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While the mission’s primary goal was focused on exoplanet detection and characterization, Kepler made and continues to make extraordinary advances in stellar physics. Stellar rotation and magnetic activity are no exceptions. Kepler allowed for these properties to be determined for tens of thousands of stars from the main sequence up to the red giant branch. From photometry, this can be achieved by investigating the brightness fluctuations due to active regions, which cause surface inhomogeneities, or through asteroseismology as oscillation modes are sensitive to rotation and magnetic fields. This review summarizes the rotation and magnetic activity properties of the single main-sequence solar-like stars within the Kepler field. We contextualize the Kepler sample by comparing it to known transitions in the stellar rotation and magnetic-activity evolution, such as the convergence to the rotation sequence (from the saturated to the unsaturated regime of magnetic activity) and the Vaughan-Preston gap. While reviewing the publicly available data, we also uncover one interesting finding related to the intermediate-rotation gap seen in Kepler and other surveys. We find evidence for this rotation gap in previous ground-based data for the X-ray luminosity. Understanding the complex evolution and interplay between rotation and magnetic activity in solar-like stars is crucial, as it sheds light on fundamental processes governing stellar evolution, including the evolution of our own Sun.

Rapid stellar rotation is an important phenomenon in stellar physics, particularly for massive and intermediate mass main-sequence stars. This affects all aspects of the star’s physics including its structure, evolution, and pulsations, and makes it necessary to use 2D numerical approaches rather than the 1D approaches typically used. In this contribution, we will review 2D numerical methods for modelling and interpreting pulsation modes in rapidly rotating stars. We will start by deriving the pulsation equations, both in an adiabatic and non-adiabatic setting, then provide a description of the 2D numerical implementation. We will then explain approximate implementations of the effects of rotation, namely first, second, and third order perturbative approaches, as well as the traditional approximation. This will then be followed by a description on how to calculate disk-integrated mode visibilities in various photometric bands, and how to apply this to mode identification in rapid rotators. Finally, we will review some of the recent works that interpret the pulsation spectra of various stars as viewed in either a single photometric band or in multiple bands, and including supplementary constraints from interferometry and spectroscopy.

This review has two parts. The first one is devoted to the Barbier–Chalonge–Divan (BCD) spectrophotometric system, also known as the Paris spectral classification system. Although the BCD system has been applied and is still used for all stellar objects from O to F spectral types, the present account mainly concerns normal and ‘active’ B-type stars. The second part treats topics related to stellar rotation, considered one of the key phenomena determining the structure and evolution of stars. The first part is eminently observational. In contrast, the second part deals with observational aspects related to stellar rotation but also recalls some supporting or basic theoretical concepts that may help better understand the gains and shortcomings of today’s existent interpretation of stellar data.

There are a number of reasons for studying hot subdwarf pulsation; the most obvious being that these stars remain a poorly understood late-stage of stellar evolution and knowledge of their interior structure, which pulsation studies reveal, constrains evolution models. Of particular interest are the red giant progenitors as in looking at a hot subdwarf we are seeing a stripped-down red giant as it would have been just before the Helium Flash. Moreover, hot subdwarfs may have formed through the merger of two helium white dwarfs and their study gives insight into how such a merger may have happened. A less obvious reason for studying pulsation in hot subdwarfs is that they provide a critical test of stellar envelope opacities and the atomic physics upon which they depend.

Massive stars are important metal factories in the Universe. They have short and energetic lives, and many of them inevitably explode as a supernova and become a neutron star or black hole. In turn, the formation, evolution and explosive deaths of massive stars impact the surrounding interstellar medium and shape the evolution of their host galaxies. Yet the chemical and dynamical evolution of a massive star, including the chemical yield of the ultimate supernova and the remnant mass of the compact object, strongly depend on the interior physics of the progenitor star. We currently lack empirically calibrated prescriptions for various physical processes at work within massive stars, but this is now being remedied by asteroseismology. The study of stellar structure and evolution using stellar oscillations—asteroseismology—has undergone a revolution in the last two decades thanks to high-precision time series photometry from space telescopes. In particular, the long-term light curves provided by the MOST, CoRoT, BRITE, Kepler/K2, and TESS missions provided invaluable data sets in terms of photometric precision, duration and frequency resolution to successfully apply asteroseismology to massive stars and probe their interior physics. The observation and subsequent modeling of stellar pulsations in massive stars has revealed key missing ingredients in stellar structure and evolution models of these stars. Thus, asteroseismology has opened a new window into calibrating stellar physics within a highly degenerate part of the Hertzsprung–Russell diagram. In this review, I provide a historical overview of the progress made using ground-based and early space missions, and discuss more recent advances and breakthroughs in our understanding of massive star interiors by means of asteroseismology with modern space telescopes.

Traditionally, stellar structure and evolution have been modeled with a series of concentric spherical shells. This description allows the star to be modeled in 1 dimension, greatly simplifying the calculations. However, as our understanding of stars becomes more advanced, the effects of non-symmetric effects must be included, which necessitates 2 or even 3 dimensional simulations. In this work, I discuss how 2D stellar models can help understand stars, improving our models of their pulsation frequencies, and allow us to place better constraints on their internal convection.

Axisymmetric magnetic activity on the Sun and sun-like stars increases the frequencies of the modes of acoustic oscillation. However, it is unclear how a corotating patch of activity affects the oscillations, since such a perturbation is unsteady in the frame of the observer. In this paper we qualitatively describe the asteroseismic signature of a large active region in the power spectrum of the dipole (ℓ = 1) and quadrupole (ℓ = 2) p modes. First we calculate the frequencies and the relative amplitudes of the azimuthal modes of oscillation in a frame that corotates with the active region, using first-order perturbation theory. For the sake of simplicity, the influence of the active region is approximated by a near-surface increase in sound speed. In the corotating frame the perturbations due to (differential) rotation and the active region completely lift the (2ℓ + 1)-fold azimuthal degeneracy of the frequency spectrum of modes with harmonic degree ℓ. Then we transform to an inertial frame to obtain the observed power spectrum. In the frame of the observer, the unsteady nature of the perturbation leads to the appearance of (2ℓ + 1)2 peaks in the power spectrum of a multiplet. These peaks blend into each other to form asymmetric line profiles. In the limit of a small active region (angular diameter less than 30°), we approximate the power spectrum of a multiplet in terms of 2 × (2ℓ + 1) peaks, whose amplitudes and frequencies depend on the latitude of the active region and the inclination angle of the star's rotation axis. In order to check the results and to explore the non-linear regime, we perform numerical simulations using the 3D time-domain pseudo-spectral linear pulsation code GLASS. For small sound-speed perturbations, we find a good agreement between the simulations and linear theory. Larger perturbation amplitudes will induce mode mixing and lead to additional complex changes in the predicted power spectrum. However linear perturbation theory provides useful guidance to search for the observational signature of large individual active regions in stellar oscillation power spectra.

In this study, we undertook a deep photometric examination of a narrowly-defined sample of solar analogs in the Kepler field, with the goals of producing a uniform and statistically meaningful sample of such stars, comparing the properties of planet hosts to those of the general stellar population, and examining the behavior of rotation and photometric activity among stars with similar overall physical parameters. We successfully derived photometric activity indicators and rotation periods for 95 planet hosts (Kepler objects of interest [KOIs]) and 954 solar analogs without detected planets; 573 of these rotation periods are reported here for the first time. Rotation periods average roughly 20 d, but the distribution has a wide dispersion, with a tail extending to P > 35 d which appears to be inconsistent with published gyrochronological relations. We observed a weak rotation-activity relation for stars with rotation periods less than about 12 d; for slower rotators, the relation is dominated by scatter. However, we are able to state that the solar activity level derived from Virgo data is consistent with the majority of stars with similar rotation periods in our sample. Finally, our KOI sample is consistently approximately 0.3 dex more variable than our non-KOIs; we ascribe the difference to a selection effect due to low orbital obliquity in the planet-hosting stars and derive a mean obliquity for our sample of χ = 6+5°-6, similar to that seen in the solar system.

An analysis of the influence of the uniform stellar rotation on masses and radii of convective cores of zero age stars is presented. The study also shows the dependence of the relative mass of the convective core on the parameters in the center (temperature, pressure) and on the surface (effective temperature, luminosity) of the star.