Population synthesis methods: discussion and tests on the solution uniqueness

We present and discuss improved versions of the population synthesis techniques introduced by Bica and Schmidt, Bica & Dottori. The base of equivalent widths used in these techniques to represent the star clusters’ spectral properties has been analysed with respect to its principal components and reduced to minimize degenerative effects due to internal correlation. A preliminary evaluation of the intrinsic domain of the components for a given problem, based on a random solution generation process, has been added to the techniques. The multi-minimization procedure has been improved by the introduction of a more rigorous statistical analysis of the set of acceptable solutions, and a representative solution is now obtained by reducing the domain of every component through a gradual convergence process. The minimization function has been modified in order to introduce an explicit dependence of its parameters on the observational errors. In order to estimate the uniqueness of the representative solution a series of tests has been performed. By building simulated composite spectra from the equivalent width base and using the present population synthesis techniques, we attempted to recover, without subjective interference, the proportions originally used. The results show that, even though a given population synthesis problem can be difficult to solve due to its degenerate nature or due to the lack of pertinent constraints, the input proportion are reproduced, in general, with an accuracy better than 5 per cent. Less accurate results, up to a factor of 3, are obtained for delicate problems for which the set of actual observable constraints is not stringent enough, such as in blue composite populations where spectral features below 3500 Å become important discriminators. Nevertheless, the characteristics most easy to identify were the maximum chemical enrichment of the simulated stellar populations and the presence of young star formation