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Asteroseismic modelling of the internal structure of main-sequence stars born with a convective core has so far been based on homogeneous analyses of space photometric Kepler light curves of 4 years duration, to which most often incomplete inhomogeneously deduced spectroscopic information was added to break degeneracies. We composed a sample of 111 dwarf gravity-mode pulsators observed by the Kepler space telescope whose light curves allowed for determination of their near-core rotation rates. For this sample we assembled HERMES high-resolution optical spectroscopy at the 1.2-m Mercator telescope. Our spectroscopic information offers additional observational input to also model the envelope layers of these non-radially pulsating dwarfs. We determined stellar parameters and surface abundances in a homogeneous way from atmospheric analysis with spectrum normalisation based on a new machine learning tool. Our results suggest a systematic overestimation of [M/H] in the literature for the studied F-type dwarfs, presumably due to normalisation limitations caused by the dense line spectrum of these rotating stars. CNO-surface abundances were found to be uncorrelated with the rotation properties of the F-type stars. For the B-type stars, we find a hint of deep mixing from C and O abundance ratios; N abundances have too large uncertainties to reveal a correlation with the rotation of the stars. Our spectroscopic stellar parameters and abundance determinations allow for future joint spectroscopic, astrometric (Gaia), and asteroseismic modelling of this legacy sample of gravity-mode pulsators, with the aim to improve our understanding of transport processes in the core-hydrogen burning phase of stellar evolution., Accepted for publication in Astronomy and Astrophysics

The Traditional Approximation of Rotation (TAR) is a treatment of the hydrodynamic equations of rotating and stably stratified fluids in which the action of the Coriolis acceleration along the direction of the entropy and chemical stratifications is neglected because it is weak in comparison with the buoyancy force. The dependent variables in the equations for the dynamics of gravito-inertial waves (GIWs) then become separable into radial and horizontal parts as in the non-rotating case. The TAR is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating. We study the feasibility of carrying out a generalisation of the TAR to account for the centrifugal acceleration in the case of strongly deformed uniformly and rapidly rotating stars (and planets), and to identify the validity domain of this approximation. We built analytically a complete formalism that allows the study of the dynamics of GIWs in spheroidal coordinates which take into account the flattening of rapidly rotating stars by assuming the hierarchies of frequencies adopted within the TAR in the spherical case and by deriving a generalised Laplace tidal equation for the horizontal eigenfunctions of the GIWs and their asymptotic wave periods, which can be used to probe the structure and dynamics of rotating deformed stars with asteroseismology. Using 2D ESTER stellar models, we determine the validity domain of the generalised TAR as a function of the rotation rate of the star normalised by its critical angular velocity and its pseudo-radius. This generalisation allows us to study the signature of the centrifugal effects on GIWs in rapidly rotating deformed stars. We found that the effects of the centrifugal acceleration in rapidly rotating early-type stars on GIWs are theoretically detectable in modern space photometry using observations from Kepler., Comment: 17 pages, 14 figures, 1 table, abstract shortened for arXiv. Accepted for publication in A&A

The Kepler and TESS missions delivered high-precision, long-duration photometric time series for hundreds of main-sequence stars with gravito-inertial (g) pulsation modes. This high precision allows us to evaluate increasingly detailed theoretical stellar models. Recent theoretical work extended the traditional approximation of rotation (TAR), a framework to evaluate the effect of the Coriolis acceleration on g-modes, to include the effects of the centrifugal acceleration in the approximation of slightly deformed stars, which so far had mostly been neglected in asteroseismology. This extension of the TAR was conceived by rederiving the TAR in a centrifugally deformed, spheroidal coordinate system. We explore the effect of the centrifugal acceleration on g modes and assess its detectability in space-based photometry. We implement the new framework to calculate the centrifugal deformation of precomputed 1D spherical stellar structure models and compute the corresponding g-mode frequencies, assuming uniform rotation. The framework is evaluated for a grid of stellar structure models covering a relevant parameter space for observed g-mode pulsators. The centrifugal acceleration modifies the effect of the Coriolis acceleration on g modes, narrowing the equatorial band in which they are trapped. Furthermore, the centrifugal acceleration causes the pulsation periods and period spacings of the most common g modes (prograde dipole modes and r modes) to increase with values similar to the observational uncertainties in Kepler and TESS data. The effect of the centrifugal acceleration on g~modes is formally detectable in modern space photometry. Implementation of the new theoretical framework in stellar structure and pulsation codes will allow for more precise asteroseismic modelling of centrifugally deformed stars, to assess its effect on mode excitation, -trapping and -damping., Comment: 14 pages, 14 figures, 1 table. Resubmitted to A&A after a positive referee report

Multi-dimensional (magneto-)hydrodynamical simulations of physical processes in stellar interiors depend on a multitude of uncalibrated free parameters, which set the spatial and time scales of their computations. We aim to provide an asteroseismic calibration of the wave and convective Rossby numbers, and of the stiffness at the interface between the convective core and radiative envelope of intermediate-mass stars. We deduce these quantities for rotating dwarfs from the observed properties of their identified gravity and gravito-inertial modes. We rely on near-core rotation rates and asteroseismic models of 26 B- and 37 F-type dwarf pulsators derived from 4-year Kepler space photometry, high-resolution spectroscopy and Gaia astrometry in the literature to deduce their convective and wave Rossby numbers. We compute the stiffness at the convection/radiation interface from the inferred maximum buoyancy frequency at the interface and the convective turnover frequency in the core. We use those asteroseismically inferred quantities to make predictions of convective penetration levels, local flux levels of gravito-inertial waves triggered by the convective core, and of the cores' potential rotational and magnetic states. Our sample of 63 gravito-inertial mode pulsators covers near-core rotation rates from almost zero up to the critical rate. The frequencies of their identified modes lead to models with stiffness values between $10^{2.69}$ and $10^{3.60}$ for the B-type pulsators, while those of F-type stars cover the range from $10^{3.47}$ to $10^{4.52}$. The convective Rossby numbers derived from the maximum convective diffusion coefficient in the convective core, based on mixing length theory and a value of the mixing length coefficient relevant for these pulsators, vary between $10^{-2.3}$ and $10^{-0.8}$ for B-type stars and $10^{-3}$ and $10^{-1.5}$ for F-type stars. (abridged), Comment: 10 pages, 8 figures, accepted for publication in Astronomy & Astrophysics, version adapted to proofs

We aim to unravel the interior mixing profile of the pulsating eclipsing binary KIC9850387 by comparing its dynamical parameters and the parameters derived through a combination of evolutionary and asteroseismic modelling. We created a grid of stellar evolutionary models using the stellar evolutionary code \textsc{mesa} and performed an isochrone-cloud (isocloud) based evolutionary modelling of the system. We then generated a grid of pulsational models using the stellar pulsation code \textsc{gyre} based on the age constraints from the evolutionary modelling. Finally, we performed asteroseismic modelling of the observed $\ell=1$ and $\ell=2$ period-spacing patterns, utilising different combinations of observational constraints, merit functions, and asteroseismic observables to obtain strong constraints on the interior properties of the primary star. Through a combination of asteroseismic modelling and dynamical constraints, we found that the system comprises two main-sequence components at an age of $1.2\pm0.1$ Gyr. We also observed that asteroseismic modelling provided stronger constraints on the interior properties than evolutionary modelling. Overall, we found high levels of interior mixing and posited that this is a result of intrinsic non-tidal mixing mechanisms due to a similar observed behaviour in single stars. We investigated the high-frequency regime of KIC9850387 and found evidence of the surface effect as well as rotational splitting in the form of a prograde-retrograde dipole g$_{1}$ mode doublet with a missing zonal mode. We find that the dynamical parameters and the parameters extracted from the asteroseismic modelling of period-spacing patterns are only barely compliant, reinforcing the need for homogeneous analyses of samples of pulsating eclipsing binaries that aim to calibrating interior mixing profiles., 21 pages, 18 figures, accepted for publication in A&A

In $\gamma$ Doradus stars, the g-mode period spacing shows an approximately linear relation with period. The slope is a new asteroseismic diagnostic, related to the rotation rate and the azimuthal order $m$. We report two automated methods, the `moving-window Fourier transform' and the `cross-correlation', to detect and measure the period spacings based on four-year light curves from the \textit{Kepler} satellite. The results show that the cross-correlation method performs better at detecting the period spacings and their slopes. In this paper, we apply our method to 22 $\gamma$ Dor stars with g-mode multiplets split by rotation. The rotation periods are similar to the g-mode period spacings, causing the multiplets to overlap. To clarify the overlapping patterns, we use the \'echelle diagram and introduce a `copy-shift' diagram to discern and measure the splittings. The first observational relation between slopes and splittings is shown. The slope deviates from zero when the splitting increases, as the theory predicts. We found that what appears to be rotational splittings in two stars is in fact caused by two nearly-identical overlapping patterns from binaries., Comment: 38 pages, 66 figures, Accepted by MNRAS

We report our survey of γ Dor stars from the 4-yr Kepler mission. These stars pulsate mainly in g modes and r modes, showing period-spacing patterns in the amplitude spectra. The period-spacing patterns are sensitive to the chemical composition gradients and the near-core rotation, hence they are essential for understanding the stellar interior. We identified period-spacing patterns in 611 γ Dor stars. Almost every star pulsates in dipole g modes, while about 30% of stars also show clear patterns for quadrupole g modes and 16% of stars present r mode patterns. We measure periods, period spacings, and the gradient of the period spacings. These three observables guide the mode identifications and can be used to estimate the near-core rotation rate. We find many stars are hotter and show longer period-spacing patterns than theory. Using the Traditional Approximation of Rotation (TAR), we inferred the asymptotic spacings, the near-core rotation rates, and the radial orders of the g and r modes. Most stars have a near-core rotation rate around 1 d−1and an asymptotic spacing around 4000 s. We also find that many stars rotate more slowly than predicted by theory for unclear reasons. 11 stars show rotational splittings with fast rotation rates. We compared the observed slope–rotation relation with the theory and find a large spread. We detected rotational modulations in 58 stars and used them to derive the core-to-surface rotation ratios. The interiors rotate faster than the cores in most stars, but by no more than 5%.

Rossby modes are the oscillations in a rotating fluid, whose restoring force is the Coriolis force. They provide an additional diagnostic to understand the rotation of stars, which complicates asteroseismic modelling. We report 82 $\gamma$\,Doradus stars for which clear period spacing patterns of both gravity and Rossby modes have been detected. The period spacings of both show a quasi-linear relation with the pulsation period but the slope is negative for the gravity modes and positive for the Rossby modes. Most Rossby modes have $k=-2, m=-1$. For only one star a series of $k=-1,m=-1$ modes is seen. For each pattern, the mean pulsation period, the mean period spacing, and the slope are measured. We find that the slope correlates with the mean period for Rossby mode patterns. The traditional approximation of rotation is used to measure the near-core rotation rate, assuming the star rotates rigidly. We report the near-core rotation rates, the asymptotic period spacings, and the radial orders of excited modes of these 82 main-sequence stars. The near-core rotation rates lie between $0.6\,\mathrm{d^{-1}}$ and $2.3\,\mathrm{d^{-1}}$. Six stars show surface rotation modulations, among which only KIC\,3341457 shows differential rotation while the other five stars have uniform rotations. The radial orders of excited modes show different distributions for the dipole and quadrupole gravity modes versus the Rossby modes.

We develop a novel method based on machine learning principles to achieve optimal initiation of CPU-intensive computations for forward asteroseismic modeling in a multi-D parameter space. A deep neural network is trained on a precomputed asteroseismology grid containing about 62 million coherent oscillation-mode frequencies derived from stellar evolution models. These models are representative of the core-hydrogen burning stage of intermediate-mass and high-mass stars. The evolution models constitute a 6D parameter space and their predicted low-degree pressure- and gravity-mode oscillations are scanned, using a genetic algorithm. A software pipeline is created to find the best fitting stellar parameters for a given set of observed oscillation frequencies. The proposed method finds the optimal regions in the 6D parameters space in less than a minute, hence providing the optimal starting point for further and more detailed forward asteroseismic modeling in a high-dimensional context. We test and apply the method to seven pulsating stars that were previously modeled asteroseismically by classical grid-based forward modeling based on a $\chi^2$ statistic and obtain good agreement with past results. Our deep learning methodology opens up the application of asteroseismic modeling in +6D parameter space for thousands of stars pulsating in coherent modes with long lifetimes observed by the $Kepler$ space telescope and to be discovered with the TESS and PLATO space missions, while applications so far were done star-by-star for only a handful of cases. Our method is open source and can be used by anyone freely., Comment: Accepted for publication in PASP Speciale Volume on Machine Learning

We present the discovery of three new $\beta$ Cep pulsators, three new pulsators with frequency groupings, and frequency patterns in a B3Ib star, all of which show pulsations with frequencies as high as about 17 d$^{-1}$, with K2 space mission photometry. Based on a Fourier analysis and iterative pre-whitening we present a classification and evaluate the potential for asteroseismic modelling. We include the lists of pulsation frequencies for three new $\beta$ Cep pulsators, CD-28 12286, CD-27 10876, LS 3978, and additional pulsation mode frequencies for the known $\beta$ Cep pulsator HD 164741. In addition we characterise the regular frequency spacing found in the new pulsator HD 169173, and discuss its origin. We place the newly discovered variables in a colour-magnitude diagram using parallaxes from Gaia-DR2, showcasing their approximate location in the massive star domain. The identified frequency lists of these multiperiodic pulsators are a good starting point for future forward seismic modelling, after identification of at least one pulsation frequency from high-resolution time series spectroscopy and/or multi-colour photometry., Comment: Accepted for publication in MNRAS, 18 pages, 12 figures, 11 tables

The space-based Kepler mission provided four years of highly precise and almost uninterrupted photometry for hundreds of $\gamma$ Doradus stars and tens of SPB stars, finally allowing us to apply asteroseismology to these gravity mode pulsators. Without rotation, gravity modes are equally spaced in period. This simple structure does not hold in rotating stars for which rotation needs to be taken into account to accurately interpret the oscillation spectrum. We aim to develop a stellar-model-independent method to analyse and interpret the oscillation spectrum of $\gamma$ Dor and SPB stars. Within the traditional approximation of rotation, we highlight the possibility of recovering the equidistance of period spacings by stretching the pulsation periods. The stretching function depends on the degree and azimuthal order of gravity modes and the rotation rate of the star. In this new stretched space, the pulsation modes are regularly spaced by the stellar buoyancy radius. On the basis of this property, we implemented a method to search for these new regularities and simultaneously infer the rotation frequency and buoyancy radius. Tests on synthetic spectra computed with a non-perturbative approach show that we can retrieve these two parameters with reasonable accuracy along with the mode identification. In uniformly rotating models of a typical $\gamma$ Dor star, and for the most observed prograde dipole modes, we show that the accuracy on the derived parameters is better than 5% on both the internal rotation rate and the buoyancy radius. Finally, we apply the method to two stars of the Kepler field, a $\gamma$ Dor and an SPB, and compare our results with those of other existing methods. We provide a stellar-model-independent method to obtain the near-core rotation rate, the buoyancy radius and mode identification from g-mode spectra of $\gamma$ Dor and SPB stars., Comment: 15 pages, 9 figures, accepted for publication in A&A

The differentially rotating outer layers of stars are thought to play a role in driving their magnetic activity, but the underlying mechanisms that generate and sustain differential rotation are poorly understood. We report the measurement of latitudinal differential rotation in the convection zones of 40 Sun-like stars using asteroseismology. For the most significant detections, the stars' equators rotate approximately twice as fast as their mid-latitudes. The latitudinal shear inferred from asteroseismology is much larger than predictions from numerical simulations., 45 pages, 11 figures, 4 tables, published in Science

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 low-degree 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 $\chi^2$ statistic and includes heteroscedasticity. It provides estimation of the unknown variance of the theoretically predicted oscillation frequencies., Comment: Accepted for publication in The Astrophysical Journal Supplement Series, 45 pages, 2 tables, 18 figures

We present the first data release of the Kepler Smear Campaign, using collateral 'smear' data obtained in the Kepler four-year mission to reconstruct light curves of 102 stars too bright to have been otherwise targeted. We describe the pipeline developed to extract and calibrate these light curves, and show that we attain photometric precision comparable to stars analyzed by the standard pipeline in the nominal Kepler mission. In this paper, aside from publishing the light curves of these stars, we focus on 66 red giants for which we detect solar-like oscillations, characterizing 33 of these in detail with spectroscopic chemical abundances and asteroseismic masses as benchmark stars. We also classify the whole sample, finding nearly all to be variable, with classical pulsations and binary effects. All source code, light curves, TRES spectra, and asteroseismic and stellar parameters are publicly available as a Kepler legacy sample., Comment: 35 pages, accepted ApJS

Space photometric time series of the most massive members of the young open cluster NGC 2264 allow us to study their different sources of variability down to the millimagnitude level and permits a search for Slowly Pulsating B (SPB) type pulsation among objects that are only a few million years old. Our goal is to conduct a homogeneous study of young B type stars in the cluster NGC 2264 using photometric time series from space in combination with high-resolution spectroscopy and spectropolarimetry obtained from the ground. The latter will be presented in a separate follow-up article. We performed frequency analyses for eleven B stars in the field of the young cluster NGC 2264 using photometric time series from the MOST, CoRoT and Spitzer space telescopes and the routines Period04 and SigSpec. We employ the MESA stellar evolution code in combination with the oscillation code GYRE to identify the pulsation modes for two SPB stars which exhibit short period spacing series. From our analysis we identify four objects that show SPB pulsations, five stars that show rotational modulation of their light curves caused by spots, one star that is identified to be a binary, and one object in the field of the cluster that is found to be a non-member Be star. In two SPB stars we detect a number of regularly spaced pulsation modes that are compatible with being members of a g mode period series. Despite NGC 2264's young age, our analysis illustrates that its B type members have already arrived on the zero-age main sequence (ZAMS). Our asteroseismic analysis yields masses between 4 and 6 Msun and ages between 1 and 6 million years, which agree well to the overall cluster age., 19 pages, 20 figures, accepted for publication in Astronomy & Astrophysics

Context: A number of pulsating stars with rotational splittings have been observed thanks to the CoRoT and Kepler missions. This is particularly true of evolved (sub-giant and giant) stars, and has led various groups to investigate their rotation profiles via different methods. Aims: We would like to set up some criteria which will help us to know whether a decreasing rotation profile, or one which satisfies Rayleigh's stability criterion, is compatible with a set of observed rotational splittings for a given reference model. Methods: We derive inequalities on the rotational splittings using a reformulated version of the equation which relates the splittings to the rotation profile and kernels. Results: These inequalities are tested out on some simple examples. The first examples show how they are able to reveal when a rotation profile is increasing somewhere or inconsistent with Rayleigh's criterion in a main sequence star, depending on the profile and the $\ell$ values of the splittings. The next example illustrates how a slight mismatch between an observed evolved star and a reference model can lead to erroneous conclusions about the rotation profile. We also show how frequency differences between the star and the model, which should normally reveal this mismatch, can be masked by frequency corrections for near-surface effects., 15 pages, 19 figures, accepted for publication in A&A