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Astron. Astrophys. 334, 953-968 (1998)

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1. Introduction

In the vast majority of the stellar evolutionary computations up today, turbulent convection has been described as a local mechanism (in spite of its intrinsic non-local character) according to the Mixing Length Theory (MLT). In the local approximation, at the Schwarzschild boundary both velocity and acceleration go to zero together with the buoyancy forces acting on the convective elements, and nothing can be known about the turbulent velocity profiles outside formally convective regions. In addition, in convective and overshooting regions instantaneous chemical mixing decoupled from nuclear evolution is generally assumed in stellar modeling, with the only noticeable exception of Sackmann et al. (1995) for the external layers of Asymptotic Giant Branch (AGB) stars, where coupling nuclear evolution and mixing is the only correct way of describing the surface lithium evolution.

And yet, both overshooting and chemical evolution in turbulent regions do affect the behavior of stars. Let us first consider overshooting alone. Some attempts have been made to predict - very often according to non-local corrections to the MLT - the amount of mixed matter (Shaviv & Salpeter 1973; Roxburgh 1978, Xiong 1985, Grossman 1996 etc.); many such models have been reviewd and criticized on theoretical grounds by Canuto (1992, 1996). When constructing stellar models, all the above approaches predict large overshooting distances ([FORMULA], being [FORMULA] the pressure scale heigth) which should lead to dramatic - and not observed - consequences at least on the evolution of massive stars in young open clusters (Maeder 1990).

Computations with a bare parametric approach to the problem have been then also tried, allowing instantaneous mixing beyond the formal convective borders up to a fraction of [FORMULA] (e.g. Maeder & Meynet 1987; Stothers & Chin 1992). According to Maeder & Meynet (1991), the main sequences of young clusters are reasonably fit with an instantaneous overshooting from the convective core [FORMULA] ; for older clusters (Turn Off (TO) masses [FORMULA]) the temporal evolution of the convective cores is more tricky, depending on details of the chemical and physical inputs (Maeder & Meynet 1987). An analogous upper value to overshooting ([FORMULA]) has been also suggested by Stothers & Chin (1992).

As for non-instantaneous mixing (and overshooting), Deng et al. (1996a,b, always in an MLT framework) suggested that it is more physically realistic to expect smooth chemical profiles outside the convective boundaries, consistent with a diffusive description of the process. In the present paper we adopt a diffusive approach too, with considerable conceptual differences with respect to all the previous studies to be discussed in details in the following.

As for the effects of coupling nuclear evolution to non-instantaneous mixing, we only found sparse references in the literature to the problem as a whole, and to possible rough solutions with complete mixing if nuclear lifetimes are longer than mixing times, locally frozen compositions in the opposite case. In the best of our knowledge, the present computations are the first ones in which the problem has been consistently and extensively addressed, apart from the already quoted case by Sackmann et al. (1995) in AGB. Full Spectrum of Turbulence (FST) convection model, and coupling between nuclear evolution and diffusive mixing, are then the main differences between the present paper and all the preceding literature.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998