CoRoT and Kepler observations of red giant stars revealed very rich spectra of non-radial solar-like oscillations. Of particular interest was the detection of mixed modes that exhibit significant amplitude, both in the core and at the surface of the
stars. It opens the possibility of probing the internal structure from their inner-most layers up to their surface along their evolution on the red giant branch as well as on the red-clump. Our objective is primarily to provide physical insight into the physical mechanism responsible for mixed-modes amplitudes and lifetimes. Subsequently, we aim at understanding the evolution and structure of red giants spectra along with their evolution. The study of energetic aspects of these oscillations is also of great importance to predict the mode parameters in the power spectrum. Non-adiabatic computations, including a time-dependent treatment of convection, are performed and provide the lifetimes of radial and non-radial mixed modes. We then combine these mode lifetimes and inertias with a stochastic excitation model that gives us their heights in the power spectra. For stars representative of CoRoT and Kepler observations, we show under which circumstances mixed modes have heights comparable to radial ones. We stress the importance of the radiative damping in the determination of the height of mixed modes. Finally, we derive an estimate for the height ratio between a g-type and a p-type mode. This can thus be used as a first estimate of the detectability of mixed-modes.
The space missions CoRoT and Kepler provide high quality data that allow us to test the transport of angular momentum in stars by the seismic determination of the internal rotation profile. Our aim is to test the validity of the seismic diagnostics f
or red giants rotation that are based on a perturbative method and to investigate the oscillation spectra when the validity does not hold. We use a non-perturbative approach implemented in the ACOR code (Ouazzani et al. 2012) that accounts for the effect of rotation on pulsations, and solves the pulsation eigenproblem directly for dipolar oscillation modes. We find that the limit of the perturbation to first order can be expressed in terms of the rotational splitting compared to the frequency separation between consecutive dipolar modes. Above this limit, non-perturbative computations are necessary but only one term in the spectral expansion of modes is sufficient as long as the core rotation rate remains significantly smaller than the pulsation frequencies. Each family of modes with different azimuthal symmetry, m, has to be considered separately. In particular, in case of rapid core rotation, the density of the spectrum differs significantly from one m-family of modes to another, so that the differences between the period spacings associated with each m-family can constitute a promising guideline toward a proper seismic diagnostic for rotation.
CoRoT and Kepler observations of red giants reveal rich spectra of non-radial solar-like oscillations allowing to probe their internal structure. We compare the theoretical spectrum of two red giants in the same region of the HR diagram but in differ
ent evolutionary phases. We present here our first results on the inertia, lifetimes and amplitudes of the oscillations and discuss the differences between the two stars.
A new two dimensional non-perturbative code to compute accurate oscillation modes of rapidly rotating stars is presented. The 2D calculations fully take into account the centrifugal distorsion of the star while the non perturbative method includes th
e full influence of the Coriolis acceleration. This 2D non-perturbative code is used to study pulsational spectra of highly distorted evolved models of stars. 2D models of stars are obtained by a self consistent method which distorts spherically averaged stellar models a posteriori. We are also able to compute gravito-acoustic modes for the first time in rapidly rotating stars. We present the dynamics of pulsation modes in such models, and show regularities in their frequency spectra.
A growing number of solar-like oscillations has been detected in red giant stars thanks to CoRoT and Kepler space-crafts. The seismic data gathered by CoRoT on red giant stars allow us to test mode driving theory in physical conditions different from
main-sequence stars. Using a set of 3D hydrodynamical models representative of the upper layers of sub- and red giant stars, we computed the acoustic mode energy supply rate (Pmax). Assuming adiabatic pulsations and using global stellar models that assume that the surface stratification comes from the 3D hydrodynamical models, we computed the mode amplitude in terms of surface velocity. This was converted into intensity fluctuations using either a simplified adiabatic scaling relation or a non-adiabatic one. From L and M (the luminosity and mass), the energy supply rate Pmax is found to scale as (L/M)^2.6 for both main-sequence and red giant stars, extending previous results. The theoretical amplitudes in velocity under-estimate the Doppler velocity measurements obtained so far from the ground for red giant stars by about 30%. In terms of intensity, the theoretical scaling law based on the adiabatic intensity-velocity scaling relation results in an under-estimation by a factor of about 2.5 with respect to the CoRoT seismic measurements. On the other hand, using the non-adiabatic intensity-velocity relation significantly reduces the discrepancy with the CoRoT data. The theoretical amplitudes remain 40% below, however, the CoRoT measurements. Our results show that scaling relations of mode amplitudes cannot be simply extended from main-sequence to red giant stars in terms of intensity on the basis of adiabatic relations because non-adiabatic effects for red giant stars are important and cannot be neglected. We discuss possible reasons for the remaining differences.
Space-borne missions CoRoT and {it Kepler} are providing a rich harvest of high-quality constraints on solar-like pulsators. Among the seismic parameters, mode damping rates remains poorly understood and thus barely used to infer physical properties
of stars. Nevertheless, thanks to CoRoT and {it Kepler} space-crafts it is now possible to measure damping rates for hundreds of main-sequence and thousands of red-giant stars with an unprecedented precision. By using a non-adiabatic pulsation code including a time-dependent convection treatment, we compute damping rates for stellar models representative for solar-like pulsators from the main-sequence to the red-giant phase. This allows us to reproduce the observations of both CoRoT and {it Kepler}, which validates our modeling of mode damping rates and thus the underlying physical mechanisms included in the modeling. Actually, by considering the perturbations of turbulent pressure and entropy (including perturbation of the dissipation rate of turbulent energy into heat) by the oscillation in our computation, we succeed in reproducing the observed relation between damping rates and effective temperature. Moreover, we discuss the physical reasons for mode damping rates to scale with effective temperature, as observationally exhibited. Finally, this opens the way for the use of mode damping rates to probe turbulent convection in solar-like stars.
Observations suggest that a relationship exists between the driving mechanism of roAp star pulsations and the heavy element distribution in these stars. We attempt to study the effects of local and global metallicity variations on the excitation mech
anism of high order p-modes in A star models. We developed stellar evolutionary models to describe magnetic A stars with different global metallicity or local metal accumulation profiles. These models were computed with CLES (Code Li`egeois devolution stellaire), and the stability of our models was assessed with the non-adiabatic oscillation code MAD. Our models reproduce the blue edge of the roAp star instability strip, but generate a red edge hotter than the observed one, regardless of metallicity. Surprisingly, we find that an increase in opacity inside the driving region can produce a lower amount of driving, which we refer to as the inverse $kappa$-mechanism.
There are many unknowns in the formation of subdwarf B stars. Different formation channels are considered to be possible and to lead to a variety of helium-burning subdwarfs. All seismic models to date, however, assume that a subdwarf B star is a pos
t-helium-flash-core surrounded by a thin inert layer of hydrogen. We examine an alternative formation channel, in which the subdwarf B star originates from a massive (>~2 Msun) red giant with a non-degenerate helium-core. Although these subdwarfs may evolve through the same region of the log g-Teff diagram as the canonical post-flash subdwarfs, their interior structure is rather different. We examine how this difference affects their pulsation modes and whether it can be observed. Using detailed stellar evolution calculations we construct subdwarf B models from both formation channels. The iron accumulation in the driving region due to diffusion, which causes the excitation of the modes, is approximated by a Gaussian function. The pulsation modes and frequencies are calculated with a non-adiabatic pulsation code. A detailed comparison of two subdwarf B models from different channels, but with the same log g and Teff, shows that their mode excitation is different. The excited frequencies are lower for the post-flash than for the post-non-degenerate subdwarf B star. This is mainly due to the differing chemical composition of the stellar envelope. A more general comparison between two grids of models shows that the excited frequencies of most post-non-degenerate subdwarfs cannot be well-matched with the frequencies of post-flash subdwarfs. In the rare event that an acceptable seismic match is found, additional information, such as mode identification and log g and Teff determinations, allows us to distinguish between the two formation channels.
