When the core hydrogen is exhausted during stellar evolution, the central region of a star contracts and the outer envelope expands and cools, giving rise to a red giant. Convection takes place over much of the star's radius. Conservation of angular momentum requires that the cores of these stars rotate faster than their envelopes; indirect evidence supports this 1,2 . Information about the angular-momentum distribution is inaccessible to direct observations, but it can be extracted from the effect of rotation on oscillation modes that probe the stellar interior. Here we report an increasing rotation rate from the surface of the star to the stellar core in the interiors of red giants, obtained using the rotational frequency splitting of recently detected 'mixed modes' 3,4 . By comparison with theoretical stellar models, we conclude that the core must rotate at least ten times faster than the surface. This observational result confirms the theoretical prediction of a steep gradient in the rotation profile towards the deep stellar interior 1,5,6 .The asteroseismic approach to studying stellar interiors exploits information from oscillation modes of different radial order n and angular degree l, which propagate in cavities extending at different depths 7 . Stellar rotation lifts the degeneracy of non-radial modes, producing a multiplet of (2l 1 1) frequency peaks in the power spectrum for each mode. The frequency separation between two mode components of a multiplet is related to the angular velocity and to the properties of the mode in its propagation region. More information on the exploitation of rotational splitting of modes may be found in the Supplementary Information. An important new tool comes from mixed modes that were recently identified in red giants 3,4 . Stochastically excited solar-like oscillations in evolved G and K giant stars 8 have been well studied in terms of theory [9][10][11][12] , and the main results are consistent with recent observations from space-based photometry 13,14 . Whereas pressure modes are completely trapped in the outer acoustic cavity, mixed modes also probe the central regions and carry additional information from the core region, which is probed by gravity modes. Mixed dipole modes (l 5 1) appear in the Fourier power spectrum as dense clusters of modes around those that are best trapped in the acoustic cavity. These clusters, the components of which contain varying amounts of influence from pressure and gravity modes, are referred to as 'dipole forests'.We present the Fourier spectra of the brightness variations of stars KIC 8366239 (Fig. 1a), KIC 5356201 ( Supplementary Fig. 3a) and KIC 12008916 ( Supplementary Fig. 5a), derived from observations with the Kepler spacecraft. The three spectra show split modes, the spherical degree of which we identify as l 5 1. These detected multiplets cannot have been caused by finite mode lifetime effects from mode damping, because that would not lead to a consistent multiplet appearance over several orders such as that shown in Fig. 1. ...

Context. The long and almost continuous observations by Kepler show clear evidence of a granulation background signal in a large sample of stars, which is interpreted as the surface manifestation of convection. It has been shown that its characteristic timescale and rms intensity fluctuation scale with the peak frequency (ν max ) of the solar-like oscillations. Various attempts have been made to quantify the observed signal, to determine scaling relations for its characteristic parameters, and to compare them to theoretical predictions. Even though they are consistent on a global scale, large systematic differences of an unknown origin remain between different methods, as well as between the observations and simulations. Aims. We aim to study different approaches to quantifying the signature of stellar granulation and to search for a unified model that reproduces the observed signal best in a wide variety of stars. We then aim to define empirical scaling relations between the granulation properties and ν max and various other stellar parameters. Methods. We use a probabilistic method to compare different approaches to extracting the granulation signal. We fit the power density spectra of a large set of Kepler targets, determine the granulation and global oscillation parameter, and quantify scaling relations between them. Results. We establish that a depression in power at about ν max /2, known from the Sun and a few other main-sequence stars, is also statistically significant in red giants and that a super-Lorentzian function with two components is best suited to reproducing the granulation signal in the broader vicinity of the pulsation power excess. We also establish that the specific choice of the background model can affect the determination of ν max , introducing systematic uncertainties that can significantly exceed the random uncertainties. We find the characteristic frequency (i.e., inverse timescale) and amplitude of both background components to tightly scale with ν max for a wide variety of stars (about 2-2000 μHz in ν max ), and quantify a mass dependency of the latter. To enable comparison with theoretical predictions (which do not include the observed power depression), we computed effective timescales and bolometric intensity fluctuations and found them to approximately scale as τ eff ∝ g −0.85 T −0.4 and A gran ∝ (g 2 M) −1/4 (or more conveniently R/M 3/4 ), respectively. Similarly, the bolometric pulsation amplitude scales approximately as A puls ∝ (g 2 M) −1/3 (or R 4/3 /M), which implicitly verifies a separate mass and luminosity dependence of A puls . We have also checked our scaling relations with solar reference values and find them in good agreement. Conclusions. We provide a thorough analysis of the granulation background signal in a large sample of stars, from which we establish a unified model that allows us to accurately extract the granulation and global oscillation parameter. The resulting scaling relations allow a simple estimate of the overall spectral shape of any solar-ty...

Aims. We investigated a sample of 28 well-known spectroscopically-identified magnetic Ap/Bp stars, with weak, poorly-determined or previously undetected magnetic fields. The aim of this study is to explore the weak part of the magnetic field distribution of Ap/Bp stars. Methods. Using the MuSiCoS and NARVAL spectropolarimeters at Télescope Bernard Lyot (Observatoire du Pic du Midi, France) and the cross-correlation technique Least Squares Deconvolution (LSD), we obtained 282 LSD Stokes V signatures of our 28 sample stars, in order to detect the magnetic field and to infer its longitudinal component with high precision (median σ = 40 G). Results. For the 28 studied stars, we obtained 27 detections of Stokes V Zeeman signatures from the MuSiCoS observations. Detection of the Stokes V signature of the 28th star (HD 32650) was obtained during science demonstration time of the new NARVAL spectropolarimeter at Pic du Midi. This result clearly shows that when observed with sufficient precision, all firmly classified Ap/Bp stars show detectable surface magnetic fields. Furthermore, all detected magnetic fields correspond to longitudinal fields which are significantly greater than some tens of G. To better characterise the surface magnetic field intensities and geometries of the sample, we phased the longitudinal field measurements of each star using new and previously-published rotational periods, and modeled them to infer the dipolar field intensity (B d , measured at the magnetic pole) and the magnetic obliquity (β). The distribution of derived dipole strengths for these stars exhibits a plateau at about 1 kG, falling off to larger and smaller field strengths. Remarkably, in this sample of stars selected for their presumably weak magnetic fields, we find only 2 stars for which the derived dipole strength is weaker than 300 G. We interpret this "magnetic threshold" as a critical value necessary for the stability of large-scale magnetic fields, and develop a simple quantitative model that is able to approximately reproduce the observed threshold characteristics. This scenario leads to a natural explanation of the small fraction of intermediate-mass magnetic stars. It may also explain the near-absence of magnetic fields in more massive B and O-type stars.

Context. The Kepler spacecraft is providing time series of photometric data with micromagnitude precision for hundreds of A-F type stars. Aims. We present a first general characterization of the pulsational behaviour of A-F type stars as observed in the Kepler light curves of a sample of 750 candidate A-F type stars, and observationally investigate the relation between γ Doradus (γ Dor), δ Scuti (δ Sct), and hybrid stars. Methods. We compile a database of physical parameters for the sample stars from the literature and new ground-based observations. We analyse the Kepler light curve of each star and extract the pulsational frequencies using different frequency analysis methods. We construct two new observables, "energy" and "efficiency", related to the driving energy of the pulsation mode and the convective efficiency of the outer convective zone, respectively. Results. We propose three main groups to describe the observed variety in pulsating A-F type stars: γ Dor, δ Sct, and hybrid stars. We assign 63% of our sample to one of the three groups, and identify the remaining part as rotationally modulated/active stars, binaries, stars of different spectral type, or stars that show no clear periodic variability. 23% of the stars (171 stars) are hybrid stars, which is a much higher fraction than what has been observed before. We characterize for the first time a large number of A-F type stars (475 stars) in terms of number of detected frequencies, frequency range, and typical pulsation amplitudes. The majority of hybrid stars show frequencies with all kinds of periodicities within the γ Dor and δ Sct range, also between 5 and 10 d −1 , which is a challenge for the current models. We find indications for the existence of δ Sct and γ Dor stars beyond the edges of the current observational instability strips. The hybrid stars occupy the entire region within the δ Sct and γ Dor instability strips and beyond. Non-variable stars seem to exist within the instability strips. The location of γ Dor and δ Sct classes in the (T eff , log g)-diagram has been extended. We investigate two newly constructed variables, "efficiency" and "energy", as a means to explore the relation between γ Dor and δ Sct stars. Conclusions. Our results suggest a revision of the current observational instability strips of δ Sct and γ Dor stars and imply an investigation of pulsation mechanisms to supplement the κ mechanism and convective blocking effect to drive hybrid pulsations. Accurate physical parameters for all stars are needed to confirm these findings.