations rely on the same cause: the physics of non-adiabatic oscillations., Comment: 90 pages, 36 pages, lectures notes, Ecole Evry Schatzman 2014 : asteroseismology and next generation stellar models, 28 Sep-3 Oct 2014 Roscoff (France)

The space-borne missions have provided us with a wealth of high-quality observational data that allows for seismic inferences of stellar interiors. This requires the computation of precise and accurate theoretical frequencies, but imperfect modeling of the uppermost stellar layers introduces systematic errors. To overcome this problem, an empirical correction has been introduced by Kjeldsen et al. (2008, ApJ, 683, L175) and is now commonly used for seismic inferences. Nevertheless, we still lack a physical justification allowing for the quantification of the surface-effect corrections. We used a grid of these simulations computed with the CO$^5$BOLD code to model the outer layers of solar-like stars. Upper layers of the corresponding 1D standard models were then replaced by the layers obtained from the horizontally averaged 3D models. The frequency differences between these patched models and the 1D standard models were then calculated using the adiabatic approximation and allowed us to constrain the Kjeldsen et al. power law, as well as a Lorentzian formulation. We find that the surface effects on modal frequencies depend significantly on both the effective temperature and the surface gravity. We further provide the variation in the parameters related to the surface-effect corrections using their power law as well as a Lorentzian formulation. Scaling relations between these parameters and the elevation (related to the Mach number) is also provided. The Lorentzian formulation is shown to be more robust for the whole frequency spectrum, while the power law is not suitable for the frequency shifts in the frequency range above $\nu_{\rm max}$., Comment: 11 pages, 14 figures, 4 tables; accepted for publication in Astronomy & Astrophysics

Asteroseismology allows us to probe the physical conditions inside the core of red giant stars. This relies on the properties of the global oscillations with a mixed character that are highly sensitive to the physical properties of the core. However, overlapping rotational splittings and mixed-mode spacings result in complex structures in the mixed-mode pattern, which severely complicates its identification and the measurement of the asymptotic period spacing. This work aims at disentangling the rotational splittings from the mixed-mode spacings, in order to open the way to a fully automated analysis of large data sets. An analytical development of the mixed-mode asymptotic expansion is used to derive the period spacing between two consecutive mixed modes. The \'echelle diagrams constructed with the appropriately stretched periods are used to exhibit the structure of the gravity modes and of the rotational splittings. We propose a new view on the mixed-mode oscillation pattern based on corrected periods, called stretched periods, that mimic the evenly spaced gravity-mode pattern. This provides a direct understanding of all oscillation components, even in the case of rapid rotation. The measurement of the asymptotic period spacing and the signature of the structural glitches on mixed modes are then made easy. This work opens the possibility to derive all seismic global parameters in an automated way, including the identification of the different rotational multiplets and the measurement of the rotational splitting, even when this splitting is significantly larger than the period spacing. Revealing buoyancy glitches provides a detailed view on the radiative core., Comment: Accepted in A&A

The space-borne missions CoRoT and Kepler have provided a large amount of precise photometric data. Among the stars observed, red giants show a rich oscillation pattern that allows their precise characterization. Long-duration observations allow for investigating the fine structure of this oscillation pattern. A common pattern of oscillation frequency was observed in red giant stars, which corresponds to the second-order development of the asymptotic theory. This pattern, called the universal red giant oscillation pattern, describes the frequencies of stellar acoustic modes. We aim to investigate the deviations observed from this universal pattern, thereby characterizing them in terms of the location of the second ionization zone of helium. We also show how this seismic signature depends on stellar evolution. We measured the frequencies of radial modes with a maximum likelihood estimator method, then we identified a modulation corresponding to the departure from the universal oscillation pattern. We identify the modulation component of the radial mode frequency spacings in more than five hundred red giants. The variation in the modulation that we observe at different evolutionary states brings new constraints on the interior models for these stars. We also derive an updated form of the universal pattern that accounts for the modulation and provides highly precise radial frequencies., Comment: 10 pages, 9 figures, accepted by A&A. AA/2014/25064

The detection of mixed modes in subgiants and red giants by the CoRoT and \emph{Kepler} space-borne missions allows us to investigate the internal structure of evolved low-mass stars. In particular, the measurement of the mean core rotation rate as a function of the evolution places stringent constraints on the physical mechanisms responsible for the angular momentum redistribution in stars. It showed that the current stellar evolution codes including the modelling of rotation fail to reproduce the observations. An additional physical process that efficiently extracts angular momentum from the core is thus necessary. Our aim is to assess the ability of mixed modes to do this. To this end, we developed a formalism that provides a modelling of the wave fluxes in both the mean angular momentum and the mean energy equations in a companion paper. In this article, mode amplitudes are modelled based on recent asteroseismic observations, and a quantitative estimate of the angular momentum transfer is obtained. This is performed for a benchmark model of 1.3 $M_{\odot}$ at three evolutionary stages, representative of the evolved pulsating stars observed by CoRoT and Kepler. We show that mixed modes extract angular momentum from the innermost regions of subgiants and red giants. However, this transport of angular momentum from the core is unlikely to counterbalance the effect of the core contraction in subgiants and early red giants. In contrast, for more evolved red giants, mixed modes are found efficient enough to balance and exceed the effect of the core contraction, in particular in the hydrogen-burning shell. Our results thus indicate that mixed modes are a promising candidate to explain the observed spin-down of the core of evolved red giants, but that an other mechanism is to be invoked for subgiants and early red giants., Comment: Accepted in A&A, 7 pages, 8 figures

Seismic observations by the space-borne mission \emph{Kepler} have shown that the core of red giant stars slows down while evolving, requiring an efficient physical mechanism to extract angular momentum from the inner layers. Current stellar evolution codes fail to reproduce the observed rotation rates by several orders of magnitude, and predict a drastic spin-up of red giant cores instead. New efficient mechanisms of angular momentum transport are thus required. In this framework, our aim is to investigate the possibility that mixed modes extract angular momentum from the inner radiative regions of evolved low-mass stars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism, introduced by Andrews \& McIntyre (1978), that allows us to consider the combined effect of both the wave momentum flux in the mean angular momentum equation and the wave heat flux in the mean entropy equation as well as their interplay with the meridional circulation. In radiative layers of evolved low-mass stars, the quasi-adiabatic approximation, the limit of slow rotation, and the asymptotic regime can be applied for mixed modes and enable us to establish a prescription for the wave fluxes in the mean equations. The formalism is finally applied to a $1.3 M_\odot$ benchmark model, representative of observed CoRoT and \emph{Kepler} oscillating evolved stars. We show that the influence of the wave heat flux on the mean angular momentum is not negligible and that the overall effect of mixed modes is to extract angular momentum from the innermost region of the star. A quantitative and accurate estimate requires realistic values of mode amplitudes. This is provided in a companion paper., Comment: Accepted in A&A, 11 pages, and 6 figures

The detection of oscillations with a mixed character in subgiants and red giants allows us to probe the physical conditions in their cores. With these mixed modes, we aim at determining seismic markers of stellar evolution. Kepler asteroseismic data were selected to map various evolutionary stages and stellar masses. Seismic evolutionary tracks were then drawn with the combination of the frequency and period spacings. We measured the asymptotic period spacing for more than 1170 stars at various evolutionary stages. This allows us to monitor stellar evolution from the main sequence to the asymptotic giant branch and draw seismic evolutionary tracks. We present clear quantified asteroseismic definitions that characterize the change in the evolutionary stages, in particular the transition from the subgiant stage to the early red giant branch, and the end of the horizontal branch.The seismic information is so precise that clear conclusions can be drawn independently of evolution models. The quantitative seismic information can now be used for stellar modeling, especially for studying the energy transport in the helium-burning core or for specifying the inner properties of stars entering the red or asymptotic giant branches. Modeling will also allow us to study stars that are identified to be in the helium-subflash stage, high-mass stars either arriving or quitting the secondary clump, or stars that could be in the blue-loop stage., Comment: Accepted In A&A (Letter) 5 pages

CoRoT and Kepler observations of red giant stars revealed very rich spectra of non-radial solar-like oscillations. Of particular interest was the detection of mixed modes that exhibit significant amplitude, both in the core and at the surface of the stars. It opens the possibility of probing the internal structure from their inner-most layers up to their surface along their evolution on the red giant branch as well as on the red-clump. Our objective is primarily to provide physical insight into the physical mechanism responsible for mixed-modes amplitudes and lifetimes. Subsequently, we aim at understanding the evolution and structure of red giants spectra along with their evolution. The study of energetic aspects of these oscillations is also of great importance to predict the mode parameters in the power spectrum. Non-adiabatic computations, including a time-dependent treatment of convection, are performed and provide the lifetimes of radial and non-radial mixed modes. We then combine these mode lifetimes and inertias with a stochastic excitation model that gives us their heights in the power spectra. For stars representative of CoRoT and Kepler observations, we show under which circumstances mixed modes have heights comparable to radial ones. We stress the importance of the radiative damping in the determination of the height of mixed modes. Finally, we derive an estimate for the height ratio between a g-type and a p-type mode. This can thus be used as a first estimate of the detectability of mixed-modes.

Solar-like oscillations have been observed by Kepler and CoRoT in many solar-type stars, thereby providing a way to probe the stars using asteroseismology. We provide the mode linewidths and mode heights of the oscillations of various stars as a function of frequency and of effective temperature. We used a time series of nearly two years of data for each star. The 23 stars observed belong to the simple or F-like category. The power spectra of the 23 main-sequence stars were analysed using both maximum likelihood estimators and Bayesian estimators, providing individual mode characteristics such as frequencies, linewidths, and mode heights. We study the source of systematic errors in the mode linewidths and mode heights, and we present a way to correct these errors with respect to a common reference fit. Using the correction, we could explain all sources of systematic errors, which could be reduced to less than $\pm$15% for mode linewidths and heights, and less than $\pm$5% for amplitude, when compared to the reference fit. The effect of a different estimated stellar background and a different estimated splitting will provide frequency-dependent systematic errors that might affect the comparison with theoretical mode linewidth and mode height, therefore affecting the understanding of the physical nature of these parameters. All other sources of relative systematic errors are less dependent upon frequency. We also provide the dependence of the so-called linewidth dip, in the middle of the observed frequency range, as a function of effective temperature. We show that the depth of the dip decreases with increasing effective temperature. The dependence of the dip on effective temperature may imply that the mixing length parameter $\alpha$ or the convective flux may increase with effective temperature., Comment: Accepted by A&A, 38 pages, 35 figures, 26 tables

Asteroseismology of evolved solar-like stars is experiencing a growing interest due to the wealth of observational data from space-borne instruments such as the \emph{CoRoT} and \emph{Kepler} spacecraft. In particular, the recent detection of mixed modes, which probe both the innermost and uppermost layers of stars, paves the way for inferring the internal structure of stars along their evolution through the subgiant and red giant phases. Mixed modes can also place stringent constraints on the physics of such stars and on their global properties (mass, age, etc...). Here, using two \emph{Kepler} stars (KIC 4351319 and KIC 6442183), we demonstrate that measurements of mixed mode characteristics allow us to estimate the mode inertias, providing a new and additional diagnostics on the mode trapping and subsequently on the internal structure of evolved stars. We however stress that the accuracy may be sensitive to non-adiabatic effects., Comment: ApJ Letter

The space-borne missions CoRoT and Kepler are indiscreet. With their asteroseismic programs, they tell us what is hidden deep inside the stars. Waves excited just below the stellar surface travel throughout the stellar interior and unveil many secrets: how old is the star, how big, how massive, how fast (or slow) its core is dancing. This paper intends to \emph{paparazze} the red giants according to the seismic pictures we have from their interiors., Comment: SF2A 2013 conference

Solar-like oscillations in red giants have been investigated with CoRoT and Kepler, while pulsations in more evolved M giants have been studied with ground-based microlensing surveys. After 3.1 years of observation with Kepler, it is now possible to make a link between these different observations of semi-regular variables. We aim to identify period-luminosity sequences in evolved red giants identified as semi-regular variables. Then, we investigate the consequences of the comparison of ground-based and space-borne observations. We have first measured global oscillation parameters of evolved red giants observed with Kepler with the envelope autocorrelation function method. We then used an extended form of the universal red giant oscillation pattern, extrapolated to very low frequency, to fully identify their oscillations. From the link between red giant oscillations observed by Kepler and period-luminosity sequences, we have identified these relations in evolved red giants as radial and non-radial solar-like oscillations. We were able to expand scaling relations at very low frequency. This helped us to identify the different sequences of period-luminosity relations, and allowed us to propose a calibration of the K magnitude with the observed frequency large separation. Interpreting period-luminosity relations in red giants in terms of solar-like oscillations allows us to investigate, with a firm physical basis, the time series obtained from ground-based microlensing surveys. This can be done with an analytical expression that describes the low-frequency oscillation spectra. The different behavior of oscillations at low frequency, with frequency separations scaling only approximately with the square root of the mean stellar density, can be used to address precisely the physics of the semi-regular variables., Comment: Accepted in A&A

PLATO 2.0 has recently been selected for ESA's M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, including potentially habitable planets? The PLATO 2.0 instrument consists of 34 small aperture telescopes (32 with 25 sec readout cadence and 2 with 2.5 sec candence) providing a wide field-of-view (2232 deg2) and a large photometric magnitude range (4-16 mag). It focusses on bright (4-11 mag) stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for these bright stars to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2%, 4-10% and 10% for planet radii, masses and ages, respectively. The planned baseline observing strategy includes two long pointings (2-3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50% of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include terrestrial planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0., Comment: 63 pages, 17 figures, submitted to Experimental Astronomy (ExA)

The solar granulation is known for a long time to be a surface manifestation of convection. Thanks to the current space-borne missions CoRoT and Kepler, it is now possible to observe in disk-integrated intensity the signature of this phenomena in a growing number of stars. The space-based photometric measurements show that the global brightness fluctuations and the lifetime associated with granulation obeys characteristic scaling relations. We thus aim at providing a simple theoretical modeling to reproduce these scaling relations and subsequently at inferring the physical properties of granulation properties across the HR diagram. We develop a simple 1D theoretical model that enable us to test any prescription concerning the time-correlation between granules. The input parameters of the model are extracted from 3D hydrodynamical models of the surface layers of stars, and the free parameters involved in the model are calibrated with solar observations. Two different prescriptions for representing the eddy time-correlation in the Fourier space are compared: a Lorentzian and an exponential form. Finally, we compare our theoretical prediction with a 3D radiative hydrodynamical (RHD) numerical modeling of stellar granulation (ab-initio approach). Provided that the free parameters are appropriately adjusted, our theoretical model satisfactorily reproduces the shape and the amplitude of the observed solar granulation spectrum. The best agreement is obtained with an exponential form. Furthermore, our theoretical model results in granulation spectra that consistently agree with the these calculated on the basis of the ab-initio approach with two 3D RHD models. Comparison between theoretical granulation spectra calculated with the present model and high precision photometry measurements of stellar granulation is undertaken in a companion paper., Comment: 10 pages, 2 figures, accepted for publication in A&A

A large set of stars observed by CoRoT and Kepler shows clear evidence for the presence of a stellar background, which is interpreted to arise from surface convection, i.e., granulation. These observations show that the characteristic time-scale (tau_eff) and the root-mean-square (rms) brightness fluctuations (sigma) associated with the granulation scale as a function of the peak frequency (nu_max) of the solar-like oscillations. We aim at providing a theoretical background to the observed scaling relations based on a model developed in the companion paper. We computed for each 3D model the theoretical power density spectrum (PDS) associated with the granulation as seen in disk-integrated intensity on the basis of the theoretical model. For each PDS we derived tau_eff and sigma and compared these theoretical values with the theoretical scaling relations derived from the theoretical model and the Kepler measurements. We derive theoretical scaling relations for tau_eff and sigma, which show the same dependence on nu_max as the observed scaling relations. In addition, we show that these quantities also scale as a function of the turbulent Mach number (Ma) estimated at the photosphere. The theoretical scaling relations for tau_eff and sigma match the observations well on a global scale. Our modelling provides additional theoretical support for the observed variations of sigma and tau_eff with nu_m max. It also highlights the important role of Ma in controlling the properties of the stellar granulation. However, the observations made with Kepler on a wide variety of stars cannot confirm the dependence of our scaling relations on Ma. Measurements of the granulation background and detections of solar-like oscillations in a statistically sufficient number of cool dwarf stars will be required for confirming the dependence of the theoretical scaling relations with Ma., Comment: 12 pages, 6 figures,accepted for publication in A&A

Scaling relations between asteroseismic quantities and stellar parameters are essential tools for studying stellar structure and evolution. We will address two of them, namely, the relation between the large frequency separation ($\Delta \nu$) and the mean density ($\bar{\rho}$) as well as the relation between the frequency of the maximum in the power spectrum of solar-like oscillations ($\nu_{\rm max}$) and the cut-off frequency ($\nu_{\rm c}$). For the first relation, we will consider the possible sources of uncertainties and explore them with the help of a grid of stellar models. For the second one, we will show that the basic physical picture is understood and that departure from the observed relation arises from the complexity of non-adiabatic processes involving time-dependent treatment of convection. This will be further discussed on the basis of a set of 3D hydrodynamical simulation of surface convection., Comment: To appear in Proceedings of Fujihara Seminar 2012: "Progress in physics of the sun and stars: a new era in helio- and asteroseismology" H. Shibahashi, ed., ASP Conf. Ser

Mixed modes seen in evolved stars carry information on their deeper layers that can place stringent constraints on their physics and on their global properties (mass, age, etc...). In this study, we present a method to identify and measure all oscillatory mode characteristics (frequency, height, width). Analyzing four subgiants stars, we present the first measure of the effect of the degree of mixture on the l=1 mixed modes characteristics. We also show that some stars have measurable l=2 mixed modes and discuss the interest of their measure to constrain the deeper layers of stars., Comment: Accepted to ApJ

CoRoT and Kepler observations of red giants reveal rich spectra of non-radial solar-like oscillations allowing to probe their internal structure. We compare the theoretical spectrum of two red giants in the same region of the HR diagram but in different evolutionary phases. We present here our first results on the inertia, lifetimes and amplitudes of the oscillations and discuss the differences between the two stars., Comment: 40th Liege International Astrophysical Colloquium, 2 pages, 3 figures

With the space-borne missions CoRoT and Kepler, a large amount of asteroseismic data is now available. So-called global oscillation parameters are inferred to characterize the large sets of stars, to perform ensemble asteroseismology, and to derive scaling relations. The mean large separation is such a key parameter. It is therefore crucial to measure it with the highest accuracy. As the conditions of measurement of the large separation do not coincide with its theoretical definition, we revisit the asymptotic expressions used for analysing the observed oscillation spectra. Then, we examine the consequence of the difference between the observed and asymptotic values of the mean large separation. The analysis is focused on radial modes. We use series of radial-mode frequencies to compare the asymptotic and observational values of the large separation. We propose a simple formulation to correct the observed value of the large separation and then derive its asymptotic counterpart. We prove that, apart from glitches due to stellar structure discontinuities, the asymptotic expansion is valid from main-sequence stars to red giants. Our model shows that the asymptotic offset is close to 1/4, as in the theoretical development. High-quality solar-like oscillation spectra derived from precise photometric measurements are definitely better described with the second-order asymptotic expansion. The second-order term is responsible for the curvature observed in the \'echelle diagrams used for analysing the oscillation spectra and this curvature is responsible for the difference between the observed and asymptotic values of the large separation. Taking it into account yields a revision of the scaling relations providing more accurate asteroseismic estimates of the stellar mass and radius., Comment: accepted in A&A

Asteroseismology with the space-borne missions CoRoT and Kepler provides a powerful mean of testing the modeling of transport processes in stars. Rotational splittings are currently measured for a large number of red giant stars and can provide stringent constraints on the rotation profiles. The aim of this paper is to obtain a theoretical framework for understanding the properties of the observed rotational splittings of red giant stars with slowly rotating cores. This allows us to establish appropriate seismic diagnostics for rotation of these evolved stars. Rotational splittings for stochastically excited dipolar modes are computed adopting a first-order perturbative approach for two $1.3 M_\odot$ benchmark models assuming slowly rotating cores. For red giant stars with slowly rotating cores, we show that the variation of the rotational splittings of $\ell=1$ modes with frequency depends only on the large frequency separation, the g-mode period spacing, and the ratio of the average envelope to core rotation rates (${\cal R}$). This leds us to propose a way to infer directly ${\cal R}$ from the observations. This method is validated using the Kepler red giant star KIC 5356201. Finally, we provide a theoretical support for the use of a Lorentzian profile to measure the observed splittings for red giant stars., Comment: 15 pages, 15 figures, accepted for publication in A&A

Rotational splittings are currently measured for several main sequence stars and a large number of red giants with the space mission Kepler. This will provide stringent constraints on rotation profiles. Our aim is to obtain seismic constraints on the internal transport and surface loss of angular momentum of oscillating solar-like stars. To this end, we study the evolution of rotational splittings from the pre-main sequence to the red-giant branch for stochastically excited oscillation modes. We modified the evolutionary code CESAM2K to take rotationally induced transport in radiative zones into account. Linear rotational splittings were computed for a sequence of $1.3 M_{\odot}$ models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations. We find that transport by meridional circulation and shear turbulence yields far too high a core rotation rate for red-giant models compared with recent seismic observations. We discuss several uncertainties in the physical description of stars that could have an impact on the rotation profiles. For instance, we find that the Goldreich-Schubert-Fricke instability does not extract enough angular momentum from the core to account for the discrepancy. In contrast, an increase of the horizontal turbulent viscosity by 2 orders of magnitude is able to significantly decrease the central rotation rate on the red-giant branch. Our results indicate that it is possible that the prescription for the horizontal turbulent viscosity largely underestimates its actual value or else a mechanism not included in current stellar models of low mass stars is needed to slow down the rotation in the radiative core of red-giant stars., Comment: 15 pages, 13 figures, accepted for publication in A&A

Seismology of stars that exhibit solar-like oscillations develops a growing interest with the wealth of observational results obtained with the CoRoT and Kepler space-borne missions. In this framework, relations between asteroseismic quantities and stellar parameters provide a unique opportunity to derive model-independent determinations of stellar parameters (e.g., masses and radii) for a large sample of stars. I review those scaling relations with particular emphasis on the underlying physical processes governing those relations, as well as their uncertainties., Comment: 16 pages, 5 figures. To appear in Proceedings of the Journ\'ees 2012 of the French Society of Astronomy & Astrophysics (SF2A)

The space mission Kepler provides us with long and uninterrupted photometric time series of red giants. We are now able to probe the rotational behaviour in their deep interiors using the observations of mixed modes. We aim to measure the rotational splittings in red giants and to derive scaling relations for rotation related to seismic and fundamental stellar parameters. We have developed a dedicated method for automated measurements of the rotational splittings in a large number of red giants. Ensemble asteroseismology, namely the examination of a large number of red giants at different stages of their evolution, allows us to derive global information on stellar evolution. We have measured rotational splittings in a sample of about 300 red giants. We have also shown that these splittings are dominated by the core rotation. Under the assumption that a linear analysis can provide the rotational splitting, we observe a small increase of the core rotation of stars ascending the red giant branch. Alternatively, an important slow down is observed for red-clump stars compared to the red giant branch. We also show that, at fixed stellar radius, the specific angular momentum increases with increasing stellar mass. Ensemble asteroseismology indicates what has been indirectly suspected for a while: our interpretation of the observed rotational splittings leads to the conclusion that the mean core rotation significantly slows down during the red giant phase. The slow-down occurs in the last stages of the red giant branch. This spinning down explains, for instance, the long rotation periods measured in white dwarfs, Comment: Accepted in A&A

A growing number of solar-like oscillations has been detected in red giant stars thanks to CoRoT and Kepler space-crafts. The seismic data gathered by CoRoT on red giant stars allow us to test mode driving theory in physical conditions different from main-sequence stars. Using a set of 3D hydrodynamical models representative of the upper layers of sub- and red giant stars, we computed the acoustic mode energy supply rate (Pmax). Assuming adiabatic pulsations and using global stellar models that assume that the surface stratification comes from the 3D hydrodynamical models, we computed the mode amplitude in terms of surface velocity. This was converted into intensity fluctuations using either a simplified adiabatic scaling relation or a non-adiabatic one. From L and M (the luminosity and mass), the energy supply rate Pmax is found to scale as (L/M)^2.6 for both main-sequence and red giant stars, extending previous results. The theoretical amplitudes in velocity under-estimate the Doppler velocity measurements obtained so far from the ground for red giant stars by about 30%. In terms of intensity, the theoretical scaling law based on the adiabatic intensity-velocity scaling relation results in an under-estimation by a factor of about 2.5 with respect to the CoRoT seismic measurements. On the other hand, using the non-adiabatic intensity-velocity relation significantly reduces the discrepancy with the CoRoT data. The theoretical amplitudes remain 40% below, however, the CoRoT measurements. Our results show that scaling relations of mode amplitudes cannot be simply extended from main-sequence to red giant stars in terms of intensity on the basis of adiabatic relations because non-adiabatic effects for red giant stars are important and cannot be neglected. We discuss possible reasons for the remaining differences., Comment: 9 pages, 5 figures, accepted for publication in Astronomy & Astrophysics ; updated references, language improvement, figure 2 rescaled