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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 slowdown occurs in the last stages of the red giant branch. This spinning down explains, for instance, the long rotation periods measured in white dwarfs.

Context. There are now more than 22 months of long-cadence data available for thousands of red giants observed with the Kepler space mission. Consequently, we are able to clearly resolve fine details in their oscillation spectra and see many components of the mixed modes that probe the stellar core. Aims. We report for the first time a parametric fit to the pattern of the = 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. Methods. 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 échelle diagrams to emphasize the detection of the gravity-dominated mixed modes. Results. 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 = 3 modes, of = 2 mixed modes, for the mode widths and amplitudes, and for the = 1 rotational splittings. Conclusions. 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.

We use asteroseismic data obtained by the NASA Kepler mission to estimate the fundamental properties of more than 500 main-sequence and sub-giant stars. Data obtained during the first 10 months of Kepler science operations were used for this work, when these solar-type targets were observed for one month each in survey mode. Stellar properties have been estimated using two global asteroseismic parameters and complementary photometric and spectroscopic data. Homogeneous sets of effective temperatures, T eff , were available for the entire ensemble from complementary photometry; spectroscopic estimates of T eff and [Fe/H] were available from a homogeneous analysis of ground-based data on a subset of 87 stars. We adopt a grid-based analysis, coupling six pipeline codes to 11 stellar evolutionary grids. Through use of these different grid-pipeline combinations we allow implicitly for the impact on the results of stellar model dependencies from commonly used grids, and differences in adopted pipeline methodologies. By using just two global parameters as the seismic inputs we are able to perform a homogenous analysis of all solar-type stars in the asteroseismic cohort, including many targets for which it would not be possible to provide robust estimates of individual oscillation frequencies (due to a combination of low signal-to-noise ratio and short dataset lengths). The median final quoted uncertainties from consolidation of the grid-based analyses are for the full ensemble (spectroscopic subset) approximately 10.8% (5.4%) in mass, 4.4% (2.2%) in radius, 0.017 dex (0.010 dex) in log g, and 4.3% (2.8%) in mean density. Around 36% (57%) of the stars have final age uncertainties smaller than 1 Gyr. These ages will be useful for ensemble studies, but should be treated carefully on a star-bystar basis. Future analyses using individual oscillation frequencies will offer significant improvements on up to 150 stars, in particular for estimates of the ages, where having the individual frequency data is most important.

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.

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 = 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.

Solar activity and helioseismology show the limitation of the standard solar model and call for the inclusion of dynamical processes in both convective and radiative zones. In this paper, we concentrate on the radiative zone. We first recall the sensitivity of boron neutrinos to the microscopic physics included in solar standard and seismic models. We confront the neutrino predictions of the seismic model to all the detected neutrino fluxes. Then we compute new models of the Sun including a detailed transport of angular momentum and chemicals due to internal rotation that includes meridional circulation and shear induced turbulence. We use two stellar evolution codes: CESAM and STAREVOL to estimate the different terms. We follow three temporal evolutions of the internal rotation which differ by their initial conditions: very slow, moderate and fast rotation, with magnetic braking at the arrival on the main sequence for the last two. bf We find that the meridional velocities in the present solar radiative zone is extremely small in comparison with those of the convective zone (smaller than 10 −6 cm/s instead of m/s). All models lead to a radial differential rotation profile in the radiative zone but with a significantly different contrast. We compare these profiles to the presumed solar internal rotation and show that if meridional circulation and shear turbulence were the only mechanisms transporting angular momentum within the Sun, a rather slow rotation in the young Sun is favored. We confirm the small influence of the transport by rotation on the sound speed profile but its potential impact on the chemicals in the transition region between radiation and convective zones. These models are physically more representative of the real Sun than the standard or seismic solar models but a high initial rotation, as it has been considered previously, increases the disagreement with neutrinos and the sound speed in the radiative zone. This present work pushes us to pursue the inclusion of the other dynamical processes to better reproduce the observed solar profile in the whole radiative zone and to better describe the young active Sun. We also need to get a better knowledge of solar gravity mode splittings to use their constraints.

The primary science goal of the Kepler Mission is to provide a census of exoplanets in the solar neighborhood, including the identification and characterization of habitable Earth-like planets. The asteroseismic capabilities of the mission are being used to determine precise radii and ages for the target stars from their solar-like oscillations. Chaplin et al. (2010) published observations of three bright G-type stars, which were monitored during the first 33.5 d of science operations. One of these stars, the subgiant KIC 11026764, exhibits a characteristic pattern of oscillation frequencies suggesting that it has evolved significantly. We have derived asteroseismic estimates of the properties of KIC 11026764 from Kepler photometry combined with ground-based spectroscopic data. We present the results of detailed modeling for this star, employing a variety of independent codes and analyses that attempt to match the asteroseismic and spectroscopic constraints simultaneously. We determine both the radius and the age of KIC 11026764 with a precision near 1%, and an accuracy near 2% for the radius and 15% for the age. Continued observations of this star promise to reveal additional oscillation frequencies that will further improve the determination of its fundamental properties.