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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.
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