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Massive and intermediate mass stars play a crucial role in astrophysics. Indeed, massive stars are the main producers of heavy elements, explode in supernovae at the end of their short lifetimes, and may be the progenitors of gamma ray bursts. Intermediate mass stars, although not destined to explode in supernovae, display similar phenomena, are much more numerous, and have some of the richest pulsation spectra. A key to understanding these stars is understanding the effects of rapid rotation on their structure and evolution. These effects include centrifugal deformation and gravity darkening which can be observed immediately, and long terms effects such as rotational mixing due to shear turbulence, which prolong stellar lifetime, modify chemical yields, and impact the stellar remnant at the end of their lifetime. In order to understand these effects, a number of models have been and are being developed over the past few years. These models lead to increasingly sophisticated predictions which need to be tested through observations. A particularly promising source of constraints is seismic observations as these may potentially lead to detailed information on their internal structure. However, before extracting such information, a number of theoretical and observational hurdles need to be overcome, not least of which is mode identification. The present proceedings describe recent progress in modelling these stars and show how an improved understanding of their pulsations, namely frequency patterns, mode visibilities, line profile variations, and mode excitation, may help with deciphering seismic observations.

Asteroseismology probes the internal structures of stars by using their natural pulsation frequencies 1 . It relies on identifying sequences of pulsation modes that can be compared with theoretical models, which has been done successfully for many classes of pulsators, including low-mass solar-type stars 2 , red giants 3 , high-mass stars 4 and white dwarfs 5 . However, a large group of pulsating stars of intermediate mass—the so-called δ Scuti stars—have rich pulsation spectra for which systematic mode identification has not hitherto been possible 6 , 7 . This arises because only a seemingly random subset of possible modes are excited and because rapid rotation tends to spoil regular patterns 8 – 10 . Here we report the detection of remarkably regular sequences of high-frequency pulsation modes in 60 intermediate-mass main-sequence stars, which enables definitive mode identification. The space motions of some of these stars indicate that they are members of known associations of young stars, as confirmed by modelling of their pulsation spectra. The pulsation spectra of intermediate-mass stars (so-called δ Scuti stars) have been challenging to analyse, but new observations of 60 such stars reveal remarkably regular sequences of high-frequency pulsation modes.

In this work, we present a new method to determine the surface gravity of δ Sct stars. We used a refined relation and the stellar parallaxes or luminosities to determine their masses and radii. A comparison with the data obtained from the binary analysis, has shown that the values found by both methods are equivalent, within the uncertainties. Moreover, thanks to the refined relation, the uncertainties in log g are of the order of those usually estimated with high-resolution spectroscopy. Because of that, this new method to determine the surface gravity is an important step forward to break the degeneracy problem in the spectroscopic analysis.

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.

Many early-type stars have been measured with high angular velocities. In such stars, mode identification is difficult as the effects of fast and differential rotation are not well known. Using fundamental parameters measured by interferometry, the ESTER structure code and the TOP oscillation code, we investigate the oscillation spectrum of α Ophiuchi, for which observations by the MOST satellite found 57 oscillations frequencies. Results do not show a clear identification of the modes and highlight the difficulties of asteroseismology for such stars with a very complex oscillation spectrum.

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.

Recently, Reese et al. (2008), Lignières & Georgeot (2008) and Lignières & Georgeot (2009) showed that the frequencies of low-degree acoustic modes in rapidly rotating stars, also known as “island modes”, follow an asymptotic formula, the coefficients of which can be deduced from ray dynamics. We investigate how this asymptotic behaviour is affected by μ gradients by comparing pulsation spectra from models with and without such a discontinuity.

We present RUBIS (Rotation code Using Barotropy conservation over Isopotential Surfaces), a fully Python-based centrifugal deformation program available at \\url{https://github.com/pierrehoudayer/RUBIS}. The code has been designed to calculate the centrifugal deformation of stars and planets resulting from a given cylindrical rotation profile, starting from a spherically symmetric non-rotating model. The underlying assumption in RUBIS is that the relationship between density and pressure is preserved during the deformation process. This leads to many procedural simplifications. For instance, RUBIS only needs to solve Poisson' equation, either in spheroidal or spherical coordinates depending on whether the 1D model has discontinuities or not. We present the benefits of using RUBIS to deform polytropic models and more complex barotropic structures, thus providing, to a certain extent, insights into baroclinic models. The resulting structures can be used for a wide range of applications, including the seismic study of models. Finally, we illustrate how RUBIS is beneficial specifically in the analysis of Jupiter's gravitational moments, thanks to its ability to handle discontinuous models while retaining a high accuracy compared to current methods.

In this work, we present a new method to determine the surface gravity of δ Sct stars. We used a refined Δv−ρ¯ relation and the stellar parallaxes or luminosities to determine their masses and radii. A comparison with the data obtained from the binary analysis, has shown that the values found by both methods are equivalent, within the uncertainties. Moreover, thanks to the refined relation, the uncertainties in log g are of the order of those usually estimated with high-resolution spectroscopy. Because of that, this new method to determine the surface gravity is an important step forward to break the degeneracy problem in the spectroscopic analysis.

Abstract Many early-type stars have been measured with high angular velocities. In such stars, mode identification is difficult as the effects of fast and differential rotation are not well known. Using fundamental parameters measured by interferometry, the ESTER structure code and the TOP oscillation code, we investigate the oscillation spectrum of [alpha] Ophiuchi, for which observations by the MOST satellite found 57 oscillations frequencies. Results do not show a clear identification of the modes and highlight the difficulties of asteroseismology for such stars with a very complex oscillation spectrum. [PUBLICATION ABSTRACT]