Over more than twenty years, Wojtek Dziembowski and I collaborated on nearly fifty papers, which were concentrated in helioseismology through the 1980s and 1990s, but extended early into the new century. In this review, I discuss the most significant results of this collaboration and some of the underlying sociology that contributed to the intensity and longevity of our collaboration. Our work began with placing limits on the Sun's buried magnetic field and ended with extracting from the solar-cycle dependent oscillation frequency changes the roles (and net result) of competing dynamical drivers of changes in the solar diameter.

Cepheids and RR Lyrae stars are important pulsating variable stars in distance scale work because they serve as standard candles. Cepheids follow well-defined period-luminosity (PL) relations defined for bands extending from optical to mid-infrared (MIR). On the other hand, RR Lyrae stars also exhibit PL relations in the near-infrared and MIR wavelengths. In this article, we review some of the recent developments and calibrations of PL relations for Cepheids and RR Lyrae stars. For Cepheids, we discuss the calibration of PL relations via the Galactic and the Large Magellanic Cloud routes. For RR Lyrae stars, we summarize some recent work in developing the MIR PL relations.

Pulsating stars of different types are in different evolutionary phases, thus allowing one to trace stellar components of different age in the host systems. The light variation caused by the cyclic expansion/contraction of the surface layers makes a pulsating star much easier to identify than constant stars in the same evolutionary phase. Pulsating stars thus offer a powerful tool to disentangle the various stellar generations in systems where stars of different age and metal abundance populate the same regions of the colour-magnitude diagram. An overview is presented of how pulsating stars can be used as tools to study the stellar populations, and the structure and formation process in Local Group galaxies.

Pulsating pre-main-sequence (PMS) stars afford the earliest opportunity in the lifetime of a star to which the concepts of asteroseismology can be applied. PMS stars should be structurally simpler than their evolved counterparts, thus (hopefully!) making any asteroseismic analysis relatively easier. Unfortunately, this isn't necessarily the case. The majority of these stars (around 80) are δ Scuti pulsators, with a couple of γ Doradus, γ Doradus – δ Scuti hybrids, and slowly pulsating B stars thrown into the mix. The majority of these stars have only been discovered within the last ten years, with the community still uncovering the richness of phenomena associated with these stars, many of which defy traditional asteroseismic analysis.

A systematic asteroseismic analysis of all of the δ Scuti PMS stars was performed in order to get a better handle on the properties of these stars as a group. Some strange results have been found, including one star pulsating up to the theoretical acoustic cut-off frequency of the star, and a number of stars in which the most basic asteroseismic analysis suggests problems with the stars' positions in the Hertzsprung-Russell diagram. From this we get an idea of the\break constraints — or lack thereof — that these results can put on PMS stellar evolution.

The projection factor used in the Baade-Wesselink method of determining the distance of Cepheids makes the link between stellar physics and the cosmological distance scale. A coherent picture of this physical quantity is now provided based on several approaches. We present the latest news on the expected projection factor for different kinds of pulsating stars in the Hertzsprung-Russell diagram.

Pre-main sequence (PMS) stars can become vibrationally unstable during their evolution to the zero-age main sequence (ZAMS). As they gain their energy from gravitational contraction and have not started nuclear fusion in their cores yet, their inner structures are significantly different to those of (post-) main sequence stars and can be probed by asteroseismology.

Using photometric time series from ground and from space (MOST, CoRoT & Spitzer) the number of confirmed pulsating pre-main sequence stars has increased significantly within the last years and allowed to find members of new classes of PMS pulsators. Apart from the well-established group of δ Scuti type PMS stars, members of the groups of PMS γ Doradus, PMS δ Scuti – γ Doradus hybrid and PMS slowly pulsating B (SPB) stars have been discovered. For five PMS δ Scuti candidates, space photometry has revealed that they only show irregular variability, but no pulsations.

The unique high-precision space data were combined with dedicated high-resolution spectra to probe the parameter space in the H-R diagram and study the properties of PMS pulsators in comparison to their evolutionary stage.

It has long been known that rotation can have an appreciable impact on stellar pulsation — by modifying the usual p and g modes found in the non-rotating case, and by introducing new classes of modes. However, it's only relatively recently that advances in numerical simulations and complementary theoretical treatments have enabled us to model these phenomena in any great detail. In this talk I'll review highlights in this area (the ‘Greatest Hits’), before considering the flip side (or the ‘B-side’, for those of us old enough to remember vinyl records) of the pulsation-rotation interaction: how pulsation can itself influence internal rotation profiles.

Our current understanding and modeling of angular momentum transport in low-mass stars are briefly reviewed. Emphasis is set on single stars slightly younger that the Sun and on subgiants and red giants observed by the space missions CoRoT and Kepler.

Recent observations of rapidly rotating stars have revealed the presence of regular patterns in their pulsation spectra. This has raised the question as to their physical origin, and, in particular, whether they can be explained by an asymptotic frequency formula for low-degree acoustic modes, as recently discovered through numerical calculations and theoretical considerations. In this context, a key question is whether compositional/density gradients can adversely affect such patterns to the point of hindering their identification. To answer this question, we calculate frequency spectra using two-dimensional ESTER stellar models. These models use a multi-domain spectral approach, allowing us to easily insert a compositional discontinuity while retaining a high numerical accuracy. We analyse the effects of such discontinuities on both the frequencies and eigenfunctions of pulsation modes in the asymptotic regime. We find that although there is more scatter around the asymptotic frequency formula, the semi-large frequency separation can still be clearly identified in a spectrum of low-degree acoustic modes.

Observations indicate that a circumstellar disk is formed around a Be star while the stellar rotation is below the break-up velocity. I propose a working hypothesis to explain this mystery by taking account of the effect of leaky waves upon angular momentum transfer.

In B-type stars near the main sequence, low-frequency nonradial oscillations are excited by the κ-mechanism in the iron bump. They transport angular momentum from the driving zone to the surface. As a consequence, the angular momentum is gradually deposited near the stellar surface. This results in a gradual increase in the “critical frequency for g-modes”, and g-modes eventually start to leak outward, long before the surface rotation reaches the break-up velocity. This leads to a substantial amount of angular momentum loss from the star, and a circumstellar disk is formed. The oscillations themselves will be soon damped owing to kinetic energy loss. Then the envelope of the star spins down and angular momentum loss stops soon. The star returns to being quiet and remains calm until nonradial oscillations are newly built up by the κ-mechanism to sufficient amplitude and a new episode begins.

According to this view, the interval of episodic Be-star activity corresponds to the growth time of the oscillation, and it seems in good agreement with observations.

A lot of effort has been devoted to the hydrodynamical modelling of Cepheids in one dimension. While the recovery of the most basic properties such as the pulsational instability itself has been achieved already a long time ago, properties such as the observed double-mode pulsation of some objects and the red-edge of the classical instability strip and their dependence on metallicity have remained a delicate issue. The uncertainty introduced by adjustable parameters and further physical approximations introduced in one-dimensional model equations motivate an investigation based on numerical simulations which use the full hydrodynamical equations. In this talk, results from such two-dimensional numerical simulations of a short period Cepheid are presented. The importance of a carefully designed numerical setup, in particular of sufficient resolution and domain extent, is discussed. The problematic issue of how to reliably choose fixed parameters for the one-dimensional model is illustrated. Results from an analysis of the interaction of pulsation with convection are shown concerning the large-scale structure of the He ii ionization zone. We also address the influence of convection on the atmospheric structure. Considering the potential of hydrodynamical simulations and the wealth of ever improving observational data an outlook on possible future work in this field of research is given.

Stellar plasmas are multicomponent anisotropic gases. Each component (chemical element) of these gases experiences specific forces related to its properties, which leads each element to diffuse with respect to the others. There is no reason why a stellar plasma should remain homogeneous except if mixing motions enforce homogeneity. Because atomic diffusion is a very slow process, the element separation only occurs in places where mixing motions are weak enough not to erase the effect of the ineluctable tendency of chemical elements to migrate. In this talk, I will present how atomic diffusion and mixing processes compete in stars (interiors as well as atmospheres), and I will show various cases where atomic diffusion is believed to have noticeable effects. This concerns several types of stars throughout the H-R diagram, including pulsating ones.

The problem of interaction of stellar pulsations with turbulence and radiation in stellar convective envelopes is central to our understanding of excitation mechanisms, oscillation amplitudes and frequency shifts. Realistic (“ab initio”) numerical simulations provide unique insights into the complex physics of pulsation-turbulence-radiation interactions, as well as into the energy transport and dynamics of convection zones, beyond the standard evolutionary theory. 3D radiative hydrodynamics simulations have been performed for several Kepler target stars, from M- to A-class along the main sequence, using a new ‘StellarBox’ code, which takes into account all essential physics and includes subgrid scale turbulence modeling. The results reveal dramatic changes in the convection and pulsation properties among stars of different mass. For relatively massive stars with thin convective envelopes, the simulations allow us to investigate the dynamics the whole envelope convection zone including the overshoot region, and also look at the excitation of internal gravity waves. Physical properties of the turbulent convection and pulsations, and the oscillation spectrum for two of these targets are presented and discussed in this paper. In one of these stars, with mass 1.47 M⊙, we simulate the whole convective zone and investigate the overshoot region at the boundary with the radiative zone.

Some Ap stars with strong magnetic fields pulsate in high-order p modes; they are called roAp (rapidly oscillating Ap) stars. The p-mode frequencies are modified by the magnetic fields. Although the large frequency separation is hardly affected, small separations are modified considerably. The magnetic field also affects the latitudinal amplitude distribution on the surface. We discuss the properties of axisymmetric p-mode oscillations in roAp stars.

Both pulsation and mass loss are commonly observed in stars and are important ingredients for understanding stellar evolution and structure, especially for massive stars. There is a growing body of evidence that pulsation can also drive and enhance mass loss in massive stars and that pulsation-driven mass loss is important for stellar evolution. In this review, I will discuss recent advances in understanding pulsation-driven mass loss in massive main-sequence stars, classical Cepheids and red supergiants and present some challenges remaining.

Observations of magnetic activity cycles in other stars provide a broader context for our understanding of the 11-year sunspot cycle. The discovery of short activity cycles in a few stars, and the recognition of analogous variability in the Sun, suggest that there may be two distinct dynamos operating in different regions of the interior. Consequently, there is a natural link between studies of magnetic activity and asteroseismology, which can characterize some of the internal properties that are relevant to dynamos. I provide a brief historical overview of the connection between these two fields (including prescient work by Wojtek Dziembowski in 2007), and I highlight some exciting results that are beginning to emerge from the Kepler mission.

During their post-main sequence evolution, massive stars pass through several short-lived phases, in which they experience enhanced mass loss in the form of clumped winds and mass ejection events of unclear origin. The discovery that stars populating the blue luminous part of the Hertzsprung-Russell diagram can pulsate suggests that stellar pulsations might influence or trigger enhanced mass loss and eruptions. We present recent results for two objects in different phases: a B[e] star at the end of the main sequence and a B-type supergiant.

High precision asteroseismic data provide a unique opportunity to test input microphysics such as stellar opacities, chemical composition or equation of state. These tests are possible because pulsational frequencies as well as amplitudes and phases of the light variations are very sensitive to the internal structure of a star. We can therefore compute pulsation models and compare them with observations. The agreement or differences should tell us whether some models are adequate or not, and which input data need to be improved.

β Cephei and SPB stars are pulsating stars for which the excitation of modes by the κ mechanism, due to the iron-group opacity peak, seems puzzling. We have first investigated the origins of the differences noticed between OP and OPAL iron and nickel opacity calculations (up to a factor 2), a fact which complicates the interpretation. To accomplish this task, new well-qualified calculations (SCO-RCG, HULLAC and ATOMIC) have been performed and compared to values of these tables, and most of the differences are now well understood. Next, we have exploited a dedicated experiment on chromium, iron and nickel, conducted at the LULI 2000 facilities. We found that, in the case of iron, detailed calculations (OP, ATOMIC and HULLAC) show good agreement, contrary to all of the non-detailed calculations. However, in the case of nickel, OP calculations show large discrepancies with the experiments but also with other codes. Thus, the opacity tables need to be revised in the thermodynamical conditions corresponding to the peak of the iron group. Consequently we study the evolution of this iron peak with changes in stellar mass, age, and metallicity to determine the relevant region where these tables should be revised.

Classical Cepheids form one of the foundations of modern cosmology and the extragalactic distance scale; however, cosmic microwave background observations measure cosmological parameters and indirectly the Hubble Constant, H0, to unparalleled precision. The coming decade will provide opportunities to measure H0 to 2% uncertainty thanks to the Gaia satellite, JWST, ELTs and other telescopes using Cepheids and other standard candles. In this work, we discuss the upcoming role for variable stars and asteroseismology in calibrating the distance scale and measuring H0 and what problems exist in understanding these stars that will feed back on these measurements.