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Context. KIC 10526294 was recently discovered to be a very slowly rotating and slowly pulsating late B-type star. Its 19 consecutive dipole gravity modes constitute a series with almost constant period spacing. This unique collection of identified modes probes the near-core environment of this star and holds the potential to reveal the size and structure of the overshooting zone above the convective core, as well as the mixing properties of the star. Aims. We revisit the asteroseismic modelling of this star with specific emphasis on the properties of the core overshooting, while considering additional diffusive mixing throughout the radiative envelope of the star. Methods. We pursued forward seismic modelling based on adiabatic eigenfrequencies of equilibrium models for eight extensive evolutionary grids tuned to KIC 10526294 by varying the initial mass, metallicity, chemical mixture, and the extent of the overshooting layer on top of the convective core. We examined models for both OP and OPAL opacities and tested the occurrence of extra diffusive mixing throughout the radiative interior. Results. We find a tight mass-metallicity relation within the ranges M ∈ [3.13, 3.25] M and Z ∈ [0.014, 0.028]. We deduce that an exponentially decaying diffusive core overshooting prescription describes the seismic data better than a step function formulation and derive a value of f ov between 0.017 and 0.018. Moreover, the inclusion of extra diffusive mixing with a value of log D mix between 1.75 and 2.00 dex (with D mix in cm 2 s −1 ) improves the goodness-of-fit based on the observed and modelled frequencies by a factor ∼11 compared to the case where no extra mixing is considered, irrespective of the (M, Z) combination within the allowed seismic range. Conclusions. The inclusion of diffusive mixing in addition to core overshooting is essential to explain the structure in the observed period spacing pattern of this star. Moreover, for the input physics and chemical mixtures we investigated, we deduce that an exponentially decaying prescription for the core overshooting is to be preferred over a step function, regardless of the adopted mixture or choice of opacity tables. Our best models for KIC 10526294 approach the seismic data to a level that they can serve future inversion of its stellar structure.

During most of their life, stars fuse hydrogen into helium in their cores. Mixing of chemical elements in the radiative envelope of stars with a convective

Context. Massive stars are important building blocks of the Universe, and their stellar structure and evolution models are fundamental cornerstones of various fields in modern astrophysics. The precision of these models is strongly limited by our lack of understanding of various internal mixing processes that significantly influence the lifetime of these objects, such as core overshoot, chemical mixing, or the internal differential rotation. Aims. Our goal is to calibrate models by extending the sample of available seismic studies of slowly pulsating B (SPB) stars, providing input for theoretical modelling efforts that will deliver precise constraints on the parameters describing the internal mixing processes in these objects. Methods. We used spectral synthesis and disentangling techniques to derive fundamental parameters and to determine precise orbital parameters from high-resolution spectra. We employed custom masks to construct light curves from the virtually uninterrupted four year long Kepler pixel data and used standard time-series analysis tools to construct a set of significant frequencies for each target. These sets were first filtered from combination frequencies, and then screened for period spacing patterns. Results. We detect gravity mode period series of modes, of the same degree with consecutive radial order n, in four new and one revisited SPB star. These series (covering typically 10 to 40 radial orders) are clearly influenced by moderate to fast rotation and carry signatures of chemical mixing processes. Furthermore, they are predominantly prograde dipole series. Our spectroscopic analysis, in addition to placing each object inside the SPB instability strip and identifying KIC 4930889 as an SB2 binary, reveals that KIC 11971405 is a fast rotator that shows very weak Be signatures. Together with the observed photometric outbursts this illustrates that this Be star is a fast rotating SPB star. We hypothesise that the outbursts might be connected to its very densely compressed oscillation spectrum.

We propose a methodological framework to perform forward asteroseismic modeling of stars with a convective core, based on gravity-mode oscillations. These probe the near-core region in the deep stellar interior. The modeling relies on a set of observed high-precision oscillation frequencies of lowdegree coherent gravity modes with long lifetimes and their observational uncertainties. Identification of the mode degree and azimuthal order is assumed to be achieved from rotational splitting and/or from period spacing patterns. This paper has two major outcomes. The first is a comprehensive list and discussion of the major uncertainties of theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory, caused by fixing choices of the input physics for evolutionary models. Guided by a hierarchy among these uncertainties of theoretical frequencies, we subsequently provide a global methodological scheme to achieve forward asteroseismic modeling. We properly take into account correlations amongst the free parameters included in stellar models. Aside from the stellar mass, metalicity and age, the major parameters to be estimated are the near-core rotation rate, the amount of convective core overshooting, and the level of chemical mixing in the radiative zones. This modeling scheme allows for maximum likelihood estimation of the stellar parameters for fixed input physics of the equilibrium models, followed by stellar model selection considering various choices of the input physics. Our approach uses the Mahalanobis distance instead of the often used χ 2 statistic and includes heteroscedasticity. It provides estimation of the unknown variance of the theoretically predicted oscillation frequencies.

Context. The unparalleled photometric data obtained by NASA's Kepler Space Telescope has led to improved understanding of red giant stars and binary stars. Seismology allows us to constrain the properties of red giants. In addition to eclipsing binaries, eccentric non-eclipsing binaries that exhibit ellipsoidal modulations have been detected with Kepler. Aims. We aim to study the properties of eccentric binary systems containing a red giant star and to derive the parameters of the primary giant component. Methods. We applied asteroseismic techniques to determine the masses and radii of the primary component of each system. For a selected target, light and radial velocity curve modelling techniques were applied to extract the parameters of the system and its primary component. Stellar evolution and its effects on the evolution of the binary system were studied from theoretical models. Results. The paper presents the asteroseismic analysis of 18 pulsating red giants in eccentric binary systems, for which masses and radii were constrained. The orbital periods of these systems range from 20 to 440 days. The results of our ongoing radial velocity monitoring programme with the Hermes spectrograph reveal an eccentricity range of e = 0.2 to 0.76. As a case study we present a detailed analysis of KIC 5006817, whose rich oscillation spectrum allows for detailed seismic analysis. From seismology we constrain the rotational period of the envelope to be at least 165 d, which is roughly twice the orbital period. The stellar core rotates 13 times faster than the surface. From the spectrum and radial velocities we expect that the Doppler beaming signal should have a maximum amplitude of 300 ppm in the light curve. Fixing the mass and radius to the asteroseismically determined values, we find from our binary modelling a value of the gravity darkening exponent that is significantly larger than expected. Through binary modelling, we determine the mass of the secondary component to be 0.29 ± 0.03 M . Conclusions. For KIC 5006817 we exclude pseudo-synchronous rotation of the red giant with the orbit. The comparison of the results from seismology and modelling of the light curve shows a possible alignment of the rotational and orbital axis at the 2σ level. Red giant eccentric systems could be progenitors of cataclysmic variables and hot subdwarf B stars.

Aims. This work presents the results obtained by CoRoT on HD 50844, the only δ Sct star observed in the CoRoT initial run (57.6 d). The aim of these CoRoT observations was to investigate and characterize for the first time the pulsational behaviour of a δ Sct star, when observed at a level of precision and with a much better duty cycle than from the ground. Methods. The 140 016 datapoints were analysed using independent approaches (SigSpec software and different iterative sine-wave fittings) and several checks performed (splitting of the timeseries in different subsets, investigation of the residual light curves and spectra). A level of 10 −5 mag was reached in the amplitude spectra of the CoRoT timeseries. The space monitoring was complemented by ground-based high-resolution spectroscopy, which allowed the mode identification of 30 terms.Results. The frequency analysis of the CoRoT timeseries revealed hundreds of terms in the frequency range 0-30 d −1 . All the crosschecks confirmed this new result. The initial guess that δ Sct stars have a very rich frequency content is confirmed. The spectroscopic mode identification gives theoretical support since very high-degree modes (up to = 14) are identified. We also prove that cancellation effects are not sufficient in removing the flux variations associated to these modes at the noise level of the CoRoT measurements. The ground-based observations indicate that HD 50844 is an evolved star that is slightly underabundant in heavy elements, located on the Terminal Age Main Sequence. Probably due to this unfavourable evolutionary status, no clear regular distribution is observed in the frequency set. The predominant term ( f 1 = 6.92 d −1 ) has been identified as the fundamental radial mode combining ground-based photometric and spectroscopic data.

The Kepler space mission provided near-continuous and high-precision photometry of about 207,000 stars, which can be used for asteroseismology. However, for successful seismic modelling it is equally important to have accurate stellar physical parameters. Therefore, supplementary ground-based data are needed. We report the results of the analysis of high-resolution spectroscopic data of A-and F-type stars from the Kepler field, which were obtained with the HERMES spectrograph on the Mercator telescope. We determined spectral types, atmospheric parameters and chemical abundances for a sample of 117 stars. Hydrogen Balmer, Fe i, and Fe ii lines were used to derive effective temperatures, surface gravities, and microturbulent velocities. We determined chemical abundances and projected rotational velocities using a spectrum synthesis technique. The atmospheric parameters obtained were compared with those from the Kepler Input Catalogue (KIC), confirming that the KIC effective temperatures are underestimated for A stars. Effective temperatures calculated by spectral energy distribution fitting are in good agreement with those determined from the spectral line analysis. The analysed sample comprises stars with approximately solar chemical abundances, as well as chemically peculiar stars of the Am, Ap, and λ Boo types. The distribution of the projected rotational velocity, v sin i, is typical for A and F stars and ranges from 8 to about 280 km s −1 , with a mean of 134 km s −1 .