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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 modeling of convection is a long standing problem in stellar physics. Up-to-now, all ad hoc models rely on a free parameter alpha (among others) which has no real physical justification and is therefore poorly constrained. However, a link exists between this free parameter and the entropy of the stellar adiabat. Prescriptions, derived from 3D stellar atmospheric models, are available that provide entropy as a function of stellar atmospheric parameters (effective temperature, surface gravity, chemical composition). This can provide constraints on alpha through the development of entropy-calibrated models. Several questions arise as these models are increasingly used. Which prescription should be used? How do uncertainties impact entropy-calibrated models? We aim to study the three existing prescriptions and determine which one should be used, and how. We implemented the entropy-calibration method into the stellar evolution code Cesam2k20 and performed comparisons with the Sun and the alpha Cen system. In addition, we used data from the CIFIST grid of 3D atmosphere models to evaluate the accuracy of the prescriptions. Of the three entropy prescriptions available, we determine which one best reproduces the entropies of the 3D models. We also demonstrate that the entropy obtained from this prescription should be corrected for the evolving chemical composition and for an entropy offset different between various EoS tables, following a precise procedure, otherwise classical parameters obtained from the models will be strongly biased. Finally, we also provide table with entropy of the adiabat of the CIFIST grid, as well as fits of these entropies. We performed a precise examination of entropy-calibrated modelling, and gave recommendations on which adiabatic entropy prescription to use, how to correct it and to implement the method into a stellar evolution code., Comment: 18 pages, 11 figures. Submitted to Astronomy and Astrophysics, recommended for publication with minor revisions

The transition between convective and radiative stellar regions is still not fully understood. The sharp variations in sound speed located in these transition regions give rise to a signature in specific seismic indicators, opening the possibility to constrain the physics of convection to radiation transition. Among those seismic indicators, the ratios of the small to large frequency separation for $l=0$ and $1$ modes ($r_{010}$) were shown to be particularly efficient to probe these transition regions. Interestingly, in the Kepler Legacy F-type stars, the oscillatory signatures left in the $r_{010}$ ratios by the sharp sound-speed variation have unexpected large amplitudes that still need to be explained. We show that the signature of the bottom of the convective envelope is amplified in the ratios $r_{010}$ by the frequency dependence of the amplitude compared to the signal seen in the frequencies themselves or the second differences. We find that among the different options of physical input investigated here, large amplitude signatures can only be obtained when convective penetration of the surface convective zone into the underlying radiative region is taken into account. In this case and even for amplitudes as large as those observed in F-type stars, the oscillating signature in the ratios can only be detected when the convective envelope is deep enough. This deep extension of the convective envelope causes doubt that the origin of the large amplitudes is due to penetrative convection as it is modelled here or implies that current stellar modelling (without penetrative convection) leads to an underestimation of the size of convective envelopes. In any case, studying the glitch signatures of a large number of oscillating F-type stars opens the possibility to constrain the physics of the stellar interior in these regions., Comment: 19 pages, 12 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

PLATO (PLAnetary Transits and Oscillations of stars) is an ESA M-class satellite planned for launch by end 2026 and dedicated to the wide-field search of transiting planets around bright and nearby stars, with a strong focus on discovering habitable rocky planets hosted by solar-like stars. The choice of the fields to be pointed at is a crucial task since it has a direct impact on the scientific return of the mission. In this paper we describe and discuss the formal requirements and the key scientific prioritization criteria that have to be taken into account in the Long-duration Observation Phase (LOP) field selection, and apply a quantitative metric to guide us in this complex optimization process. We identify two provisional LOP fields, one for each hemisphere (LOPS1, LOPN1), and discuss their properties and stellar content. While additional fine-tuning shall be applied to LOP selection before the definitive choice (to be made two years before launch), we expect their position will not move by more than a few degrees with respect to what is proposed in this paper., Comment: 17 pages, 10 figures, 3 tables, A&A in press (accepted: October 26, 2021). Some typos corrected. Author list corrected

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

Context. The ESA PLAnetary Transits and Oscillations of stars (PLATO) mission will search for terrestrial planets in the habitable zone of solar-type stars. Because of telemetry limitations, PLATO targets need to be pre-selected. Aims. In this paper, we present an all sky catalogue that will be fundamental to selecting the best PLATO fields and the most promising target stars, deriving their basic parameters, analysing the instrumental performances, and then planing and optimising follow-up observations. This catalogue also represents a valuable resource for the general definition of stellar samples optimised for the search of transiting planets. Methods. We used Gaia Data Release 2 (DR2) astrometry and photometry and 3D maps of the local interstellar medium to isolate FGK (V$\leq$13) and M (V$\leq$16) dwarfs and subgiant stars. Results. We present the first public release of the all-sky PLATO Input Catalogue (asPIC1.1) containing a total of 2 675 539 stars including 2 378 177 FGK dwarfs and subgiants and 297 362 M dwarfs. The median distance in our sample is 428 pc for FGK stars and 146 pc for M dwarfs, respectively. We derived the reddening of our targets and developed an algorithm to estimate stellar fundamental parameters (Teff, radius, mass) from astrometric and photometric measurements. Conclusions. We show that the overall (internal+external) uncertainties on the stellar parameter determined in the present study are $\sim$230 K (4%) for the effective temperatures, $\sim$0.1 R$_{\odot}$ (9%) for the stellar radii, and $\sim$0.1 M$_{\odot}$ (11%) for the stellar mass. We release a special target list containing all known planet hosts cross-matched with our catalogue., Comment: Accepted for publication in Astronomy & Astrophysics

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

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 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

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

Chemical element transport processes are among the crucial physical processes needed for precise stellar modelling. Atomic diffusion by gravitational settling nowadays is usually taken into account, and is essential for helioseismic studies. On the other hand, radiative accelerations are rarely accounted for, act differently on the various chemical elements, and can strongly counteract gravity in some stellar mass domains. In this study we aim at determining whether radiative accelerations impact the structure of solar-like oscillating main-sequence stars observed by asteroseismic space missions. We implemented the calculation of radiative accelerations in the CESTAM code using the Single-Valued Parameter method. We built and compared several grids of stellar models including gravitational settling, but some with and others without radiative accelerations. We found that radiative accelerations may not be neglected for stellar masses larger than 1.1~M$_{\odot}$ at solar metallicity. The difference in age due to their inclusion in models can reach 9\% for the more massive stars of our grids. We estimated that the percentage of the PLATO core program stars whose modelling would require radiative accelerations ranges between 33 and 58\% depending on the precision of the seismic data. We conclude that, in the context of Kepler, TESS, and PLATO missions, which provide (or will provide) high quality seismic data, radiative accelerations can have a significant effect when inferring the properties of solar-like oscillators properly. This is particularly important for age inferences. However, the net effect for each individual star results from the competition between atomic diffusion including radiative accelerations and other internal transport processes. This will be investigated in a forthcoming companion paper., Comment: 13 pages, 9 figures, accepted for publication in A&A

Helioseismology and asteroseismology of red giant stars have shown that the distribution of angular momentum in stellar interiors, and its evolution with time remains an open issue in stellar physics. Owing to the unprecedented quality of Kepler photometry, we are able to seismically infer internal rotation rates in \gamma Doradus stars, which provide the MS counterpart to the red-giants puzzle. We confront these internal rotation rates to stellar evolution models with rotationally induced transport of angular momentum, in order to test angular momentum transport mechanisms. We used a stellar model-independent method developed by Christophe et al. in order to obtain seismically inferred, buoyancy radii and near-core rotation for 37 \gamma Doradus stars observed by Kepler. We show that the buoyancy radius can be used as a reliable evolution indicator for field stars on the MS. We computed rotating evolutionary models including transport of angular momentum in radiative zones, following Zahn and Maeder, with the CESTAM code. This code calculates the rotational history of stars from the birth line to the tip of the RGB. The initial angular momentum content has to be set initially, which is done by fitting rotation periods in young stellar clusters. We show a clear disagreement between the near-core rotation rates measured in the sample and the rotation rates obtained from evolutionary models including rotationally induced transport following Zahn (1992). These results show a disagreement similar to that of the Sun and red giant stars. This suggests the existence of missing mechanisms responsible for the braking of the core before and along the MS. The efficiency of the missing mechanisms is investigated. The transport of angular momentum as formalized by Zahn and Maeder cannot explain the measurements of near-core rotation in main-sequence intermediate-mass stars we have at hand., Comment: 10 pages, 7 figures, submitted to A&A

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

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

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 detection of mixed modes that are split by rotation in Kepler red giants has made it possible to probe the internal rotation profiles of these stars, which brings new constraints on the transport of angular momentum in stars. Mosser et al. (2012) have measured the rotation rates in the central regions of intermediate-mass core helium burning stars (secondary clump stars). Our aim was to exploit& the rotational splittings of mixed modes to estimate the amount of radial differential rotation in the interior of secondary clump stars using Kepler data, in order to place constraints on angular momentum transport in intermediate-mass stars. We selected a subsample of Kepler secondary clump stars with mixed modes that are clearly rotationally split. By applying a thorough statistical analysis, we showed that the splittings of both gravity-dominated modes (trapped in central regions) and p-dominated modes (trapped in the envelope) can be measured. We then used these splittings to estimate the amount of differential rotation by using inversion techniques and by applying a simplified approach based on asymptotic theory (Goupil et al. 2013). We obtained evidence for a weak radial differential rotation for six of the seven targets that were selected, with the central regions rotating $1.8\pm0.3$ to $3.2\pm1.0$ times faster than the envelope. The last target was found to be consistent with a solid-body rotation. This demonstrates that an efficient redistribution of angular momentum occurs after the end of the main sequence in the interior of intermediate-mass stars, either during the short-lived subgiant phase, or once He-burning has started in the core. In either case, this should bring constraints on the angular momentum transport mechanisms that are at work., Comment: 16 pages, 8 figures, accepted in A&A

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

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

Context : We still do not know which mechanisms are responsible for the transport of angular momentum inside stars. The recent detection of mixed modes that contain the signature of rotation in the spectra of Kepler subgiants and red giants gives us the opportunity to make progress on this issue. Aims: Our aim is to probe the radial dependance of the rotation profiles for a sample of Kepler targets. For this purpose, subgiants and early red giants are particularly interesting targets because their rotational splittings are more sensitive to the rotation outside the deeper core than is the case for their more evolved counterparts. Methods: We first extract the rotational splittings and frequencies of the modes for six young Kepler red giants. We then perform a seismic modeling of these stars using the evolutionary codes CESAM2k and ASTEC. By using the observed splittings and the rotational kernels of the optimal models, we perform inversions of the internal rotation profiles of the six stars. Results: We obtain estimates of the mean rotation rate in the core and in the convective envelope of these stars. We show that the rotation contrast between the core and the envelope increases during the subgiant branch. Our results also suggest that the core of subgiants spins up with time, contrary to the RGB stars whose core has been shown to spin down. For two of the stars, we show that a discontinuous rotation profile with a deep discontinuity reproduces the observed splittings significantly better than a smooth rotation profile. Interestingly, the depths that are found most probable for the discontinuities roughly coincide with the location of the H-burning shell, which separates the layers that contract from those that expand. These results will bring observational constraints to the scenarios of angular momentum transport in stars., Comment: Accepted in A&A, 27 pages, 18 figures

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)

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

The space missions CoRoT and Kepler provide high quality data that allow us to test the transport of angular momentum in stars by the seismic determination of the internal rotation profile. Our aim is to test the validity of the seismic diagnostics for red giants rotation that are based on a perturbative method and to investigate the oscillation spectra when the validity does not hold. We use a non-perturbative approach implemented in the ACOR code (Ouazzani et al. 2012) that accounts for the effect of rotation on pulsations, and solves the pulsation eigenproblem directly for dipolar oscillation modes. We find that the limit of the perturbation to first order can be expressed in terms of the rotational splitting compared to the frequency separation between consecutive dipolar modes. Above this limit, non-perturbative computations are necessary but only one term in the spectral expansion of modes is sufficient as long as the core rotation rate remains significantly smaller than the pulsation frequencies. Each family of modes with different azimuthal symmetry, m, has to be considered separately. In particular, in case of rapid core rotation, the density of the spectrum differs significantly from one m-family of modes to another, so that the differences between the period spacings associated with each m-family can constitute a promising guideline toward a proper seismic diagnostic for rotation., Comment: 5 pages, 5 figures, accepted for publication in A&A

We present and discuss results of a recently developped two dimensional non-perturbative method to compute accurate adiabatic oscillation modes of rapidly rotating stars . The 2D calculations fully take into account the centrifugal distorsion of the star while the non-perturbative method includes the full influence of the Coriolis acceleration. These characteristics allows us to compute oscillation modes of rapid rotators - from high order p-modes in $\delta$Scuti stars, to low order p- and g-modes in $\beta$ Cephei or Be stars., Comment: 4 pages, 1 figure, proceedings of the 4th HELAS International Conference, Lanzarote feb 2010, Astronomical Notes, 2010, 331, P 45

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

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

Rotation is expected to have an important influence on the structure and the evolution of stars. However, the mechanisms of angular momentum transport in stars remain theoretically uncertain and very complex to take into account in stellar models. To achieve a better understanding of these processes, we desperately need observational constraints on the internal rotation of stars, which until very recently were restricted to the Sun. In this paper, we report the detection of mixed modes - i.e. modes that behave both as g modes in the core and as p modes in the envelope - in the spectrum of the early red giant KIC7341231, which was observed during one year with the Kepler spacecraft. By performing an analysis of the oscillation spectrum of the star, we show that its non-radial modes are clearly split by stellar rotation and we are able to determine precisely the rotational splittings of 18 modes. We then find a stellar model that reproduces very well the observed atmospheric and seismic properties of the star. We use this model to perform inversions of the internal rotation profile of the star, which enables us to show that the core of the star is rotating at least five times faster than the envelope. This will shed new light on the processes of transport of angular momentum in stars. In particular, this result can be used to place constraints on the angular momentum coupling between the core and the envelope of early red giants, which could help us discriminate between the theories that have been proposed over the last decades., Comment: Accepted in ApJ, 39 pages, 16 figures

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

Information about the rotation rate is contained in the low frequency part of power spectra, where signatures of nonuniform surface rotation are expected, as well as in the frequency splittings induced by the internal rotation rate. We wish to figure out whether the differences between the seismic rotation period as determined by a mean rotational splitting, and the rotation period measured from the low frequency peak in the Fourier spectrum (observed for some of CoRoT's targets) can provide constraints on the rotation profile. For uniform moderate rotators,perturbative corrections to second and third order in terms of the rotation angular velocity \Omega, may mimic differential rotation. We apply our perturbation method to evaluate mode frequencies accurate up to \Omega^3 for uniform rotation. Effects of latitudinal dependence are calculated in the linear approximation. In \beta Cephei pulsators models, third order effects become comparable to that of a horizontal shear similar to the solar one at rotation rates well below the breakup values. We show how a clean signature of the latitudinal shear may be extracted. Our models of two CoRoT target HD 181906 and HD 181420, represent lower main sequence objects. These are slow rotators and nonlinear effects in splittings are accordingly small. We use data on one low frequency peak and one splitting of a dipolar mode to constrain the rotation profile in HD 181420 and HD 181906. The relative influence of the two effects strongly depends on the type of the oscillation modes in the star and on the magnitude of the rotation rate. Given mean rotational splitting and the frequency of a spot signature, it is possible to distinguish between the two hypothesis, and in the case of differential rotation in latitude, we propose a method to determine the type of rotation profile and a range of values for the shear., Comment: 17 pages, 12 figures, A&A accepted

We report for the first time a parametric fit to the pattern of the \ell = 1 mixed modes in red giants, which is a powerful tool to identify gravity-dominated mixed modes. With these modes, which share the characteristics of pressure and gravity modes, we are able to probe directly the helium core and the surrounding shell where hydrogen is burning. We propose two ways for describing the so-called mode bumping that affects the frequencies of the mixed modes. Firstly, a phenomenological approach is used to describe the main features of the mode bumping. Alternatively, a quasi-asymptotic mixed-mode relation provides a powerful link between seismic observations and the stellar interior structure. We used period \'echelle diagrams to emphasize the detection of the gravity-dominated mixed modes. The asymptotic relation for mixed modes is confirmed. It allows us to measure the gravity-mode period spacings in more than two hundred red giant stars. The identification of the gravity-dominated mixed modes allows us to complete the identification of all major peaks in a red giant oscillation spectrum, with significant consequences for the true identification of \ell = 3 modes, of \ell = 2 mixed modes, for the mode widths and amplitudes, and for the \ell = 1 rotational splittings. The accurate measurement of the gravity-mode period spacing provides an effective probe of the inner, g-mode cavity. The derived value of the coupling coefficient between the cavities is different for red giant branch and clump stars. This provides a probe of the hydrogen-shell burning region that surrounds the helium core. Core contraction as red giants ascend the red giant branch can be explored using the variation of the gravity-mode spacing as a function of the mean large separation., Comment: Accepted in A&A

Determining the mass of stars is crucial both to improving stellar evolution theory and to characterising exoplanetary systems. Asteroseismology offers a promising way to estimate stellar mean density. When combined with accurate radii determinations, such as is expected from GAIA, this yields accurate stellar masses. The main difficulty is finding the best way to extract the mean density from a set of observed frequencies. We seek to establish a new method for estimating stellar mean density, which combines the simplicity of a scaling law while providing the accuracy of an inversion technique. We provide a framework in which to construct and evaluate kernel-based linear inversions which yield directly the mean density of a star. We then describe three different inversion techniques (SOLA and two scaling laws) and apply them to the sun, several test cases and three stars. The SOLA approach and the scaling law based on the surface correcting technique described by Kjeldsen et al. (2008) yield comparable results which can reach an accuracy of 0.5 % and are better than scaling the large frequency separation. The reason for this is that the averaging kernels from the two first methods are comparable in quality and are better than what is obtained with the large frequency separation. It is also shown that scaling the large frequency separation is more sensitive to near-surface effects, but is much less affected by an incorrect mode identification. As a result, one can identify pulsation modes by looking for an l and n assignment which provides the best agreement between the results from the large frequency separation and those from one of the two other methods. Non-linear effects are also discussed as is the effects of mixed modes. In particular, it is shown that mixed modes bring little improvement as a result of their poorly adapted kernels., Comment: Accepted for publication in A&A, 20 pages, 19 figures

The G6 giant HR\,2582 (HD\,50890) was observed by CoRoT for approximately 55 days. Mode frequencies are extracted from the observed Fourier spectrum of the light curve. Numerical stellar models are then computed to determine the characteristics of the star (mass, age, etc...) from the comparison with observational constraints. We provide evidence for the presence of solar-like oscillations at low frequency, between 10 and 20\,$\mu$Hz, with a regular spacing of $(1.7\pm0.1)\mu$Hz between consecutive radial orders. Only radial modes are clearly visible. From the models compatible with the observational constraints used here, We find that HR\,2582 (HD\,50890) is a massive star with a mass in the range (3--\,5\,$M_{\odot}$), clearly above the red clump. It oscillates with rather low radial order ($n$ = 5\,--\,12) modes. Its evolutionary stage cannot be determined with precision: the star could be on the ascending red giant branch (hydrogen shell burning) with an age of approximately 155 Myr or in a later phase (helium burning). In order to obtain a reasonable helium amount, the metallicity of the star must be quite subsolar. Our best models are obtained with a mixing length significantly smaller than that obtained for the Sun with the same physical description (except overshoot). The amount of core overshoot during the main-sequence phase is found to be mild, of the order of 0.1\,$H_{\rm p}$., Comment: Accepted in A&A

We aim to describe the oscillation power excess observed in Kepler red giants, and to investigate empirical scaling relations governing these parameters. From these scalings relations, we derive new physical properties of red giant oscillations. Various different methods were compared in order to validate the processes and to derive reliable output values. For consistency, a single method was then used to determine scaling relations for the relevant global asteroseismic parameters: mean mode height, mean height of the background signal superimposed on the oscillation power excess, width of the power excess, bolometric amplitude of the radial modes and visibility of non-radial modes. A method for deriving oscillation amplitudes is proposed, which relies on the complete identification of the red giant oscillation spectrum. The comparison of the different methods has shown the important role of the way the background is modelled. The convergence reached by the collaborative work enables us to derive significant results concerning the oscillation power excess. We obtain several scaling relations, and identify the influence of the stellar mass and the evolutionary status. The effect of helium burning on the red giant interior structure is confirmed: it yields a strong mass-radius relation for clump stars. We find that none of the amplitude scaling relations motivated by physical considerations predict the observed mode amplitudes of red giant stars. In parallel, the degree-dependent mode visibility exhibits important variations. Both effects seem related to the significant influence of the high mode mass of non-radial mixed modes. A family of red giants with very weak dipole modes is identified, and its properties are analyzed., Comment: Accepted in A&A

The CoRoT mission has provided thousands of red-giant light curves. The analysis of their solar-like oscillations allows us to characterize their stellar properties. Up to now, the global seismic parameters of the pressure modes remain unable to distinguish red-clump giants from members of the red-giant branch. As recently done with Kepler red giants, we intend to analyze and use the so-called mixed modes to determine the evolutionary status of the red giants observed with CoRoT. We also aim at deriving different seismic characteristics depending on evolution. The complete identification of the pressure eigenmodes provided by the red-giant universal oscillation pattern allows us to aim at the mixed modes surrounding the l=1 expected eigenfrequencies. A dedicated method based on the envelope autocorrelation function is proposed to analyze their period separation. We have identified the mixed-mode signature separation thanks to their pattern compatible with the asymptotic law of gravity modes. We have shown that, independent of any modelling, the g-mode spacings help to distinguish the evolutionary status of a red-giant star. We then report different seismic and fundamental properties of the stars, depending on their evolutionary status. In particular, we show that high-mass stars of the secondary clump present very specific seismic properties. We emphasize that stars belonging to the clump were affected by significant mass loss. We also note significant population and/or evolution differences in the different fields observed by CoRoT.

The CoRoT satellite has made available high precision photometric observations of a large number of stars of different spectral types. Continuous photometric time series allow the characterization of stellar microvariability in a systematic way. We determine an index indicating the level of activity, derived from photometric data, for a large sample of stars with different color temperatures. We also assess to what extent this index can be related to an estimated Rossby number for stars whose rotation period can be estimated. We also estimate a characteristic lifetime of the surface heterogeneities. Our work is based on the Fourier analysis of stellar light curves. We analyzed the Fourier power spectra of 430 selected light curves obtained by CoRoT during three observation runs. The low-frequency contribution of the stellar variability is modelled by a "generalized semi-lorentzian" profile. An activity index is derived from the fitted amplitude and width of the semi-lorentzian model. Some of the Fourier spectra exhibit a rotational modulation which enables the determination of the rotation period. In addition, a convective turnover time is derived from a grid of stellar models, so that a Rossby number can be estimated. A characteristic lifetime of the phenomena causing the observed power at low frequency is assessed from the fitted model of the power spectrum and is compared to the rotation period. Higher values of the microvariability index are observed among the coolest stars from our sample. 28 light curves show a clear rotational modulation. The estimated Rossby number of most of the observed stars with a rotational modulation is less than 1. The activity index decreases with increasing Rossby number. The quality of the CoRoT data enables the determination of the characteristic lifetime of active structures. It is shown to increase with the rotation period., Comment: second revised version submitted to A&A on April 11, 2011 10 pages, 8 figures

Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum ($\nu_{\rm max}$) of solar-like oscillations and the cut-off frequency ($\nu_{\rm c}$). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called \emph{plateau} of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between $\nu_{\rm max}$ and $\nu_{\rm c}$, with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter., Comment: 8 pages, 11 figures. Accepted in A&A

Context. The advent of space-borne missions such as CoRoT or Kepler providing photometric data has brought new possibilities for asteroseismology across the H-R diagram. Solar-like oscillations are now observed in many stars, including red giants and main- sequence stars. Aims. Based on several hundred identified pulsating red giants, we aim to characterize their oscillation amplitudes and widths. These observables are compared with those of main-sequence stars in order to test trends and scaling laws for these parameters for both main-sequence stars and red giants. Methods. An automated fitting procedure is used to analyze several hundred Fourier spectra. For each star, a modeled spectrum is fitted to the observed oscillation spectrum, and mode parameters are derived. Results. Amplitudes and widths of red-giant solar-like oscillations are estimated for several hundred modes of oscillation. Amplitudes are relatively high (several hundred ppm) and widths relatively small (very few tenths of a {\mu}Hz). Conclusions. Widths measured in main-sequence stars show a different variation with the effective temperature than red giants. A single scaling law is derived for mode amplitudes of both red giants and main-sequence stars versus their luminosity to mass ratio. However, our results suggest that two regimes may also be compatible with the observations., Comment: Accepted in A&A on 2011 February 8th, now includes corrections (results now more precise on \Gamma and A_max in Section 4.3 and 4.4, fig. 7 corrected consequently)

Modelling amplitudes of stochastically excited oscillations in stars is a powerful tool for understanding the properties of the convective zones. For instance, it gives us information on the way turbulent eddies are temporally correlated in a very large Reynolds number regime. We discuss the way the time correlation between eddies is modelled and we present recent theoretical developments as well as observational results. Eventually, we discuss the physical underlying meaning of the results by introducing the Ornstein-Uhlenbeck process, which is a sub-class of a Gaussian Markov process., Comment: GONG 2010 - SoHO 24, A new era of seismology of the Sun and solar-like stars, to be published in the Journal of Physics: Conference Series (JPCS)

We review some major, open issues in the current modelling of low and intermediate mass, main sequence stars based on seismological studies. In the present paper, the solar case is discussed together with current problems that are common to the Sun and stars with a structure similar to that of the Sun. Several additional issues specific to main sequence stars other than the Sun are reviewed and illustrated with a few stars observed with CoRoT in a companion paper., Comment: GONG 2010 - SoHO 24, A new era of seismology of the Sun and solar-like stars. To be published in the Journal of Physics: Conference Series (JPCS)

We review some major open issues in the current modelling of low and intermediate mass, main sequence stars based on seismological studies. The solar case was discussed in a companion paper, here several issues specific to other stars than the Sun are illustrated with a few stars observed with CoRoT and expectations from Kepler data., Comment: GONG 2010 - SoHO 24, A new era of seismology of the Sun and solar-like stars, To be published in the Journal of Physics: Conference Series (JPCS)