Numerical simulations of the initial mass function and star-formation history using a grid of evolutionary models for star clusters

Numerical simulations are used to investigate the possibility of determining the physical properties of young star-forming complexes by finding the global minimum of a so-called deviation functional, which assigns each evolutionary model for a stellar population a number characterizing the deviation of the observed photometric properties from their model values. The deviation functional is calculated using a grid of evolutionary models computed at the Institute of Astronomy of the Russian Academy of Sciences. The parameters of the initial mass function (IMF) and the age corresponding to the global minimum of the deviation functional are strongly correlated with the IMF and age of the test model. The accuracy of the parameters of the IMF and the age are related to the random errors of the colors of the test models and the number of input parameters. A special series of numerical Simulations is used to demonstrate the possibility of using the deviation functional to determine the interstellar extinction and the fraction of Lyman photons that do not contribute to the ionization of gas in a star-forming complex. The simulation results can be used to assess the accuracy of the IMF parameters and ages of young star-forming complexes based on the observational data available.