On the proper use of the Schwarzschild and Ledoux criteria in stellar evolution computations

The era of detailed asteroseismic analyses opened by space missions such as CoRoT and $\textit{Kepler}$ has highlighted the need for stellar models devoid of numerical inaccuracies, in order to be able to diagnose which physical aspects are being ignored or poorly treated in standard stellar modeling. We tackle here the important problem of fixing convective zones boundaries in the frame of the local mixing length theory. First we show that the only correct way to locate a convective zone boundary is to find, at each iteration step, through interpolations or extrapolations from points $\textit{within the convective zone}$, the mass where the radiative luminosity is equal to the total one. We then discuss two misuses of the boundary condition and the way they affect stellar modeling and stellar evolution. The first one consists in applying the neutrality condition for convective instability on the $\textit{radiative}$ side of the convective boundary. The second way of misusing the boundary condition comes from the process of fixing the convective boundary through the search for a change of sign of a possibly \textit{discontinuous} function. We show that these misuses can lead to completely wrong estimates of convective core sizes with important consequences for the following evolutionary phases. We point out the advantages of using a double mesh point at each convective zone boundaries. The specific problem of a convective shell is discussed and some remarks concerning overshooting are given.Comment: 14 pages, 10 figures, to appear in A&

Inference from adiabatic analysis of solar-like oscillations in Red giants

The clear detection with CoRoT and KEPLER of radial and non-radial solar-like oscillations in many red giants paves the way to seismic inferences on the structure of such stars. We present an overview of the properties of the adiabatic frequencies and frequency separations of radial and non-radial oscillation modes, highlighting how their detection allows a deeper insight into the properties of the internal structure of red giants. In our study we consider models of red giants in different evolutionary stages, as well as of different masses and chemical composition. We describe how the large and small separations computed with radial modes and with non-radial modes mostly trapped in the envelope depend on the stellar global parameters and evolutionary state, and we compare our theoretical predictions and first KEPLER data.Finally, we find that the properties of dipole modes constitute a promising seismic diagnostic of the evolutionary state of red-giant stars.Comment: 6 pages, 5 figures. Proceedings of IV Helas International Conference: "Seismological Challenges for Stellar Structure", Lanzarote (Canary Islands, Spain), 1-5 February 201

Ledoux's convection criterion in evolution and asteroseismology of massive stars

Saio et al. (2006) have shown that the presence of an intermediate convective zone (ICZ) in post-main sequence models could prevent the propagation of g-modes in the radiative interior and hence avoid the corresponding radiative damping. The development of such a convective region highly depends on the structure of the star in the mu-gradient region surrounding the convective core during the main sequence phase. In particular,the development of this ICZ depends on physical processes such as mass loss, overshooting (Chiosi & Maeder 1986, Chiosi et al. 1992, see also Godart et al., these proceedings) and convective instability criterion (Schwarzschild's or Ledoux's criteria). In this paper we study the consequences of adopting the Ledoux's criterion on the evolution of the convective regions in massive stars (15 and 20 Msun), and on the pulsation spectrum of these new B-type variables (also called SPBsg).Comment: Contribution to the Proceedings of the 38th LIAC/HELAS-ESTA/BAG, 2008 Accepted for publication in CoAs

The AGB bump: a calibrator for the core mixing

The efficiency of convection in stars affects many aspects of their evolution and remains one of the key-open questions in stellar modelling. In particular, the size of the mixed core in core-He-burning low-mass stars is still uncertain and impacts the lifetime of this evolutionary phase and, e.g., the C/O profile in white dwarfs. One of the known observables related to the Horizontal Branch (HB) and Asymptotic Giant Branch (AGB) evolution is the AGB bump. Its luminosity depends on the position in mass of the helium-burning shell at its first ignition, that is affected by the extension of the central mixed region. In this preliminary work we show how various assumptions on near-core mixing and on the thermal stratification in the overshooting region affect the luminosity of the AGB bump, as well as the period spacing of gravity modes in core-He-burning models.Comment: Submitted to EPJ Web of Conferences, to appear in the Proceedings of the 3rd CoRoT Symposium, Kepler KASC7 joint meeting; 2 pages, 2 figure

The Enigma of B-type Pulsators in the SMC

Since the early nineties it is accepted that the excitation mechanism of B-type pulsators on the main sequence is due to the opacity peak in the iron-group elements at $T\approx 200,000$ K. The Fe content plays then a major role in the excitation of $\beta$ Cep and SPB pulsations. While theoretical non-adiabatic computations predict no $\beta$ Cep pulsators and only a small number of SPBs for low metallicity environments such as that of the Magellanic Clouds (MCs), recent variability surveys of B stars in the SMC have reported the detection of a significant number of SPB and $\beta$ Cep candidates. Since the SMC is the metal poorest (Z$\approx$0.001-0.004) of the MCs, it constitutes an interesting object for investigating the disagreement between theory and observations. We approach the problem by calling into question some of the hypotheses made in previous studies: given the different chemical evolution of the SMC compared with our local galactic environment, is it appropriate to describe the chemical composition of SMC B stars by scaling the solar mixture to lower $Z$? Is that composition uniform in space and time? In this paper we present the results of a stability analysis of B-type stellar models computed with a revised chemical composition and metallicity specific to the SMC.Comment: 3 pages, 3 figures, proceeding for "Stellar Pulsation: Challenges for Theory and Observation", Santa Fe 200

Hybrid gamma Doradus/delta Scuti Stars: Comparison Between Observations and Theory

Gamma Doradus are F-type stars pulsating with high order g-modes. Their instability strip (IS) overlaps the red edge of the delta Scuti one. This observation has led to search for objects in this region of the HR diagram showing p and g-modes simultaneously. The existence of such hybrid pulsators has recently been confirmed (Handler 2009) and the number of candidates is increasing (Matthews 2007). From a theoretical point of view, non-adiabatic computations including a time-dependent treatment of convection (TDC) predict the existence of gamma Dor/delta Sct hybrid pulsators (Dupret et al. 2004; Grigahcene et al. 2006). Our aim is to confront the properties of the observed hybrid candidates with the theoretical predictions from non-adiabatic computations of non-radial pulsations including the convection-pulsation interaction.Comment: 3 pages, 3 figures, Poster at "Stellar Pulsation: challenges for theory and observation", Santa Fe, June 200

Upward Revision of the Individual Masses in Α Cen: Implications for the Evolutionary State of the System

The recent upward revisions of the individual masses of the components of the binary system α Centauri (Pourbaix D., this meeting) led us to perform new calibrations of the system. The possibility of the onset a convective core in α Cen A is discussed together with its implications on the p-mode oscillation frequencies

Determining the metallicity of the solar envelope using seismic inversion techniques

peer reviewedThe solar metallicity issue is a long-lasting problem of astrophysics, impacting multi- ple fields and still subject to debate and uncertainties. While spectroscopy has mostly been used to determine the solar heavy elements abundance, helioseismologists at- tempted providing a seismic determination of the metallicity in the solar convective enveloppe. However, the puzzle remains since two independent groups prodived two radically different values for this crucial astrophysical parameter. We aim at provid- ing an independent seismic measurement of the solar metallicity in the convective enveloppe. Our main goal is to help provide new information to break the current stalemate amongst seismic determinations of the solar heavy element abundance. We start by presenting the kernels, the inversion technique and the target function of the inversion we have developed. We then test our approach in multiple hare-and-hounds exercises to assess its reliability and accuracy. We then apply our technique to solar data using calibrated solar models and determine an interval of seismic measurements for the solar metallicity. We show that our inversion can indeed be used to estimate the solar metallicity thanks to our hare-and-hounds exercises. However, we also show that further dependencies in the physical ingredients of solar models lead to a low accuracy. Nevertheless, using various physical ingredients for our solar models, we determine metallicity values between 0.008 and 0.014

Pulsations in hot supergiants

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