EDP Sciences
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Volume 434, Number 3, May II 2005
Page(s) 1055 - 1062
Section Stellar structure and evolution
DOI http://dx.doi.org/10.1051/0004-6361:20041816

A&A 434, 1055-1062 (2005)
DOI: 10.1051/0004-6361:20041816

Convection-pulsation coupling

I. A mixing-length perturbative theory
A. Grigahcène1, M.-A. Dupret1, M. Gabriel2, R. Garrido1 and R. Scuflaire2

1  Instituto de Astrofísica de Andalucía-CSIC, Apartado 3004, 18080 Granada, Spain
2  Institut d'Astrophysique et de Géophysique de l'Université de Liège, Belgium

(Received 9 August 2004 / Accepted 31 October 2004 )

We present in details a time-dependent convection treatment in the frame of the Mixing-Length Theory (MLT). Following the original ideas by Unno (1967, PASJ, 19, 140), this theory has been developed by Gabriel et al. (1974, Bull. Ac. Roy. Belgique, Classe des Sciences, 60, 866) and Gabriel (1996, Bull. Astron. Soc. India, 24, 233). In this paper, we present it in a united form, we detail the basic derivations and approximations and give final improvements. A new perturbation of the energy closure equation is proposed for the first time, making it possible to avoid the occurrence of short wavelength spatial oscillations of the thermal eigenfunctions. This theory accounts for the perturbation of the convective flux, the turbulent Reynolds stress and the turbulent kinetic energy dissipation. It has been numerically implemented in a non-radial non-adiabatic pulsation code and the first results published in a Letter by Dupret et al. (2004a, A&A, 414, L17) indicate that the theory predicts the observed red border of the lower end of the instability strip and the driving mechanism of the recently discovered $\gamma$ Dor stars.

Key words: stars: oscillations -- convection -- stars: interiors

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