The problem of normal oscillations of a viscous stratified fluid with an elastic membrane

Normal oscillations of a viscous stratified fluid partially filling an arbitrary vessel and bounded above by an elastic horizontal membrane are studied. In this case, we consider a scalar model problem that reflects the main features of the vector spatial problem. The characteristic equation for the eigenvalues of the model problem is obtained, the structure of the spectrum and the asymptotics of the branches of the eigenvalues are studied. Assumptions are made about the structure of the oscillation spectrum of a viscous stratified fluid bounded by an elastic membrane for an arbitrary vessel. It is proved that the spectrum of the problem is discrete, located in the right complex half-plane symmetrically with respect to the real axis, and has a single limit point $+\infty$. Moreover, the spectrum is localized in a certain way in the right half-plane, the location zone depends on the dynamic viscosity of the fluid.

Relativistic asteroseismology

The ideas behind gravitational-wave asteroseismology are introduced and motivated by a set of phenomenological relations. The impact of general relativity on different classes of stellar oscillation modes is outlined and the emergence of a new family of modes (the w-modes) associated with the dynamcis of spacetime itself is explained. The impact of relevant physics on a given neutron star’s oscillation spectrum is discussed. The instability of the f-mode in fast-spinning neutron stars is considered.

Comprehensive stellar seismic analysis

Aims. We develop a method that provides a comprehensive analysis of the oscillation spectra of solar-like pulsators. We define new seismic indicators that should be as uncorrelated and as precise as possible and should hold detailed information about stellar interiors. This is essential to improve the quality of the results obtained from asteroseismology as it will provide better stellar models which in turn can be used to refine inferences made in exoplanetology and galactic archaeology. Methods. The presented method – WhoSGlAd – relies on Gram-Schmidt’s orthogonalisation process. A Euclidean vector sub-space of functions is defined and the oscillation frequencies are projected over an orthonormal basis in a specific order. This allowed us to obtain independent coefficients that we combined to define independent seismic indicators. Results. The developed method has been shown to be stable and to converge efficiently for solar-like pulsators. Thus, detailed and precise inferences can be obtained on the mass, the age, the chemical composition and the undershooting in the interior of the studied stars. However, attention has to be paid when studying the helium glitch as there seems to be a degeneracy between the influence of the helium abundance and that of the heavy elements on the glitch amplitude. As an example, we analyse the 16CygA (HD 186408) oscillation spectrum to provide an illustration of the capabilities of the method.

Seismic characterization of red giants going through the helium-core flash

Context. First-ascent red giants in the approximate mass range 0.7 ≲ M/M⊙ ≲ 2 ignite helium in their degenerate core as a flash. Stellar evolution codes predict that the He flash consists of a series of consecutive subflashes. Observational evidence of the existence of the He flash and subflashes is lacking. The detection of mixed modes in red giants from space missions CoRoT and Kepler has opened new opportunities to search for such evidence. Aims. During a subflash, the He-burning shell is convective, which splits the cavity of gravity modes in two. We here investigate how this additional cavity modifies the oscillation spectrum of the star. We also address the question of the detectability of the modes, to determine whether they could be used to seismically identify red giants passing through the He flash. Methods. We calculate the asymptotic mode frequencies of stellar models going through a He subflash using the Jeffreys-Wentzel-Kramers-Brillouin (JWKB) approximation. To predict the detectability of the modes, we estimate their expected heights, taking into account the effects of radiative damping in the core. Our results are then compared to the oscillation spectra obtained by numerically calculating the mode frequencies during a He subflash. Results. We show that during a He subflash, the detectable oscillation spectrum mainly consists of modes trapped in the acoustic cavity and in the outer g-mode cavity. The spectrum should thus at first sight resemble that of a core-helium-burning giant. However, we find a list of clear, detectable features that could enable us to identify red giants passing through a He subflash. In particular, during a He subflash, several modes that are trapped in the innermost g-mode cavity are expected to be detectable. We show that these modes could be identified by their frequencies or by their rotational splittings. Other features, such as the measured period spacing of gravity modes or the location of the H-burning shell within the g-mode cavity could also be used to identify stars going through a He subflash. Conclusions. The features derived in this study can now be searched for in the large datasets provided by the CoRoT and Kepler missions.

Deciphering the oscillation spectrum of γ Doradus and SPB stars

Context. The space-based Kepler mission provided four years of highly precise and almost uninterrupted photometry for hundreds of γ Doradus stars and tens of slowly pulsating B-type (SPB) stars, finally allowing us to apply asteroseismology to these gravity mode pulsators. Without rotation, gravity modes are equally spaced in period. This simple structure does not hold in rotating stars for which rotation needs to be taken into account to accurately interpret the oscillation spectrum. Aims. We aim to develop a stellar-model-independent method to analyse and interpret the oscillation spectrum of γ Dor and SPB stars. Methods. Within the traditional approximation of rotation, we highlight the possibility of recovering the equidistance of period spacings by stretching the pulsation periods. The stretching function depends on the degree and azimuthal order of gravity modes and the rotation rate of the star. In this new stretched space, the pulsation modes are regularly spaced by the stellar buoyancy radius. Results. On the basis of this property, we implemented a method to search for these new regularities and simultaneously infer the rotation frequency and buoyancy radius. Tests on synthetic spectra computed with a non-perturbative approach show that we can retrieve these two parameters with reasonable accuracy along with the mode identification. In uniformly rotating models of a typical γ Dor star, and for the most observed prograde dipole modes, we show that the accuracy on the derived parameters is better than 5% on both the internal rotation rate and the buoyancy radius. Finally, we apply the method to two stars of the Kepler field, a γ Dor and an SPB, and compare our results with those of other existing methods. Conclusions. We provide a stellar-model-independent method to obtain the near-core rotation rate, the buoyancy radius, and the mode identification from gravity-mode spectra of γ Dor and SPB stars.