In the context of the space missions CoRoT, Kepler, Gaia, TESS, and PLATO, precise and accurate stellar ages, masses, and radii are of paramount importance. We aim at quantifying how detailed stellar ...modelling can improve the accuracy and precision on age and mass of individual stars. To that end, we adopt a multifaceted approach where we carefully examine how the number of observational constraints as well as the uncertainties on observations and on model input physics affect the results of age-dating and weighing. We demonstrate that asteroseismology allows us to substantially improve the age accuracy that can be achieved with other methods. We emphasize that the knowledge of the mean properties of stellar oscillations -- such as the large frequency separation -- is not enough to derive accurate ages. Our results emphasize the importance of precise classical stellar parameters and oscillation frequencies such as will be obtained by the Gaia and PLATO missions.
The
cesam
code is a consistent set of programs and routines which perform calculations of 1D quasi-hydrostatic stellar evolution including microscopic diffusion of chemical species and diffusion of ...angular momentum. The solution of the quasi-static equilibrium is performed by a collocation method based on piecewise polynomials approximations projected on a B-spline basis; that allows stable and robust calculations, and the exact restitution of the solution, not only at grid points, even for the discontinuous variables. Other advantages are the monitoring by only one parameter of the accuracy and its improvement by super-convergence. An automatic mesh refinement has been designed for adjusting the localisations of grid points according to the changes of unknowns. For standard models, the evolution of the chemical composition is solved by stiffly stable schemes of orders up to four; in the convection zones mixing and evolution of chemical are simultaneous. The solution of the diffusion equation employs the Galerkin finite elements scheme; the mixing of chemicals is then performed by a strong turbulent diffusion. A precise restoration of the atmosphere is allowed for.
Context. Our poor understanding of the boundaries of convective cores generates large uncertainties on the extent of these cores and thus on stellar ages. The detection and precise characterization ...of solar-like oscillations in hundreds of main-sequence stars by CoRoT and Kepler has given the opportunity to revisit this problem. Aims. Our aim is to use asteroseismology to consistently measure the extent of convective cores in a sample of main-sequence stars whose masses lie around the mass limit for having a convective core. Methods. We first tested and validated a seismic diagnostic that was proposed to probe the extent of convective cores in a model-dependent way using the so-called r010 ratios, which are built with l = 0 and l = 1 modes. We applied this procedure to 24 low-mass stars chosen among Kepler targets to optimize the efficiency of this diagnostic. For this purpose, we computed grids of stellar models with both the Cesam2k and mesa evolution codes, where the extensions of convective cores were modeled either by an instantaneous mixing or as a diffusion process. Results. We found that 10 stars in our sample are in fact subgiants. Among the other targets, were able to unambiguously detect convective cores in eight stars, and we obtained seismic measurements of the extent of the mixed core in these targets with a good agreement between the Cesam2k and mesa codes. By performing optimizations using the Levenberg-Marquardt algorithm, we then obtained estimates of the amount of extra mixing beyond the core that is required in Cesam2k to reproduce seismic observations for these eight stars, and we showed that this can be used to propose a calibration of this quantity. This calibration depends on the prescription chosen for the extra mixing, but we found that it should also be valid for the code mesa, provided the same prescription is used. Conclusions. This study constitutes a first step toward calibrating the extension of convective cores in low-mass stars, which will help reduce the uncertainties on the ages of these stars.
Context. The detection of oscillations with a mixed character in subgiants and red giants allows us to probe the physical conditions in their cores. Aims. With these mixed modes, we aim at ...determining seismic markers of stellar evolution. Methods. 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. Results. We measured the asymptotic period spacing for 1178 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. Conclusions. 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.
Context. Chemical element transport processes are among the crucial physical processes needed for precise stellar modelling. Atomic diffusion by gravitational settling 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. The resulting variations in the abundance profiles may significantly affect the structure of the star. Aims. The aim of this study is to determine whether radiative accelerations impact the structure of solar-like oscillating main-sequence stars observed by asteroseismic space missions. Methods. We implemented the calculation of radiative accelerations operating on C, N, O, Ne, Na, Mg, Al, Si, S, Ca, and Fe in the CESTAM code using the single-valued parameter method. We built and compared several grids of stellar models including gravitational settling, some with and others without radiative accelerations. We considered masses in the range 0.9, 1.5 M⊙ and three values of the metallicity around the solar value. For each metallicity we determined the mass range where differences between models due to radiative accelerations exceed the uncertainties of global seismic parameters of the Kepler Legacy sample or expected for PLATO observations. Results. We found that radiative accelerations may not be neglected for stellar masses higher than 1.1 M⊙ 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. Conclusions. 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 properly inferring the properties of solar-like oscillators. 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. Rotationally induced transport processes for instance are believed to reduce the effects of atomic diffusion. This will be investigated in a forthcoming companion paper.
Asteroseismology based on observations from the space-borne missions CoRoT and Kepler provides a powerful means 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 the rotation of these evolved stars. Rotational splittings were computed for stochastically excited dipolar modes by adopting a first-order perturbative approach for two 1.3 M sub(bigodot) benchmark models that assume slowly rotating cores. For red giant stars with slowly rotating cores, we show that the variation in the rotational splittings of l = 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 (R). This led us to propose a way to infer directly R from the observations. This method is validated using the Kepler red giant star KIC 5356201. Finally, we provide theoretical support for using a Lorentzian profile to measure the observed splittings for red giant stars.
Context. 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. Aims. Our aim is to obtain seismic constraints on the internal transport and surface loss of the 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. Methods. 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 sub(middot in circle) models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations. Results. 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. Conclusions. 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.
Context.
The space-borne missions CoRoT and
Kepler
opened up a new opportunity for better understanding stellar evolution by probing stellar interiors with unrivalled high-precision photometric data.
...Kepler
has observed stellar oscillation for four years, which gave access to excellent frequency resolution that enables deciphering the oscillation spectrum of evolved red giant branch and asymptotic giant branch stars.
Aims.
The internal structure of stars in the upper parts of the red and asymptotic giant branches is poorly constrained, which makes the distinction between red and asymptotic giants difficult. We perform a thorough seismic analysis to address the physical conditions inside these stars and to distinguish them.
Methods.
We took advantage of what we have learnt from less evolved stars. We studied the oscillation mode properties of ∼2.000 evolved giants in a model described by the asymptotic pressure-mode pattern of red giants, which includes the signature of the helium second-ionisation zone. Mode identification was performed with a maximum cross-correlation method. Then, the modes were fitted with Lorentzian functions following a maximum likelihood estimator technique.
Results.
We derive a large set of seismic parameters of evolved red and asymptotic giants. We extracted the mode properties up to the degree
ℓ
= 3 and investigated their dependence on stellar mass, metallicity, and evolutionary status. We identify a clear difference in the signature of the helium second-ionisation zone between red and asymptotic giants. We also detect a clear shortage of the energy of
ℓ
= 1 modes after the core-He-burning phase. Furthermore, we note that the mode damping observed on the asymptotic giant branch is similar to that observed on the red giant branch.
Conclusions.
We highlight that the signature of the helium second-ionisation zone varies with stellar evolution. This provides us with a physical basis for distinguishing red giant branch stars from asymptotic giants. Here, our investigation of stellar oscillations allows us to constrain the physical processes and the key events that occur during the advanced stages of stellar evolution, with emphasis on the ascent along the asymptotic giant branch, including the asymptotic giant branch bump.
Aims. We aim at characterizing the inward transition from convective to radiative energy transport at the base of the convective envelope of the solar-like oscillator HD 52265 recently observed by ...the CoRoT satellite. Methods. We investigated the origin of one specific feature found in the HD 52265 frequency spectrum. We modelled the star to derive the internal structure and the oscillation frequencies that best match the observations and used a seismic indicator sensitive to the properties of the base of the envelope convection zone. Results. The seismic indicators clearly reveal that to best represent the observed properties of HD 52265, models must include penetrative convection below the outer convective envelope. The penetrative distance is estimated to be ~0.95HP, which corresponds to an extent over a distance representing 6.0 per cents of the total stellar radius, significantly larger than what is found for the Sun. The inner boundary of the extra-mixing region is found at 0.800 ± 0.004 R where R = 1.3 R⊙ is the stellar radius. Conclusions. These results contribute to the tachocline characterization in stars other than the Sun.
Context. Modeling the convection process is a long-standing problem in stellar physics. To date, all ad hoc models have relied on a free parameter, α , (among others) that 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. There are existing prescriptions, derived from 3D stellar atmospheric models, that treat entropy as a function of stellar atmospheric parameters (effective temperature, surface gravity, and chemical composition). This can offer sufficient constraints on α through the development of entropy-calibrated models. However, several questions have arisen as these models are increasingly used with respect to which prescription should be used and whether it ought to be used in its original form, along with the impacts of uncertainties on entropy-calibrated models. Aims. We aim to study the three existing prescriptions in detail and determine which of them demonstrate the most optimal performance and how it should be applied. Methods. We implemented the entropy-calibration method into the stellar evolution code (Cesam2k20) and performed comparisons with the Sun and the α Cen system. In addition, we used data from the CIFIST grid of 3D atmosphere models to evaluate the accuracy of the prescriptions. Results. Of the three entropy prescriptions currently available, we determined the one that has the best functional form for reproducing the entropies of the 3D models. However, the coefficients involved in this formulation must not be taken from the original paper because they were calibrated against a flawed set of entropies. 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. This must be done following a precise procedure to ensure that the classical parameters obtained from the models are not strongly biased. Finally, we provide a data table with entropy of the adiabat of the CIFIST grid, along with the fits for these entropies. Conclusions. Thanks to a precise examination of entropy-calibrated modeling, we are able to offer our recommendations with respect to which adiabatic entropy prescription to use, how to correct it, and how to implement the method into a stellar evolution code.
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