8 Summary

We have derived a set of empirical fitting functions describing the behaviour of the break at $\lambda 4000$ Å in terms of the atmospheric stellar parameters: effective temperature, metallicity and surface gravity. This calibration can be easily incorporated into stellar population models to provide accurate predictions of the D₄₀₀₀ for composite systems. In a forthcoming paper we will analyze the measurements of the break in old stellar populations at the light of the predictions of such models. Considering the volume covered by the employed stellar library (Lick/IDS + Pickles' hot subsample) in the stellar parameter space, the derived fitting functions suit the requirements to provide accurate D₄₀₀₀ predictions for populations with ages larger than about 0.1 Gyr, and $-1\le {\rm [Fe/H]} \le +0.5$ dex (see also W94). Note however that, since the break could be contaminated by nebular emission in galaxies with ongoing star formation, it is necessary to include this effect in the population modelling in order to predict reliable D₄₀₀₀ indices for such stellar populations. It should also be noted that the applicability of the derived fitting functions is safe as far as the abundance ratios of the library stars reflect those in the modeled stellar populations.

In order to facilitate the usage of the present D₄₀₀₀ fitting functions we have written a FORTRAN subroutine, available from:
http://www.ucm.es/info/Astrof/D4000/D4000.html
This routine computes the value of the D₄₀₀₀ as a function of the input stellar parameters $T_{\rm eff}$, [Fe/H] and $\log g$. The code performs smooth interpolations among temperature and gravity ranges, providing also an estimate of the error in the predicted index,

Acknowledgements

We thank Jesús Gallego (runs 3 and 5) and Jaime Zamorano (run 3) for carrying out the observations of some stars of the sample. We also thank Emilios Harlaftis, Martín Guerrero and Reynier Peletier, the support astronomers who performed the service time observations of runs 7, 10 and 12, respectively. We are grateful to the anonymous referee for useful suggestions. The JKT, INT and WHT are operated on the island of La Palma by the Royal Greenwich Observatory at the Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. The Calar Alto Observatory is operated jointly by the Max-Planck-Institute für Astronomie, Heidelberg, and the Spanish Comisión Nacional de Astronomía. This research has made use of the Simbad database (operated at CDS, Strasbourg, France), the NASA's Astrophysics Data System Article Service, and the Hipparcos Catalogue. This work was supported by the Spanish "Programa Sectorial de Promoción del Conocimiento'' under grant No. PB96-610.