Evolution of elemental abundances in planetary nebulae

We study the evolution of elemental abundances in an ensemble of Galactic planetary nebulae as a function of the masses of the central stars (M (cs)) and their progenitors (M (ini)). We derive the dependences of the C, N, Ne, Cl, Ar, and S abundances on M (cs) and M (ini) for a large sample of nebulae. We calculate the theoretical elemental abundances in nebulae under the assumption of complete mixing of the progenitor's matter ejected at different stages of its evolution. The theoretical dependences of the C and N abundances on M (ini) have been found to correspond to the observed ones. At the same time, the observed mean O abundance is approximately half its theoretical value. The Ne, Cl, Ar, and S abundances monotonically increase with increasing mass of the progenitor star, which reflects an increase in the mean abundances of heavy elements during the chemical evolution of the Galaxy. We have derived the relation between the abundances of the elements under consideration in planetary nebulae and the masses of their central stars. This relation is used to construct the mass function for the nuclei of planetary nebulae.