Toulouse-Geneva Evolution Code Research Articles

Radiative acceleration calculation methods and abundance anomalies in Am stars

Atomic diffusion with radiative levitation is a major transport process to consider to explain abundance anomalies in Am stars. Radiative accelerations vary from one species to another, yielding different abundance anomalies at the stellar surface. Radiative accelerations can be computed using different methods: some evolution codes use an analytical approximation, while others calculate them from monochromatic opacities. We compared the abundance evolutions predicted using these various methods. Our models were computed with the Toulouse-Geneva evolution code, in which both an analytical approximation (the single-valued parameter method) and detailed calculations from Opacity Project (OP) atomic data are implemented for the calculation of radiative accelerations. The time evolutions of the surface abundances were computed using macroscopic transport processes that are able to reproduce observed Am star surface abundances in presence of atomic diffusion, namely an ad hoc turbulent model or a global mass loss. The radiative accelerations obtained with the various methods are globally in agreement for all the models below the helium convective zone, but can be much greater between the bottom of the hydrogen convective zone and that of helium. The time evolutions of the surface abundances mostly agree within the observational error, but the abundance of some elements can exceed this error for the least massive mass-loss model. The gain in computing time from using analytical approximations is significant compared to sequential calculations from monochromatic opacities for the turbulence models and for the least massive wind model; the gain is small otherwise. Test calculations of turbulence models with the tabulated OPAL opacities yield quite similar abundances as OP for most elements but in a much shorter time, meaning that determining Am star parameters can be done using a two-step method.

Modelling of the scandium abundance evolution in AmFm stars

Context. Scandium is a key element of the Am star phenomenon since its surface under-abundance is one of the criteria that characterise such stars. Thanks to the availability of a sufficiently complete set of theoretical atomic data for this element, reliable radiative accelerations for Sc can now be computed, which allows its behaviour under the action of atomic diffusion to be modelled. Aims. We explore the required conditions, in terms of mixing processes or mass loss, for our models to reproduce the observed surface abundances of Sc in Am stars. Methods. The models are computed with the Toulouse-Geneva evolution code, which uses the parametric single-valued parameter method for the calculation of radiative accelerations. Fingering mixing is included, using a prescription that comes from 3D hydrodynamical simulations. Other parameter-dependent turbulent mixing processes are also considered. A global mass loss is also implemented. Results. When no mass loss is considered, the observed abundances of Sc are rather in favour of the models whose superficial layers are fully mixed down to the iron accumulation zone, although other mixing prescriptions are also able to reproduce the observations for the most massive model presented here (2.0 M⊙). The models including mass loss with rates in the range of [10−13; 10−14] M⊙ yr−1 are compatible with some of the observations, while other observations suggest that the mass-loss rate could be lower. The constraints brought by the modelling of Sc are consistent with those derived using other chemical elements.

New nickel opacities and their impact on stellar models

Context. The chemical element nickel is of particular interest in stellar physics. In the layers in which the Fe-peak elements dominate the mean opacity (the so-called Z-bump), Ni is the second contributor to the Rosseland opacity after iron, according to the Opacity Project data. Reliable nickel cross sections are therefore mandatory for building realistic stellar models, especially for main-sequence pulsators such as β Cep and slowly pulsating B stars, whose oscillations are triggered by the κ-mechanism of the Fe-peak elements. Unfortunately, the Opacity Project data for Ni were extrapolated from those of Fe, and previous studies have shown that they were underestimated in comparison to detailed calculations. Aims. We investigate the impact of newly computed monochromatic cross sections on the Rosseland mean opacity of Ni and on the structure of main-sequence massive pulsators. We compare our results with the widely used Opacity Project and OPAL data. Methods. Monochromatic cross sections for Ni were obtained with the SCO-RCG code. The Toulouse-Geneva evolution code was used to build the stellar models. Results. With the new data, the Rosseland opacities of Ni are roughly the same as those of the Opacity Project or OPAL at high temperatures (log T > 6). At lower temperatures, significant departures are observed; the ratios are up to six times higher with SCO-RCG. These discrepancies span a wider temperature range in the comparison with OPAL than in comparison with the Opacity Project. For massive star models, the results of the comparison with a structure computed with Opacity Project data show that the Rosseland mean of the global stellar mixture is only marginally altered in the Z-bump. The maximum opacity is shifted towards slightly more superficial layers. A new maximum appears in the temperature derivative of the mean opacity, and the driving of the pulsations should be affected.

Stellar models with self-consistent Rosseland opacities

Context. The building of a stellar structure requires knowing the Rosseland mean opacity at each layer of the model. This mean opacity is very often interpolated in pre-computed tables due to the overwhelming time to compute it from monochromatic cross sections. The main drawback to using tables is that the opacities can be inconsistent with the actual local chemical composition, for instance in the regions of the star where nucleosynthesis occurs. Aims. We study the effects of self-consistent Rosseland mean opacity calculations on the stellar structure and evolution, in comparison with models where the metal mixture remains equal to the initial one. Methods. We developed a strategy that allows very fast calculations of Rosseland opacities from monochromatic cross sections. We are then able to compute evolutionary tracks with models whose Rosseland opacities are fully consistent with the chemical mix everywhere in the star. This method has been implemented in the Toulouse-Geneva evolution code. Results. Our self-consistent models show very small structural differences compared to models where the Rosseland opacity is computed with a fixed metal mixture. As a consequence, the main-sequence evolutionary tracks are almost the same for models of mass ranging from 2 to 8 M⊙. At a given surface gravity the relative difference in age is lower than 2% and generally below 1% between the two kinds of calculations, the self-consistent model being younger most of the time. Unless such a precision in age is sought out, the use of tabulated Rosseland opacities with a metal content defined globally is still acceptable, at least in main-sequence stars where the chemical mix changes only through nucleosynthesis.

Role of atomic diffusion in the opacity enhancement inside B-type stars

Context. The pulsation frequencies of early B-type stars cannot be reproduced using stellar models with homogeneous abundances. A suitable match requires a dedicated enhancement of the opacity in the layers where its main contributors are the iron-peak elements (the so-called Z-bump), which trigger the oscillations in these stars. Aim. Our aim is to test whether the abundance stratification induced by atomic diffusion in these stellar layers is able to modify the local opacity as needed to account for the asteroseismic observations. Methods. Models representing a typical pulsating B-star were evolved during the main sequence using the Toulouse–Geneva evolution code in an improved version. The migration of the chemicals involves radiative accelerations, which were computed with the single-valued parameter method, and fingering mixing with parameters constrained by three-dimensional simulations. The possible effect of mass-loss was also considered. Results. We show that atomic diffusion modifies the abundance profiles inside the star, leading to an overabundance of the iron-peak elements in the upper part of the envelope. The opacities may become as high as required, provided that fingering mixing, which extends the size of the overabundance zone, is taken into account. A zero-flux of the elements at the surface leading to unphysical accumulations, mass-loss is also required to evolve the model until the end of the main sequence.

Asteroseismology of the exoplanet-host F-type star 94 Ceti: Impact of atomic diffusion on the stellar parameters

Context. A precision of the order of one percent is needed on the parameters of exoplanet-hosts stars to correctly characterise the planets themselves. This can be achieved by asteroseismology. It is important in this context to test the influence of introducing atomic diffusion with radiative accelerations in the models upon the derived parameters. In this paper, we begin this study with the case of the star 94 Ceti A. Aims. We aim to perform a complete asteroseismic analysis of the exoplanet-host F-type star 94 Ceti A, from the first radial-velocity observations with the High Accuracy Radial velocity Planet Searcher (HARPS) up to the final computed best models. We also aim to test the influence of atomic diffusion, including radiative accelerations, upon the computed frequencies and on the determined stellar parameters. 94 Ceti A is hot enough to suffer these effects. We also aim to test the effect of including a complete atmosphere in the stellar models. Methods. The radial velocity observations were performed with HARPS in 2007. The low degree modes were derived and identified using classical methods and compared with the results obtained from stellar models computed with the Toulouse Geneva Evolution Code (TGEC). Results. We obtained precise parameters for the star 94 Ceti A. We showed that including atomic diffusion with radiative accelerations can modify the age by a few percent, whereas adding a complete atmosphere does not change the results by more than one percent. Conclusions. Atomic diffusion including radiative accelerations should be taken into account in all the computations of stellar models with masses larger than 1.3 M⊙ in order to determine accurate parameters for observed stars.

Mass effect on the lithium abundance evolution of open clusters: Hyades, NGC 752, and M 67

Lithium abundances in open clusters provide an effective way of probing mixing processes in the interior of solar-type stars and convection is not the only mixing mechanism at work. To understand which mixing mechanisms are occurring in low-mass stars, we test non-standard models, which were calibrated using the Sun, with observations of three open clusters of different ages, the Hyades, NGC 752, and M67. We collected all available data, and for the open cluster NGC 752, we redetermine the equivalent widths and the lithium abundances. Two sets of evolutionary models were computed, one grid of only standard models with microscopic diffusion and one grid with rotation-induced mixing, at metallicity [Fe/H] = 0.13, 0.0, and 0.01 dex, respectively, using the Toulouse-Geneva evolution code. We compare observations with models in a color-magnitude diagram for each cluster to infer a cluster age and a stellar mass for each cluster member. Then, for each cluster we analyze the lithium abundance of each star as a function of mass. The data for the open clusters Hyades, NGC 752, and M67, are compatible with lithium abundance being a function of both age and mass for stars in these clusters. Our models with meridional circulation qualitatively reproduce the general trend of lithium abundance evolution as a function of stellar mass in all three clusters. This study points out the importance of mass dependence in the evolution of lithium abundance as a function of age. Comparison between models with and without rotation-induced mixing shows that the inclusion of meridional circulation is essential to account for lithium depletion in low-mass stars. However, our results suggest that other mechanisms should be included to explain the Li-dip and the lithium dispersion in low-mass stars.

Hydrodynamical instabilities induced by atomic diffusion in A stars and their consequences

Aims. Atomic diffusion, including the effect of radiative accelerations on individual elements, leads to important variations of the chemical composition inside the stars. The accumulation in specific layers of the elements, which are the main contributors of the local opacity, leads to hydrodynamical instabilities that modify the internal stellar structure and surface abundances. Our aim is to study these effects and compare the resulting surface abundances with spectroscopic observations Methods. We computed the detailed structure of A-type stars including these effects. We used the Toulouse-Geneva Evolution Code (TGEC), where radiative accelerations are computed using the Single Valued Parameter (SVP) method, and we added double-diffusive convection with mixing coefficients deduced from three-dimensional (3D) simulations. Results. We show that the modification of the initial chemical composition has important effects on the internal stellar mixing and leads to different surface abundances of the elements. The results fit the observed surface chemical composition well if the layers, which are individually mixed by double-diffusive convection, are connected.

Accretion of planetary matter and the lithium problem in the 16 Cygni stellar system

The 16 Cyg system is composed of two solar analogs with similar masses and ages. A red dwarf is in orbit around 16 Cyg A whereas 16 Cyg B hosts a giant planet. The abundances of heavy elements are similar in the two stars but lithium is much more depleted in 16 Cyg B that in 16 Cyg A, by a factor of at least 4.7. The interest of studying the 16 Cyg system is that the two star have the same age and the same initial composition. The presently observed differences must be due to their different evolution, related to the fact that one of them hosts a planet contrary to the other one. We computed models of the two stars which precisely fit the observed seismic frequencies. We used the Toulouse Geneva Evolution Code (TGEC) that includes complete atomic diffusion (including radiative accelerations). We compared the predicted surface abundances with the spectroscopic observations and confirmed that another mixing process is needed. We then included the effect of accretion-induced fingering convection. The accretion of planetary matter does not change the metal abundances but leads to lithium destruction which depends on the accreted mass. A fraction of earth mass is enough to explain the lithium surface abundances of 16 Cyg B. We also checked the beryllium abundances. In the case of accretion of heavy matter onto stellar surfaces, the accreted heavy elements do not remain in the outer convective zones but they are mixed downwards by fingering convection induced by the unstable $\mu$-gradient. Depending on the accreted mass, this mixing process may transport lithium down to its nuclear destruction layers and lead to an extra lithium depletion at the surface. A fraction of earth mass is enough to explain a lithium ratio of 4.7 in the 16 Cyg system. In this case beryllium is not destroyed. Such a process may be frequent in planet host stars and should be studied in other cases in the future.

FINGERING CONVECTION INDUCED BY ATOMIC DIFFUSION IN STARS: 3D NUMERICAL COMPUTATIONS AND APPLICATIONS TO STELLAR MODELS

Iron-rich layers are known to form in the stellar subsurface through a combination of gravitational settling and radiative levitation. Their presence, nature and detailed structure can affect the excitation process of various stellar pulsation modes, and must therefore be modeled carefully in order to better interpret Kepler asteroseismic data. In this paper, we study the interplay between atomic diffusion and fingering convection in A-type stars, and its role in the establishment and evolution of iron accumulation layers. To do so, we use a combination of three-dimensional idealized numerical simulations of fingering convection, and one-dimensional realistic stellar models. Using the three-dimensional simulations, we first validate the mixing prescription for fingering convection recently proposed by Brown et al. (2013), and identify what system parameters (total mass of iron, iron diffusivity, thermal diffusivity, etc.) play a role in the overall evolution of the layer. We then implement the Brown et al. (2013) prescription in the Toulouse-Geneva Evolution code to study the evolution of the iron abundance profile beneath the stellar surface. We find, as first discussed by Th\'eado et al. (2009), that when the concurrent settling of helium is ignored, this accumulation rapidly causes an inversion in the mean molecular weight profile, which then drives fingering convection. The latter mixes iron with the surrounding material very efficiently, and the resulting iron layer is very weak. However, taking helium settling into account partially stabilizes the iron profile against fingering convection, and a large iron overabundance can accumulate. The opacity also increases significantly as a result, and in some cases ultimately triggers dynamical convection.

Modeling: connecting interior and atmosphere

The computation of the outermost layers of a star (the atmosphere) requires to solve in details the radiative transfer equation, whereas an analytical formula provides the radiative flux in optically thick layers, which is the case for the inner structure. Then, to have a complete stellar model from the center up to the optically thin layers, one should compute the inner structure on one hand and the uppermost part on the other, and connect the two in some way.After a non-exhaustive review of what is done with other evolutionary codes, we will describe how we deal with the problems met while performing the junction of an inner structure computed with the Toulouse-Geneva Evolution Code (TGEC) and an ATLAS9 atmosphere. Global behaviour of some physical quantities when considering the complete model will be shown, along with the effect on the oscillation frequencies.

Lithium in M 67: From the main sequence to the red giant branch

Lithium abundances in open clusters are a very effective probe of mixing processes, and their study can help to understand the large depletion of lithium in the Sun. Due to its age and metallicity, the open cluster M67 is especially interesting on this regard. Many studies on lithium abundances in M67 have already been performed, but a homogeneous global analysis of lithium in stars from subsolar up to the most massive members, was never accomplished for a large sample based on high-quality spectra. We tested our non-standard models, which were calibrated using the Sun with observational data. We collected literature data to follow, for the first time in a homogeneous way, NLTE lithium abundances of all observed single stars in M67 more massive than about 0.9 solar masses. Our grid of evolutionary models were computed with non-standard mixing at metallicity [Fe/H] = 0.01, using the Toulouse-Geneva evolution code. The analysis is started from the entrance in the ZAMS. Lithium in M67 is a tight function of mass for stars more massive than the Sun, apart of a few outliers. A plateau in lithium abundances is observed for turn-off stars. Both less massive and more massive stars are more depleted than those in the plateau. There is a significant scatter in lithium abundances for any given mass lower than M <= 1.1 solar masses. Our models qualitatively reproduce most of the features described above, although the predicted depletion of lithium is 0.45 dex smaller than observed for masses in the plateau region, i.e. between 1.1 and 1.28 solar masses. Clearly, more work is needed to throughly match the observations. Despite hints that chromospheric activity and rotation play a role in lithium depletion, no firm conclusion can be drawn with the presently available data.

WHAT ROLE DOES CONVECTION PLAY IN THE SYNCHRONIZATION AND CIRCULARIZATION OF BINARIES WITH EVOLVED COMPONENTS?

Binary stars are important for understanding stellar structure and evolution. Binary systems with an evolved component give us an important constraint about the role played by convection on the characteristic time for tidal synchronization and circularization. On this study, we discuss about the role of convection in binary stars with evolved components. Base on a stellar sample composed by 260 binary stars with surface convective mass determined from evolutionary models computed with the Toulouse-Geneva Evolution Code (TGEC) as in do Nascimento et al. (2009). The stars with different convective deepening are represented in the Hertzsprung-Russell diagram (HR diagram). We are focused on the important question of how convection influence the evolution of the tidal synchronization and circularization of binary systems with an evolved component.

Solar twins in M 67: evolutionary status and lithium abundance

We determine the age and mass of the three best solar twin candidates in open cluster M67 through lithium evolutionary models. We computed a grid of evolutionary models with non-standard mixing at metallicity [Fe/H] = 0.01 with the Toulouse-Geneva evolution code for a range of stellar masses. We estimated the mass and age of 10 solar analogs belonging to the open cluster M67. We made a detailed study of the three solar twins of the sample, YPB637, YPB1194, and YPB1787. We obtained a very accurate estimation of the mass of our solar analogs in M67 by interpolating in the grid of evolutionary models. The three solar twins allowed us to estimate the age of the open cluster, which is 3.87+0.55-0.66 Gyr, which is better constrained than former estimates. Our results show that the 3 solar twin candidates have one solar mass within the errors and that M67 has a solar age within the errors, validating its use as a solar proxy. M67 is an important cluster when searching for solar twins.

The Toulouse–Geneva Evolution Code (TGEC)

In the framework of the CoRoT-ESTA, we present the Toulouse–Geneva Evolution Code (TGEC) at its present stage.

Low abundances of heavy elements in the solar outer layers: comparisons of solar models with helioseismic inversions

Recent solar photospheric abundance analyses have led to a significant reduction of the metal abundances compared to the previous determinations. The solar models computed with standard opacities and diffusion processes using these new abundances give poor agreement with helioseismic inversions for the sound-speed profile, the surface helium abundance, and the convective zone depth. We attempt to obtain a good agreement between helioseismic inversions and solar models which present the "old" mixture in the interior and new chemical composition in the convective zone. To reach this result, we assume an undermetallic accretion at the beginning of the main sequence. We compute solar models with the Toulouse-Geneva Evolution Code, in which we simulate an undermetallic accretion in the early stages of the main sequence, in order to obtain new mixture in the outer convective zone. We compare the sound-speed profile, the convective zone depth, and the surface helium abundance with those deduced from helioseismology. The model with accretion but without any mixing process inside is in better agreement with helioseismology than the solar model with the new abundances throughout. There is, however, a spike under the convective zone which reaches 3.4%. Furthermore, the convective zone depth and the surface helium abundance are too low. Introducing undershooting below the convective zone allows us to recover the good convective zone radius and the addition of rotation-induced mixing and tachocline allows us to reconcile the surface helium abundance. But in any case the agreement of the sound-speed profile with helioseismic inference is worse than obtained with the old abundances.