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Solar analogues are important stars to study for understanding the properties of the Sun. Combined with seismic and spectroscopic analysis, evolutionary modelling becomes a powerful method to characterize stellar intrinsic parameters, such as mass, radius, metallicity and age. However, these characteristics, relevant for other aspects of astrophysics or exoplanetary system physics, for example, are difficult to obtain with high precision and/or accuracy. The goal of this study is to characterize the two solar analogues, HD 42618 and HD 43587, observed by CoRoT. In particular, we aim to infer their precise mass, radius and age, using evolutionary modelling constrained by spectroscopic, photometric and seismic analysis. These stars show evidence of being older than the Sun but with a relatively large lithium abundance. We present the seismic analysis of HD 42618, and the modelling of the two solar analogues, HD 42618 and HD 43587 using the cestam stellar evolution code. Models were computed to reproduce the spectroscopic (effective temperature and metallicity) and seismic (mode frequency) data, and the luminosity of the stars, based on Gaia parallaxes. We infer very similar values of mass and radius for both stars compared with the literature, within the uncertainties, and we reproduce correctly the seismic constraints. The modelling shows that HD 42618 is slightly less massive and older than the Sun, and that HD 43587 is more massive and older than the Sun, in agreement with previous results. The use of chemical clocks improves the reliability of our age estimates. [ABSTRACT FROM AUTHOR]

Context. The seismic data provided by the space-borne missions 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. Aims. We aim to 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. Methods. A semi-analytical excitation model was used to estimate the angular momentum wave flux. The characteristic timescale associated with the angular momentum transport by IGW was computed and compared to the contraction timescale throughout the radiative region of stellar models at different evolutionary stages. Results. 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 in the radiative region 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 because of an excessive radiative damping. Conclusions. IGW generated by penetrative convection are able to efficiently extract angular momentum from the core of stars on the subgiant branch and accordingly have to be taken into account. Moreover, agreements with the observations reinforce the idea that their effect is essential to regulate the amplitude of the radial-differential rotation in subgiant stars. On the red giant branch, another transport mechanism must likely be invoked. [ABSTRACT FROM AUTHOR]

The detection of mixed modes in subgiants and red giants by the CoRoT and Kepler space-borne missions allows us to investigate the internal structure of evolved low-mass stars, from the end of the main sequence to the central helium-burning phase. 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 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. [ABSTRACT FROM AUTHOR]

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⊙ 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. [ABSTRACT FROM AUTHOR]

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⊙ 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. [ABSTRACT FROM AUTHOR]

Context. 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. Aims. We aim to measure the rotational splittings in red giants and to derive scaling relations for rotation related to seismic and fundamental stellar parameters. Methods. 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. Results. 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. Conclusions. 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. [ABSTRACT FROM AUTHOR]

Context. Determining the mass of stars is crucial both for improving stellar evolution theory and for characterising exoplanetary systems. Asteroseismology offers a promising way for estimating the stellar mean density. When combined with accurate radii determinations, such as are expected from Gaia, this yields accurate stellar masses. The main difficulty is finding the best way to extract the mean density of a star from a set of observed frequencies. Aims. We seek to establish a new method for estimating the stellar mean density, which combines the simplicity of a scaling law while providing the accuracy of an inversion technique. Methods. We provide a framework in which to construct and evaluate kernel-based linear inversions that directly yield 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, α Cen B, HD 49933 and HD 49385, two of which are observed by CoRoT. Results. The SOLA (subtractive optimally localised averages) approach and the scaling law based on the surface correcting technique described by Kjeldsen et al. (2008, ApJ, 683, L175) yield comparable results that 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, we show that mixed modes bring little improvement to the mean density estimates because of their poorly adapted kernels. [ABSTRACT FROM AUTHOR]