1 Introduction

The determination of stellar ages provides numerous clues on the evolution of the Milky May and its components. While the classical method for globular clusters relies on morphological features in the Hertzsprung-Russell-diagram (HRD), for example an age-dependent turn-off (TO) brightness, direct age determinations of individual stars is progressively becoming a feasible alternative. In this case, the age is obtained from the position of the star on an evolutionary track. Typical examples for this method are eclipsing binary systems such as AI Phe ([Andersen et al. 1988]; [Milone et al. 1992]) or $\zeta$ Aur ([Bennett et al. 1996]; [Schröder et al. 1997]), for which accurate masses and radii can be determined from the light-curves (photometry and spectroscopy needed), and the stellar composition is either assumed or obtained from spectral analysis. In this case, the requirement that both components should have the same age provides an independent test for stellar evolution theory. If the distance to a single star is known accurately (e.g. from HIPPARCOS parallaxes) and its composition, gravity and effective temperature can be determined spectroscopically, the same procedure can be applied as well. For example, this method has recently been used for metal-poor stars by [Fuhrmann 2000] ([Fuhrmann 1998], [Fuhrmann 2000]) to deduce the formation history of bulge, thick and thin disk, and halo of the Milky Way. In the future, detached eclipsing binaries will hopefully be detected in globular clusters by massive photometric searches (e.g. in $\omega$ Cen, [Kaluzny et al. 1996] and [Kaluzny et al. 1997a], and in M 4, [Kaluzny et al. 1997b]) and will then allow age determinations of individual cluster stars ([Paczynski 1997]).

To be prepared for this case, we provide a grid of evolutionary tracks for low-mass, metal-poor stars typical for Pop II. The grid not only extends over stellar mass (from $0.6\cdots 1.3 \,M_\odot$) but also over composition, both in metallicity Z and helium content Y. The latter parameter usually is kept at a fixed value (typically 0.23) or coupled to Z via an assumption about the chemical evolution. Due to the small absolute value of Z for Pop II stars, this is however an almost negligible effect. According to [Paczynski 1997] it might be feasible to determine age and helium content of members of detached eclipsing binary systems and therefore calculations for different values of the initial helium abundance are necessary.

As a further effect microscopic diffusion has to be considered. Although it has become evident that it is operating in the Sun ([Richard et al. 1996]; [Guenther & Demarque 1997]), there are also arguments that diffusion may not be as efficient as calculated, as can be seen from the high abundance of $^7{\rm Li}$ still present in the photosphere of metal-poor low-mass stars ([Vauclair & Charbonnel 1998]). Therefore, calculations with and without diffusion have been performed to cover the whole possible range.

In Sect. 2 we will summarize the main properties of our stellar evolution code and the calculations done. After this, the results will be presented. We make available tables with the full evolutionary properties of all cases calculated. These can be used for isochrone calculations as well, if needed. We avoid transformations into observed colours and magnitudes for several reasons: firstly, such transformations always involve a further source of uncertainty (see [Weiss & Salaris 1999] for a discussion); secondly, they can, if needed, easily be applied, since the tables contain all necessary data; and finally, the data expected from the analysis of binary lightcurves and from spectroscopy will yield physical quantities, anyhow. To facilitate the derivation of the stellar age from given values of the global stellar properties, fitting formulae and the corresponding coefficients will be supplied as well. In Sect. 4 we will finally discuss the accuracy of such direct age determinations with special emphasis laid upon the comparison with other, independent work, because this will provide insight into the inherent systematic uncertainties of theoretical stellar evolution calculations. In the absence of suitable binary systems, we have applied our results to a few nearby single stars with known absolute parameters. This will be presented in Sect. 4 as well, before the conclusions close the paper.