The primary Kepler Mission provided nearly continuous monitoring of ∼200,000 objects with unprecedented photometric precision. We present the final catalog of eclipsing binary systems within the 105 deg 2 Kepler field of view. This release incorporates the full extent of the data from the primary mission (Q0-Q17 Data Release). As a result, new systems have been added, additional false positives have been removed, ephemerides and principal parameters have been recomputed, classifications have been revised to rely on analytical models, and eclipse timing variations have been computed for each system. We identify several classes of systems including those that exhibit tertiary eclipse events, systems that show clear evidence of additional bodies, heartbeat systems, systems with changing eclipse depths, and systems exhibiting only one eclipse event over the duration of the mission. We have updated the period and galactic latitude distribution diagrams and included a catalog completeness evaluation. The total number of identified eclipsing and ellipsoidal binary systems in the Kepler field of view has increased to 2878, 1.3% of all observed Kepler targets. An online version of this catalog with downloadable content and visualization tools is maintained at http://keplerEBs.villanova.edu.

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. While rotation has a major impact on stellar structure and evolution, its effects are not well understood. Thanks to highquality and long timebase photometric observations obtained with recent space missions, we are now able to study stellar rotation more precisely. Aims. We aim to constrain radial differential rotation profiles in γ Doradus (γ Dor) stars, and to develop new theoretical seismic diagnosis for such stars with rapid and potentially non-uniform rotation. Methods. We derive a new asymptotic description which accounts for the impact of weak differential near-core rotation on gravitymode period spacings. The theoretical predictions are illustrated from pulsation computations with the code GYRE and compared with observations of γ Dor stars. When possible, we also derive the surface rotation rates in these stars by detecting and analysing signatures of rotational modulation, and compute the core-to-surface rotation ratios. Results. Stellar rotation has to be strongly differential before its effects on period spacing patterns can be detected, unless multiple period spacing patterns can be compared. Six stars in our sample exhibit a single unexplained period spacing pattern of retrograde modes. We hypothesise that these are Yanai modes. Finally, we find signatures of rotational spot modulation in the photometric data of eight targets.Conclusions. If only one period spacing pattern is detected and analysed for a star, it is difficult to detect differential rotation. A rigidly rotating model will often provide the best solution. Differential rotation can only be detected when multiple period spacing patterns have been found for a single star or its surface rotation rate is known as well. This is the case for eight stars in our sample, revealing surface-to-core rotation ratios between 0.95 and 1.05.

Almost all massive stars explode as supernovae and form a black hole or neutron star. The remnant mass and the impact of the chemical yield on subsequent star formation and galactic evolution strongly depend on the internal physics of the progenitor star, which is currently not well understood. The theoretical uncertainties of stellar interiors accumulate with stellar age, which is particularly pertinent for the blue supergiant phase. Stellar oscillations represent a unique method of probing stellar interiors, yet inference for blue supergiants is hampered by a dearth of observed pulsation modes. Here we report the detection of diverse variability in blue supergiants using the K2 and TESS space missions. The discovery of pulsation modes or an entire spectrum of low-frequency gravity waves in these stars allow us to map the evolution of hot massive stars towards the ends of their lives. Future asteroseismic modelling will provide constraints on ages, core masses, interior mixing, rotation and angular momentum transport. The discovery of variability in blue supergiants is a step towards a data-driven empirical calibration of theoretical evolution models for the most massive stars in the Universe.Stars born with masses larger than approximately eight times the mass of the Sun play a significant role in the evolution of galaxies. They are the chemical factories that produce and expel heavy elements through their wind and when they end their lives as supernovae and form a black hole or neutron star 1-3 . However, the chemical yields that enrich the interstellar medium and the remnant mass strongly depend on the progenitor star's interior properties 4 . The detectable progenitors of supernovae include blue supergiant stars, which are hot massive stars in a shell-hydrogen or core-helium burning stage of stellar evolution. Stellar evolution models of these post-main sequence stars contain by far the largest uncertainties in stellar astrophysics, as observational constraints on interior mixing, rotation and angular momentum transport are missing. These phenomena are further compounded when coupled with mass loss, binarity and magnetic fields 1-3 . Across astrophysics, from star formation to galactic evolution, it is imperative to calibrate theoretical models of massive stars using observations because they determine the evolution of the cosmos.A unique methodology for probing stellar interiors is asteroseismology 5 , which -similarly to seismology of earthquakes -uses oscillations to derive constraints on the structure of stars.The study of stellar interiors of low-mass stars like the Sun has undergone a revolution in

The large-scale magnetic fields detected at the surface of about 10 % of hot stars extend into the stellar interior, where they may alter the structure. Deep inner regions of stars are only observable using asteroseismology. Here, we investigated the pulsating magnetic B3.5V star HD 43317, inferred its interior properties and assessed whether the dipolar magnetic field with a surface strength of B p = 1312 ± 332 G caused different properties compared to those of non-magnetic stars. We analysed the latest version of the star's 150 d CoRoT light curve and extracted 35 significant frequencies, 28 of which were determined to be independent and not related to the known surface rotation period of P rot = 0.897673 d. We performed forward seismic modelling based on non-magnetic, nonrotating 1D MESA models and the adiabatic module of the pulsation code GYRE, utilizing a grid-based approach. Our aim was to estimate the stellar mass, age, and convective core overshooting. The GYRE calculations were done for uniform rotation with P rot . This modelling was able to explain 16 of the 28 frequencies as gravity modes belonging to retrograde modes with ( , m) = (1, −1) and (2, −1) period spacing patterns and one distinct prograde (2, 2) mode. The modelling resulted in a stellar mass M = 5.8 +0.1 −0.2 M , a central hydrogen mass fraction X c = 0.54 +0.01 −0.02 , and exponential convective core overshooting parameter f ov = 0.004 +0.014 −0.002 . The low value for f ov is compatible with the suppression of near-core mixing due to a magnetic field but the uncertainties are too large to pinpoint such suppression as the sole physical interpretation. We assessed the frequency shifts of pulsation modes caused by the Lorentz and the Coriolis forces and found magnetism to have a lower impact than rotation for this star. Including magnetism in future pulsation computations would be highly relevant to exploit current and future photometric time series spanning at least one year, such as those assembled by the Kepler space telescope and expected from the TESS (Continuous Viewing Zone) and PLATO space missions.

The asteroseismic modelling of period spacing patterns from gravito-inertial modes in stars with a convective core is a high-dimensional problem. We utilise the measured period spacing pattern of prograde dipole gravity modes (acquiring Π 0 ), in combination with the effective temperature (T eff ) and surface gravity (log g) derived from spectroscopy, to estimate the fundamental stellar parameters and core properties of 37 γ Doradus (γ Dor) stars whose rotation frequency has been derived from Kepler photometry. We make use of two 6D grids of stellar models, one with step core overshooting and one with exponential core overshooting, to evaluate correlations between the three observables Π 0 , T eff , and log g and the mass, age, core overshooting, metallicity, initial hydrogen mass fraction and envelope mixing. We provide multivariate linear model recipes relating the stellar parameters to be estimated to the three observables (Π 0 , T eff , log g). We estimate the (core) mass, age, core overshooting and metallicity of γ Dor stars from an ensemble analysis and achieve relative uncertainties of ∼ 10 per cent for the parameters. The asteroseismic age determination allows us to conclude that efficient angular momentum transport occurs already early on during the main sequence. We find that the nine stars with observed Rossby modes occur across almost the entire main-sequence phase, except close to core-hydrogen exhaustion. Future improvements of our work will come from the inclusion of more types of detected modes per star, larger samples, and modelling of individual mode frequencies.

Early-type stars are predicted to excite an entire spectrum of internal gravity waves (IGWs) at the interface of their convective cores and radiative envelopes. Numerical simulations of IGWs predict stochastic low-frequency variability in photometric observations, yet the detection of IGWs in early-type stars has been limited by a dearth of high-quality photometric time series. We present observational evidence of stochastic low-frequency variability in the CoRoT photometry of a sample of O, B, A and F stars. The presence of this stochastic low-frequency variability in stars across the upper main-sequence cannot be universally explained as granulation or stellar winds, but its morphology is found to be consistent with predictions from IGW simulations.

Context. Eclipsing, spectroscopic double-lined binary star systems (SB2) are excellent laboratories for calibrating theories of stellar interior structure and evolution. Their precise and accurate masses and radii measured from binary dynamics offer model-independent constraints and challenge current theories of stellar evolution. Aims. We aim to investigate the mass discrepancy in binary stars. This is the significant difference between stellar components' masses measured from binary dynamics and those inferred from models of stellar evolution via positions of the components in the T eff -log g Kiel diagram. We study the effect of near-core mixing on the mass of the convective core of the stars and interpret the results in the context of the mass discrepancy. Methods. We fit stellar isochrones computed from a grid of mesa stellar evolution models to a homogeneous sample of eleven highmass binary systems. Two scenarios are considered, where individual stellar components of a binary system are treated independent of each other and where they are forced to have the same age and initial chemical composition. We also study the effect of the microturbulent velocity and turbulent pressure on the atmosphere model structure and stellar spectral lines, and its link with the mass discrepancy.Results. We find that the mass discrepancy is present in our sample and that it is anti-correlated with the surface gravity of the star. No correlations are found with other fundamental and atmospheric parameters, including the stellar mass. The mass discrepancy can be partially accounted for by increasing the amount of near-core mixing in stellar evolution models. We also find that ignoring the microturbulent velocity and turbulent pressure in stellar atmosphere models of hot evolved stars results in overestimation of their effective temperature by up to 8%. Together with enhanced near-core mixing, this can almost entirely account for the ∼30% mass discrepancy found for the evolved primary component of V380 Cyg. Conclusions. We find a strong link between the mass discrepancy and the convective core mass. The mass discrepancy can be solved by considering the combined effect of extra near-core boundary mixing and consistent treatment in the spectrum analysis of hot evolved stars. Our binary modelling results in convective core masses between 17 and 35% of the stellar mass, in excellent agreement with results from gravity-mode asteroseismology of single stars. This implies larger helium core masses near the end of the main sequence than anticipated so far.