Maurice Gabriel

Proper use of Schwarzschild Ledoux criteria in stellar evolution computations

The era of detailed asteroseismic analyses opened by space missions such as CoRoT and 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 zone 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 within the convective zone, the mass where the radiative luminosity is equal to the total luminosity. We then discuss two misuses of the boundary condition and the ways they a ect stellar modeling and stellar evolution. The first consists in applying the neutrality condition for convective instability on the 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 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 boundary. The specific problem of a convective shell is discussed and some remarks concerning overshooting are given. It appears that there is a misunderstanding concerning which criterion should be used to fix the boundaries of convective zones and also concerning which numerical procedure should be used to find them. The numerous methods tested recently by Paxton et al. (2013) clearly show that stellar evolution results are very sensitive to the choice that is made. The answer to these questions cannot be found from comparing numerical results obtained with di erent assumptions in stellar evolution codes since other uncertainties a ect stellar modeling. Therefore we think it is useful to cite some very basic physical facts which allow us to discuss the problem correctly and to bring a theoretical answer to the questions presently discussed. The extent of convective cores in stars is crucial in order to fix the time frame of their evolution and is of particular importance for stellar and galactic evolution. Moreover, since models are often used to interpret seismic data, it is important that they be free from any numerical inaccuracy caused by an incorrect positioning of the convective zones boundaries so that any discrepancy between observation and theory may be attributed to inaccuracies in the physics. It is interesting to point out that when comparing stellar models obtained with di erent codes, as was done in the frame of the ‘CoRoT Evolution and Seismic Tools Activity” (http://www.astro.up.pt/esta/) of the Seismology Working Group of the CoRoT Mission (http://corot.oamp.fr/), the main di erences are found in the location of convective zone boundaries

Stability ofG+ modes in a 30M⊙ star

The evolution of a Population I 30M⊙ star has been computed during the Main Sequence phases without taking semi-convection into account. These models have a temperature gradient larger than the adiabatic value in the inhomogeneous region. The models have been tested for stability towardsg+ modes of non-radial oscillations to see whether Katos mechanism leads to an instability. Whereas the models are stable during the early Main Sequence phases, they become unstable for low enough central hydrogen abundance.

Influence of the Perturbation of the Reynolds Tensor on the Stability of the Solar 5 Minute Oscillations

The excitation mechanism of the 5 min. oscillations is not yet understood. So far two mechanisms have been discussed. The first one is the linear vibrational instability. The second one is the non linear coupling between convection and pulsation discussed by Goldreich and Keeley (1977) and Goldreich and Kumar (1986).

Nonradial oscillations of solar models with an initial discontinuity in hydrogen abundance

Solar models are calculated with low central hydrogen abundance. The stability of these models is investigated. The eigenspectrum is computed and compared with the SCLERA observations of solar oscillation.

Towards Precise Asteroseismology of Solar-Like Stars

Adiabatic modeling of solar-like oscillations cannot exceed a certain level of precision for fitting individual frequencies. This is known as the problem of near-surface effects on the mode physics. We present a theoretical study which addresses the problem of frequency precision in non-adiabatic models using a time-dependent convection treatment. We find that the number of acceptable model solutions is significantly reduced and more precise constraints can be imposed on the models. Results obtained for a specific star (β Hydri) lead to very good agreement with both global and local seismic observables. This indicates that the accuracy of model fitting to seismic data is greatly improved when a more complete description of the interaction between convection and pulsation is taken into account.