Abstract. We apply here the Time Dependent Convection (TDC) treatment presented in our earlier paper in this series to the study of δ Sct and γ Dor pulsating stars. Stabilization of the δ Sct p-modes at the red edge of the Instability Strip (IS) and the driving of the γ Dor g-modes are explained by our models. Theoretical IS obtained with different values of the Mixing Length (ML) parameter α are compared to observations and a good agreement is obtained for α between 1.8 and 2. The influence of each term of our TDC treatment (perturbation of convective flux, turbulent pressure, and turbulent kinetic energy dissipation) on the eigenfrequencies and on the driving and damping mechanisms is investigated. Finally, we show that our TDC models predict the likely existence of hybrid stars with both δ Sct p-modes and γ Dor g-modes oscillations.

Abstract. 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 γ Dor stars.

New theoretical instability strips for δ Sct and γ Dor stars are presented. These results have been obtained taking into account the perturbation of the convective flux following the treatment of Gabriel (1996). For the first time, the red edge of the δ Sct instability strip for non-radial modes is obtained. The influence of this time-dependent convection (TDC) on the driving of the γ Dor gravity modes is investigated. The results obtained for different values of the mixing-length parameter α are compared for the γ Dor models. A good agreement with observations is found for models with α between 1.8 and 2.0.

We have gathered and analyzed 1493 high-quality multicolor Geneva photometric data taken over 21 years of the B3Vstar HD 129929. We detect six frequencies, among which appear the effects of rotational splitting with a spacing of ∼0.0121 cycles per day, which implies that the star rotates very slowly. A nonadiabatic analysis of the oscillations allows us to constrain the metallicity of the star to Z ϵ [0.017,0.022], which agrees with a similar range derived from spectroscopic data. We provide evidence for the occurrence of core convective overshooting in the star, with α ov = 0.10 ± 0.05, and we rule out rigid rotation.