1 Introduction

Convective transport of energy in a stellar atmosphere is one of the most complex astrophysical problems. Many of the approximations usually admitted for the stellar interior, such as diffusive radiative transfer, are no longer valid. Moreover, throughout most of a convective stellar atmosphere, radiative losses are large enough to make convection less efficient in transporting energy than radiation. Only stars which have a surface convection zone (CZ) extending deep into the stellar envelope can maintain efficient convective energy transfer near the bottom of their atmosphere. On the other hand, inefficient convection appears in all stars near the boundary of a convection zone close to locally stable regions. The modelling of inefficient convection requires a detailed knowledge about the effect of radiative gains and losses on the fluid flow. The situation is particularly complex for stars which are cool enough to develop a granulation pattern, such as the sun. In this case, at identical geometrical depths, vastly different physical conditions may be encountered depending on whether upflow in a granule or downflow in an intergranular lane is considered. The former may be optically thick while the latter is already optically thin, a consequence of the extreme temperature sensitivity of the dominant opacity source in the solar photosphere, the H^- ion (cf. also Stein & Nordlund 1998).

Currently, only very simple convection models are available for routine computation of extended grids of model atmospheres, while detailed numerical simulations are still unaffordable for applications that require the calculation of many thousands of individual model atmospheres over the HR diagram. Our intention here is first to review the convection models which are available for use together with the popular ATLAS9 model atmosphere code by Kurucz (1993, 1998) (see also Castelli et al. 1997). We provide an overview on what is known about the effects of the different convection treatments on model atmosphere structure and consequently on observable quantities.

The second purpose of the present paper is to determine to what extent the precision of fundamental parameters derived from the observed stellar spectrum, i.e. $T_{\rm eff}$, gravity and metallicity depends on the model atmosphere. Another objective is to obtain very accurate colors and more importantly very accurate derivatives of colors, color indices and limb darkening coefficients. These quantities are needed in the procedure of pulsation mode identification which is the first and a crucial step in any seismological study. Indeed probing the stellar interior of a pulsating star requires the knowledge of the resonant cavity within which each mode propagates, i.e. the physical nature of the pulsation mode associated with each observed oscillation frequency. One such procedure is based on the computation of oscillation amplitude ratios and phase differences which in turn depend on the variation of the colors with effective temperature and gravity. The results of this application of the model atmosphere grids will be presented in the next papers of this series (Barban et al. 2002; Garrido et al. 2002). Finally, due to their enhanced resolution the new model grids are also useful to improve the outer boundary conditions of stellar structure calculations (Montalbán et al. 2001; D'Antona et al. 2002).

These goals are part of a program performed in the framework of preparing the COROT space mission (see COROT web site). To achieve these purposes, we have used the ATLAS9 code in several versions modified for the convection zone treatment to compute new grids of model atmospheres, corresponding fluxes, surface intensities, uvby colors, synthetic spectra for some representative lines, and compared them with relevant observations. We have three versions of the ATLAS9 code at our disposal:

1.

The original version from CDROM13 of Kurucz (Kurucz 1993) in which the convection zone is treated using mixing length theory (MLT). While ATLAS versions from 5 to 8 remained basically close to the formulations given in Böhm-Vitense (1958) and in Cox & Giuli (1968), some improvements were added in ATLAS9 (cf. Castelli et al. 1997). In Sect. 2 we discuss the reasons for our specific selection among these improvements.

2.

The other two versions were provided by one of the authors (FK) who modified the code to include turbulent convection models from Canuto & Mazzitelli (1991, CM), and from Canuto et al. (1996, CGM).

Each convection model has been extensively used in the model atmosphere grid computations which we describe below. All the convection models are of local type and thus require the prescription of a characteristic length scale. Formally, it is possible to interchange the different length scales associated with the convection models. The motivation for doing so and a particular example will be discussed in the next paper of this series (Kupka et al. 2002).

This paper is organized as follows. In Sect. 2 we review previous works about the effect of the model structure on theoretical photometric colors and justify the need for new grids of model atmospheres. In Sect. 3 we describe the specific different convection treatments used and discuss their physical content.

In Sect. 4 we give details of the grid computations. In Sect. 5 we set out and comment the role of the convection treatments and convection parameters on the model structure, as well as its dependence on effective temperature, surface gravity, and metallicity. Finally, we discuss the consequences on observable quantities such as Balmer line profiles, flux distributions, and colors.