Monte Carlo Markov Chain parameter estimation in semi-analytic models of galaxy formation

We present a statistical exploration of the parameter space of the De Lucia and Blaizot version of the Munich semi-analytic (SA) model built upon the Millennium dark matter simulation. This is achieved by applying a Monte Carlo Markov Chain method to constrain the six free parameters that define the stellar and black hole mass functions 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, separately and combined, to obtain mean values, confidence limits and likelihood contours for the best-fitting model. Using each observational data set independently, we discuss how the SA model parameters affect each galaxy property and find that there are strong correlations between them. We analyse to what extent these are simply reflections of the observational constraints, or whether they can lead to improved understandings of the physics of galaxy formation. When all the observations are combined, we find reasonable agreement between the majority of the previously published parameter values and our confidence limits. However, the need to suppress dwarf galaxy formation requires the strength of the supernova feedback to be significantly higher in our best-fitting solution than in previous work. To balance this, we require the feedback to become ineffective in haloes of lower mass than before, so as to permit the formation of sufficient high-luminosity galaxies: unfortunately, this leads to an excess of galaxies around L*. Although the best fit is formally consistent with the data, there is no region of parameter space that reproduces the shape of galaxy luminosity function across the whole magnitude range. For our best fit, we present the model predictions for the b(J)-band luminosity and stellar mass functions. We find a systematic disagreement between the observed mass function and the predictions from the K-band constraint, which we explain in light of recent works that suggest uncertainties of up to 0.3 dex in the mass determination from stellar population synthesis models. We discuss modifications to the SA model that might simultaneously improve the fit to the observed mass function and reduce the reliance on excessive supernova feedback in small haloes.