Quadratic programming applied to the problem of galaxy population synthesis.

Summary. The technique of quadratic programming as applied to the problem of galaxy population synthesis is described. The method offers significant advantages over the trial-and-error approach usually employed. This technique is applied to 38-color data on the nuclei of M 31, M 32, and M 81 and to integrated 10- color photometry for elliptical galaxies. The results indicate that estimates of mean line strengths in external galaxies by means of population synthesis are well determined. Ages based on the main-sequence turnoff point are uncertain by a factor of two. The method is not sensitive to the number of stars on the main sequence between K 0 V and M 7 V. Consequently the slope of the luminosity function below turnoff cannot be determined. The mass-to-light ratio of the computed population for M 31 is uncertain by a factor of 4. The corresponding factors for M 32 and M 81 are 50 and 16 respectively. Models for elliptical galaxies suggest that the mean metal abundance of the stellar population increases with increasing galaxy luminosity. Key words: galaxies - M 31 - stellar populations - elliptical galaxies