The Blazhko effect is the conspicuous amplitude and phase modulation of the pulsation of RR Lyrae stars that was discovered in the early 20th century. The field of study of this mysterious modulation has recently been invigorated thanks to the space photometric missions providing long, uninterrupted, ultra-precise time-series data. In this paper I give a brief overview of the new observational findings related to the Blazhko effect, such as extreme modulations, irregular modulation cycles and additional periodicities. I argue that these findings together with dedicated ground-based efforts provide us now with a fairly complete picture and a good starting point to theoretical investigations. Indeed, new, unpredicted dynamical phenomena have been discovered in Blazhko RR Lyrae stars, such as period doubling, high-order resonances, three-mode pulsation and low-dimensional chaos. These led to the proposal of a new explanation to this century-old enigma, namely a high-order resonance between radial modes. Along these lines I present the latest efforts and advances from the theoretical point of view. Lastly, amplitude variations in Cepheids are discussed.

I review different types of multi-mode pulsations observed in classical Cepheids and in RR Lyrae-type stars. The presentation concentrates on the newest results, with special emphasis on recently detected nonradial oscillations.

Four years into the Kepler mission, an updated review on the results for RR Lyrae stars is in order. More than 50 RR Lyrae stars in the Kepler field are observed with Kepler and each one of them can provide us with new insight into this class of pulsating stars. Ground-based spectroscopy of the Kepler targets allows us to narrow down their physical parameters. Previously, we already reported a 50% occurrence rate of modulation in the RRab stars, a large variety of modulation behavior, period doubling in several Blazhko stars, the detection of higher- overtone radial modes, probable non-radial modes and new types of multiple-mode RR Lyrae pulsators, among both the RRab and the RRc stars. In addition, the quasi-continuous photometry obtained over several years with Kepler allows one to observe changes in Blazhko behavior and additional longer cycles. These observations have sparked new theoretical modelling efforts. In this short paper we showcase RR Lyr itself. The star has been observed with Kepler in short cadence, and some remarkable features of its pulsation behavior are unveiled in this long-studied prototype, through the Kepler photometry and additional spectroscopic data.

This article reports some preliminary results on an analysis of line bisectors of metal absorption lines of RR Lyrae, the prototype of its class of pulsators. The extensive data set used for this study consists of a time series of spectra obtained at various pulsation phases as well as different Blazhko phases. This setup should allow a comparison of the atmospheric behaviour, especially of the function of radial velocity versus depth at differing Blazhko phases, but (almost) identical pulsation phase, making it possible to investigate whether the modulation causes a change in the atmospheric motion of RR Lyrae. While the nature of the Blazhko modulation has often been investigated photometrically and described as a change in the light curve, studies on time series of high resolution spectra are rare. We present for the first time work on line bisectors at different phases of RR Lyr.

In this review we focus on non-linear phenomena in pulsating stars: mode selection and amplitude limitation. Of many linearly excited modes, only a fraction is detected in pulsating stars. Which of them are excited, and why (the problem of mode selection), and to what amplitude (the problem of amplitude limitation) are intrinsically non-linear and still unsolved problems. Tools for studying these problems are briefly discussed and our understanding of mode selection and amplitude limitation in selected groups of self-excited pulsators is presented. We focus on classical pulsators (Cepheids and RR Lyrae stars) and main-sequence variables (δ Scuti and β Cephei stars). Directions of future studies are briefly discussed.

We first present a brief description of the six distinct families of pulsating white dwarfs that are now known. These are all opacity-driven pulsators showing low- to mid-order, low-degree gravity modes. We then discuss some recent highlights that have come up in the field of white dwarf asteroseismology.

Massive pulsating white dwarf stars are extremely rare, because of their small size and because they are the final product of high-mass stars, which are less common. Because of their intrinsic smaller size, they are fainter than the normal size white dwarf stars. The motivation to look for this type of stars is to be able to study in detail their internal structure and also derive generic properties for the sub-class of variables, the massive ZZ Ceti stars. Our goal is to investigate whether the internal structures of these stars differ from the lower-mass ones, which in turn could have been resultant from the previous evolutionary stages.

In this paper, we present the ensemble seismological analysis of the known massive pulsating white dwarf stars. Some of these pulsating stars might have substantial crystallized cores, which would allow us to probe solid physics in extreme conditions.

We explore quantitatively the low but sufficient sensitivity of oscillation modes to probe both the core composition and the details of the chemical stratification of pulsating white dwarfs. Until recently, applications of asteroseismic methods to pulsating white dwarfs have been far and few, and have generally suffered from an insufficient exploration of parameter space. To remedy this situation, we apply to white dwarfs the same double-optimization technique that has been used quite successfully in the context of pulsating hot B subdwarfs. Based on the frequency spectrum of the pulsating white dwarf R548, we are able to unravel in a robust way the unique onion-like stratification and the chemical composition of the star. Independent confirmations from both spectroscopic analyses and detailed evolutionary calculations including diffusion provide crucial consistency checks and add to the credibility of the inferred seismic model. More importantly, these results boost our confidence in the reliability of the forward method for sounding white dwarf internal structure with asteroseismology.

We briefly introduce hot subdwarfs and their evolutionary status before discussing the different types of known pulsators in more detail. Currently, at least six apparently distinct types of variable are known among hot subdwarfs, encompassing p- as well as g-mode pulsators and objects in the Galactic field as well as in globular clusters. Most of the oscillations detected can be explained in terms of an iron opacity mechanism, and quantitative asteroseismology has been very successful for some of the pulsators. In addition to helping constrain possible evolutionary scenarios, studies focussing on stellar pulsations have also been used to infer planets and characterize the rotation of the host star.

Stars consume hydrogen in their interiors but, generally speaking, their surfaces continue to contain some 70% hydrogen (by mass) throughout their lives. Nevertheless, many types of star can be found with hydrogen-deficient surfaces, in some cases with as little as one hydrogen atom in 10 000. Amongst these, the luminous B- and A-type extreme helium stars are genuinely rare; only ~15 are known within a very substantial volume of the Galaxy.

Evidence from surface composition suggests a connection to the cooler R CrB variables and some of the hotter helium-rich subdwarf O stars. Arguments currently favour an origin in the merger of two white dwarfs; thus there are also connections with AM CVn variables and Type Ia supernovae. Pulsations in many extreme helium stars provide an opportune window into their interiors. These pulsations have unusual properties, some being “strange” modes, and others being driven by Z-bump opacities. They have the potential to deliver distance-independent masses and to provide a unique view of pulsation physics.

We review the evolutionary origin and pulsations of these stars, and introduce recent progress and continuing challenges.

Asteroseismic modeling of subdwarf B (sdB) stars provides measurements of their fundamental parameters with a very good precision; in particular, the masses and radii determined from asteroseismology are found to typically reach a precision of 1% containing various uncertainties associated with their inner structure and the underlying microphysics (composition and transition zones profiles, nuclear reaction rates, etc.). Therefore, the question of the accuracy of the stellar parameters derived by asteroseismology is legitimate. We present here the seismic modeling of the pulsating sdB star in the eclipsing binary PG 1336–018, for which the mass and the radius are independently and precisely known from the modeling of the reflection/irradiation effect and the eclipses observed in the light curve. This allows us to quantitatively evaluate the reliability of the seismic method and test the impact of uncertainties in our stellar models on the derived parameters. We conclude that the sdB star parameters inferred from asteroseismology are precise, accurate, and robust against model uncertainties.

We present a study of KIC 10670103, a pulsating hot subdwarf in the Kepler field. By means of Fourier analysis, we investigate periodic signals associated with pulsations. Using asymptotic relationships and rotational multiplets we identify degrees of modes. The Fourier spectrum appears to be rich in l=1 and l=2 multiplets allowing derivation of a ~90-day rotation period of the star from rotational splittings. Comparing the identified gravity-mode period spacing pattern with theoretical models we show that KIC 10670103 has to be a thick-envelope sdBV.

Massive stars are the cosmic engines that shape and drive our Universe. Many issues such as their formation, their stability and the mass loss effects, are far from being completely understood. Recent ground-based and space observations have shown pulsations in massive MS and post-MS stars, such as acoustic and gravity modes excited by the κ-mechanism and even solar-like oscillations. Theoretical studies emphasized the presence of strange modes in massive models, and recent theoretical analyses have shown that hot supergiants can pulsate in oscillatory convective modes. We review the instability domains of massive stars as well as their excitation mechanisms and present the latest results.

We present results of pulsation analyses of B-type supergiant models with masses of 14 – 18 M⊙, considering evolutionary stages before and after helium core ignition. Using a non-adiabatic pulsation code, we compute instability domains for low-degree modes. For selected models in these two evolutionary phases, we compare properties of pulsation modes. Significant differences are found in oscillation spectra and the kinetic energy density of pulsation modes.

Thanks to significant improvements in high-resolution spectrographs and the launch of dedicated space missions MOST, CoRoT and Kepler, the number of subgiants and red-giant stars with detected oscillations has increased significantly over the last decade. The amount of detail that can now be resolved in the oscillation patterns does allow for in-depth investigations of the internal structures of these stars. One phenomenon that plays an important role in such studies are mixed modes. These are modes that carry information of the inner radiative region as well as from the convective outer part of the star allowing to probe different depths of the stars.

Here, we describe mixed modes and highlight some recent results obtained using mixed modes observed in subgiants and red-giant stars.

Convective envelopes in stars on the main sequence are usually connected only with stars of spectral types F5 or later. However, observations as well as theory indicate that the convective outer layers in hotter stars, despite being shallow, are still effective and turbulent enough to stochastically excite oscillations. Because of the low amplitudes, exploring stochastically excited pulsations became possible only with space missions such as Kepler and CoRoT. Here I review the recent results and discuss among others, pulsators such as δ Scuti, γ Doradus, roAp, β Cephei, Slowly Pulsating B and Be stars, all in the context of solar-like oscillations.

CoRoT and Kepler observations of red giants reveal a large variety of spectra of nonradial solar-like oscillations. So far, we understood pretty well the link between the global properties of the star (radius, mass, evolutionary state) and the properties of the oscillation spectrum (Δν, νmax, period spacing). We are interested here in the theoretical predictions of two other components of a power spectrum, the mode linewidths and heights. The study of the energy of the oscillations is of great importance to predict the peak parameters in the power spectrum. We will discuss circumstances under which mixed modes are detectable for red-giant stellar models from 1 to 2 M⊙, with emphasis on the effect of the evolutionary status of the star along the red-giant branch on theoretical power spectra.

We discuss the potential of asteroseismic inversion to study the internal dynamics of solar-type stars and to reconstruct the evolution of the internal rotation from the main sequence to the red-giant phase. In particular, we consider the use of gravity and mixed modes and the application of different inversion methods.

In addition to well-known mechanisms of excitation of solar and stellar oscillations by turbulent convection and instabilities, the oscillations can be excited by an impulsive localized force caused by the energy release in solar and stellar flares. Such oscillations have been observed on the Sun (‘sunquakes’), and created a lot of interesting discussions about physical mechanisms of the impulsive excitation and their relationship to the flare physics. The observation and theory have shown that most of a sunquake's energy is released in high-degree, high-frequency p modes. In addition, there have been reports on helioseismic observations of low-degree modes excited by strong solar flares. Much more powerful flares observed on other stars can cause ‘starquakes’ of substantially higher amplitude. Observations of such oscillations can provide new asteroseismic information and also constraints on mechanisms of stellar flares. I discuss the basic properties of sunquakes, and initial attempts to detect flare-excited oscillations in Kepler short-cadence data.

During the past decades, stellar oscillations and exoplanet searches were developed in parallel, and the observations were done with the same instruments: radial velocity method, essentially with ground-based instruments, and photometric methods (light curves) from space. The same observational data on one star could lead to planet discoveries at large time scales (days to years) and to the detection of stellar oscillations at small time scales (minutes), such as for the star μ Arae. Since the beginning, it seemed interesting to investigate the differences between stars with and without observed planets. Also, a precise determination of the stellar parameters is important to characterize the detected exoplanets. With the thousands of exoplanet candidates discovered by Kepler, automatic procedures and pipelines are needed with large data bases to characterize the central stars. However, precise asteroseismic studies of well-chosen stars are still important for a deeper insight.