1 Introduction

For many astrophysical applications, an accurate knowledge of the silicon abundance is required. Silicon is not only an important reference element for comparing various types of cosmic matter (e.g. meteorites) with the Sun but also one of the main electron contributors (next to Fe and Mg) and opacity sources in the near UV in the atmospheres of cool stars. Furthermore, the C/Si abundance ratio is an indicator of gas-dust separation in A stars with superficial abundance anomalies like $\lambda$ Boo stars (Stürenburg 1993).
The most widely used sources of solar (photospheric) abundances, the compilation by Anders & Grevesse (1989) and its updates (e.g. Grevesse & Sauval 1998), are based on standard abundance analyses employing 1D solar models and, in most cases, assuming LTE (local thermodynamic equilibrium). But for a accurate abundance determination, the simplifying assumption of LTE should be replaced by a detailed non-LTE study.
In the Sun, abundance deviations due to non-LTE effects are generally small, as can be seen from former calculations: +0.05 dex for Fe I (Steenbock 1985), -0.07 dex for C I (Stürenburg & Holweger 1991) and -0.05 dex ( $-0.01 \,...\, -0.06$ dex) for N I/II (Rentzsch-Holm 1996). Nevertheless, exact solar values are indispensable, as the Sun serves as a reference for investigations of other stars.
The A0V star Vega (HR 7001) is well studied in the context of abundance determination, and non-LTE calculations have been carried out for various elements (e.g. Gigas 1988; Takeda 1992). Its chemical composition shows a metal deficiency with respect to the Sun resembling the pattern of $\lambda$ Boo stars (Venn & Lambert 1990; Holweger & Rentzsch-Holm 1995). Therefore the former standard star Vega has turned into an important example of A stars with abundance anomalies.
For most elements, non-LTE corrections are small but not negligible, for example -0.05 dex ( $-0.16 \,...\, 0.00$ dex) for C I (Stürenburg & Holweger 1990), -0.32 dex
($-0.16 \,...\, -0.53$ dex) for N I/II (Rentzsch-Holm 1996), $-1 \,...\, -0.02$ dex for O I (Takeda 1992).
The presented calculations were carried out with the Kiel non-LTE code (Steenbock & Holweger 1984) which uses the computational scheme developed by Auer & Heasley (1976). Non-LTE calculations require various input data, such as a stellar atmosphere and a model atom which accounts for the relevant atomic properties. The resulting silicon abundances were derived with the program LINFOR, an updated and augmented Fortran version of the program by Baschek et al. (1966) devised by H. Holweger, M. Steffen and W. Steenbock at Kiel.
In Sect. 2 the atomic data used for the model atom are described. In Sects. 3 and 4 the non-LTE calculations and abundance determination are outlined for the Sun and for Vega, respectively.