Hybrid galaxy evolution modelling: Monte Carlo Markov Chain parameter estimation in semi-analytic models of galaxy formation

We introduce a statistical exploration of the parameter space of the Munich semi-analytic model built upon the Millennium dark matter simulation. This is achieved by applying a Monte Carlo Markov Chain (MCMC) method to constrain the 6 free parameters that define the stellar mass function at redshift zero. The model is tested against three different observational data sets, including the galaxy K-band luminosity function, B -V colours, and the black hole-bulge mass relation, to obtain mean values, confidence limits and likelihood contours for the best fit model. We discuss how the model parameters affect each galaxy property and find that there are strong correlations between them. We analyze to what extent these are simply reflections of the observational constraints, or whether they can lead to improved understanding of the physics of galaxy formation. When all the observations are combined, the need to suppress dwarf galaxies requires the strength of the supernova feedback to be significantly higher in our best-fit solution than in previous work. We interpret this fact as an indication of the need to improve the treatment of low mass objects. As a possible solution, we introduce the process of satellite disruption, caused by tidal forces exerted by central galaxies on their merging companions. We apply similar MCMC sampling techniques to the new model, which allows us to discuss the impact of disruption on the basic physics of the model. The new best fit model has a likelihood four times better than before, reproducing reasonably all the observational constraints, as well as the metallicity of galaxies and predicting intra-cluster light. We interpret this as an indication of the need to include the new recipe. We point out the remaining limitations of the semi-analytic model and discuss possible improvements that might increase its predictive power in the future.