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. ...

We present the first detection of a rotationally affected series consisting of 36 consecutive high-order sectoral dipole gravity modes in a slowly pulsating B (SPB) star. The results are based on the analysis of four years of virtually uninterrupted photometric data assembled with the Kepler Mission, and high-resolution spectra acquired using the HERMES spectrograph at the 1.2 m Mercator Telescope. The specroscopic measurements place KIC 7760680 inside the SPB instability strip, near the cool edge, given its fundamental parameters of The photometric analysis reveals the longest unambiguous series of gravity modes of the same degree ℓ with consecutive radial order n, which carries clear signatures of chemical mixing and rotation. With such exceptional observational constraints, this star should be considered as the Rosetta stone of SPBs for future modeling, and brings us a step closer to the much-needed seismic calibration of stellar structure models of massive stars.

We present a detailed study based on infrared photometry of all Galactic RV Tauri stars from the General Catalogue of Variable Stars (GCVS). RV Tauri stars are the brightest among the population II Cepheids. They are thought to evolve away from the asymptotic giant branch (AGB) towards the white dwarf domain. IRAS detected several RV Tauri stars because of their large IR excesses and it was found that they occupy a specific region in theWe used the all sky survey of WISE to extend these studies and compare the infrared properties of all RV Tauri stars in the GCVS with a selected sample of post-AGB objects with the goal to place the RV Tauri pulsators in the context of post-AGB evolution. Moreover, we correlated the IR properties of both the RV Tauri stars and the comparison sample with other observables like binarity and the presence of a photospheric chemical anomaly called depletion. We find that Galactic RV Tauri stars display a range of infrared properties and we differentiate between disc sources, objects with no IR excess and objects for which the spectral energy distribution (SED) is uncertain. We obtain a clear correlation between disc sources and binarity. RV Tauri stars with a variable mean magnitude are exclusively found among the disc sources. We also find evidence for disc evolution among the binaries. Furthermore our studies show that the presence of a disc seems to be a necessary but not sufficient condition for the depletion process to become efficient.

Context. During the last few decades, it became more evident that binarity is a prevalent phenomenon amongst RV Tauri stars with a disc. This study is a contribution in comprehending the role of binarity upon late stages of stellar evolution. Aims. In this paper we determine the binary status of six Galactic RV Tauri stars, namely DY Ori, EP Lyr, HP Lyr, IRAS 17038−4815, IRAS 09144−4933 and TW Cam, which are surrounded by a dusty disc. The radial velocities are contaminated by high amplitude pulsations. We disentangle the pulsations from the orbital signal in order to determine accurate orbital parameters. We also place them on the HR diagram, thereby establishing their evolutionary nature. Methods. We used high resolution spectroscopic time series obtained from the HERMES and CORALIE spectrographs mounted on the Flemish Mercator and Swiss Leonhard Euler Telescopes, respectively. An updated ASAS/AAVSO photometric time series is analysed to complement the spectroscopic pulsation search and to clean the radial velocities from the pulsations. The pulsation-cleaned orbits are fitted with a Keplerian model to determine the spectroscopic orbital parameters. We also calibrated a PLC relationship using type II cepheids in the LMC and apply the relation to our Galactic sample to obtain accurate distances and hence luminosities. Results. All the six Galactic RV Tauri stars included in this study are binaries with orbital periods ranging between ∼ 650 and 1700 days and with eccentricities between 0.2 and 0.6. The mass functions range between 0.08 to 0.55 M which points to an unevolved low mass companion. In the photometric time series we detect a long-term variation on the time-scale of the orbital period for IRAS 17038−4815, IRAS 09144−4933 and TW Cam. Our derived stellar luminosities indicate that all except DY Ori and EP Lyr, are post-AGB stars. DY Ori and EP Lyr are likely examples of the recently discovered dusty post-RGB stars.Conclusions. The orbital parameters strongly suggest that the evolution of these stars was interrupted by a strong phase of binary interaction during or even prior to the AGB. The observed eccentricities and long orbital periods among these stars provides a challenge to the standard theory of binary evolution.

Context. Many post-asymptotic giant branch (post-AGB) stars in binary systems have an infrared (IR) excess arising from a dusty circumbinary disk. The disk formation, current structure, and further evolution are, however, poorly understood. Aims. We aim to constrain the structure of the circumstellar material around the post-AGB binary and RV Tauri pulsator AC Her. We want to constrain the spatial distribution of the amorphous and of the crystalline dust. Methods. We present very high-quality mid-IR interferometric data that were obtained with the MIDI/VLTI instrument. We analyze the MIDI visibilities and differential phases in combination with the full spectral energy distribution, using the MCMax radiative transfer code, to find a good structure model of AC Her's circumbinary disk. We include a grain size distribution and midplane settling of dust self-consistently in our models. The spatial distribution of crystalline forsterite in the disk is investigated with the mid-IR features, the 69 µm band and the 11.3 µm signatures in the interferometric data. Results. All the data are well fitted by our best model. The inclination and position angle of the disk are precisely determined at i = 50 ± 8• and PA = 305 ± 10 • . We firmly establish that the inner disk radius is about an order of magnitude larger than the dust sublimation radius. The best-fit dust grain size distribution shows that significant grain growth has occurred, with a significant amount of mm-sized grains now being settled to the midplane of the disk. A large total dust mass ≥10 −3 M is needed to fit the mm fluxes. By assuming α turb = 0.01, a good fit is obtained with a small grain size power law index of 3.25, combined with a small gas/dust ratio ≤10. The resulting gas mass is compatible with recent estimates employing direct gas diagnostics. The spatial distribution of the forsterite is different from the amorphous dust, as more warm forsterite is needed in the surface layers of the inner disk. Conclusions. The disk in the AC Her system is in a very evolved state, as shown by its small gas/dust ratio and large inner hole. Mid-IR interferometry offers unique constraints, complementary to mid-IR features, for studying the mineralogy in disks. A better uv coverage is needed to constrain in detail the distribution of the crystalline forsterite in the disk of AC Her, but we find strong similarities with the protoplanetary disk HD 100546.

Aims. We present the first near-IR milli-arcsecond-scale image of a post-AGB binary that is surrounded by hot circumbinary dust. Methods. A very rich interferometric data set in six spectral channels was acquired of IRAS 08544-4431 with the new RAPID camera on the PIONIER beam combiner at the Very Large Telescope Interferometer (VLTI). A broadband image in the H-band was reconstructed by combining the data of all spectral channels using the SPARCO method. Results. We spatially separate all the building blocks of the IRAS 08544-4431 system in our milliarcsecond-resolution image. Our dissection reveals a dust sublimation front that is strikingly similar to that expected in early-stage protoplanetary disks, as well as an unexpected flux signal of ∼4% from the secondary star. The energy output from this companion indicates the presence of a compact circum-companion accretion disk, which is likely the origin of the fast outflow detected in Hα. Conclusions. Our image provides the most detailed view into the heart of a dusty circumstellar disk to date. Our results demonstrate that binary evolution processes and circumstellar disk evolution can be studied in detail in space and over time.

Context. Post-Asymptotic Giant Branch (AGB) binaries are surrounded by stable dusty and gaseous disks similar to the ones around young stellar objects. Whereas significant effort is spent on modeling observations of disks around young stellar objects, the disks around post-AGB binaries receive significantly less attention, even though they pose significant constraints on theories of disk physics and binary evolution. Aims. We want to examine the structure of and phenomena at play in circumbinary disks around post-AGB stars. We continue the analysis of our near-infrared interferometric image of the inner rim of the circumbinary disk around IRAS08544-4431. We want to understand the physics governing this inner disk rim. Methods. We use a radiative transfer model of a dusty disk to reproduce simultaneously the photometry as well as the near-infrared interferometric dataset on IRAS08544-4431. The model assumes hydrostatic equilibrium and takes dust settling self-consistently into account.Results. The best-fit radiative transfer model shows excellent agreement with the spectral energy distribution up to mm wavelengths as well as with the PIONIER visibility data. It requires a rounded inner rim structure, starting at a radius of 8.25 au. However, the model does not fully reproduce the detected over-resolved flux nor the azimuthal flux distribution of the inner rim. While the asymmetric inner disk rim structure is likely to be the consequence of disk-binary interactions, the origin of the additional over-resolved flux remains unclear. Conclusions. As in young stellar objects, the disk inner rim of IRAS08544-4431 is ruled by dust sublimation physics. Additional observations are needed to understand the origin of the extended flux and the azimuthal perturbation at the inner rim of the disk.

Context. The presence of stable disks around post-asymptotic giant branch (post-AGB) binaries is a widespread phenomenon. Also, the presence of (molecular) outflows is now commonly inferred in these systems. Aims. In the first paper of this series, a surprisingly large fraction of optical light was found to be resolved in the 89 Her post-AGB binary system. The data showed that this flux arises from close to the central binary. Scattering off the inner rim of the circumbinary disk, or scattering in a dusty outflow were suggested as two possible origins. With detailed dust radiative transfer models of the circumbinary disk, we aim to discriminate between the two proposed configurations. Methods. By including Herschel/SPIRE photometry, we extend the spectral energy distribution (SED) such that it now fully covers UV to sub-mm wavelengths. The MCMax Monte Carlo radiative transfer code is used to create a large grid of disk models. Our models include a self-consistent treatment of dust settling as well as of scattering. A Si-rich composition with two additional opacity sources, metallic Fe or amorphous C, are tested. The SED is fit together with archival mid-IR (MIDI) visibilities, and the optical and near-IR visibilities of Paper I. In this way we constrain the structure of the disk, with a focus on its inner rim. Results. The near-IR visibility data require a smooth inner rim, here obtained with a double power-law parameterization of the radial surface density distribution. A model can be found that fits all of the IR photometric and interferometric data well, with either of the two continuum opacity sources. Our best-fit passive models are characterized by a significant amount of ∼mm-sized grains, which are settled to the midplane of the disk. Not a single disk model fits our data at optical wavelengths because of the opposing constraints imposed by the optical and near-IR interferometric data. Conclusions. A geometry in which a passive, dusty, and puffed-up circumbinary disk is present, can reproduce all of the IR, but not the optical observations of 89 Her. Another dusty component (an outflow or halo) therefore needs to be added to the system.