Theory of stellar population synthesis with an application to

Aims. We present here a new theoretical approach to population synthesis. The aim is to predict colour magnitude diagrams (CMDs) for huge numbers of stars. With this method we generate synthetic CMDs for N-body simulations of galaxies. Sophisticated hydrodynamic N-body models of galaxies require equal quality simulations of the photometric properties of their stellar content. The only prerequisite for the method to work is very little information on the star formation and chemical enrichment histories, i.e. the age and metallicity of all star-particles as a function of time. The method takes into account the gap between the mass of real stars and that of the star-particles in N-body simulations, which best correspond to the mass of star clusters with different age and metallicity, i.e. a manifold of single stellar sopulations (SSP). Methods. The theory extends the concept of SSP to include the phase-space (position and velocity) of each star. Furthermore, it accelerates the building up of simulated CMD by using a database of theoretical SSPs that extends to all ages and metallicities of interest. Finally, it uses the concept of distribution functions to build up the CMD. The technique is independent of the mass resolution and the way the N-body simulation has been calculated. This allows us to generate CMDs for simulated stellar systems of any kind: from open clusters to globular clusters, dwarf galaxies, or spiral and elliptical galaxies. Results. The new theory is applied to an N-body simulation of a disc galaxy to test its performance and highlight its flexibility