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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.

Thus far, KIC 7760680 is the richest slowly pulsating B star, exhibiting 36 consecutive dipole (ℓ = 1) gravity (g-) modes. The monotonically decreasing period spacing of the series, in addition to the local dips in the pattern, confirm that KIC 7760680 is a moderate rotator with clear mode trapping in chemically inhomogeneous layers. We employ the traditional approximation of rotation to incorporate rotational effects on g-mode frequencies. Our detailed forward asteroseismic modeling of this g-mode series reveals that KIC 7760680 is a moderately rotating B star with mass ∼3.25 M e . By simultaneously matching the slope of the period spacing and the number of modes in the observed frequency range, we deduce that the equatorial rotation frequency of KIC 7760680 is 0.4805 day −1 , which is 26% of its Roche break up frequency. The relative deviation of the model frequencies and those observed is less than 1%. We succeed in tightly constraining the exponentially decaying convective core overshooting parameter to f ov ≈ 0.024 ± 0.001. This means that convective core overshooting can coexist with moderate rotation. Moreover, models with exponentially decaying overshoot from the core outperform those with the classical step-function overshoot. The best value for extra diffusive mixing in the radiatively stable envelope is confined to »  D log 0.75 0.25 ext (with D ext in cm 2 s −1 ), which is notably smaller than theoretical predictions.

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.

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 internal angular momentum distribution of a star is the key to determining its evolution. Fortunately, stellar internal rotation can be probed through studies of rotationally split nonradial oscillation modes. In particular, the detection of nonradial gravity modes (g modes) in massive young stars has recently become feasible thanks to the Kepler space mission. Our goal is to derive the internal rotation profile of the Kepler B8V star KIC 10526294 through asteroseismology. We interpret the observed rotational splittings of its dipole g modes using four different approaches based on the best seismic models of the star and their rotational kernels. We show that these kernels can resolve differential rotation within the radiative envelope if a smooth rotational profile is assumed and if the observational errors are small. Based on Kepler data, we find that the rotation rate near the core-envelope boundary is well constrained to 163 ± 89 nHz. The seismic data are consistent with rigid rotation but a profile with counterrotation within the envelope has a statistical advantage over constant rotation. Our study should be repeated for other massive stars with a variety of stellar parameters in order to determine the physical conditions that control the internal rotation profile of young massive stars, with the aim of improving the input physics of their models.

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.

Context. Massive stars are important for the chemical enrichment of the universe. Since internal mixing processes influence their lives, it is very important to place constraints on the corresponding physical parameters, such as core overshooting and the internal rotation profile, so as to calibrate their stellar structure and evolution models. Although asteroseismology has been shown to be able to deliver the most precise constraints so far, the number of detailed seismic studies delivering quantitative results is limited. Aims. Our goal is to extend this limited sample with an in-depth case study and provide a well-constrained set of asteroseismic parameters, contributing to the ongoing mapping efforts of the instability strips of the β Cep and slowly pulsating B (SPB) stars. Methods. We derived fundamental parameters from high-resolution spectra using spectral synthesis techniques. We used custom masks to obtain optimal light curves from the original pixel level data from the Kepler satellite. We used standard time-series analysis tools to construct a set of significant pulsation modes that provide the basis for the seismic analysis carried out afterwards. Results. We find that KIC 10526294 is a cool SPB star, one of the slowest rotators ever found. Despite this, the length of Kepler observations is sufficient to resolve narrow rotationally split multiplets for each of its nineteen quasi-equally spaced dipole modes. The number of detected consecutive (in radial order) dipole modes in this series is higher than ever before. The observed amount of splitting shows an increasing trend towards longer periods, which -largely independent of the seismically calibrated stellar modelspoints towards a non-rigid internal rotation profile. From the average splitting we deduce a rotation period of ∼188 days. From seismic modelling, we find that the star is young with a central hydrogen mass fraction X c > 0.64; it has a core overshooting α ov ≤ 0.15.