Bayesian inference of galaxy formation from the K-band luminosity function of galaxies: tensions between theory and observation

We conduct Bayesian model inferences from the observed K-band luminosity function of galaxies in the local Universe, using the semi-analytic model (SAM) of galaxy formation introduced in Lu et al (2011). The prior distributions for the 14 free parameters include a large range of possible models. We find that some of the free parameters, e.g. the characteristic scales for quenching star formation in both high-mass and low-mass halos, are already tightly constrained by the single data set. The posterior distribution includes the model parameters adopted in other SAMs. By marginalising over the posterior distribution, we make predictions that include the full inferential uncertainties for the colour-magnitude relation, the Tully-Fisher relation, the conditional stellar mass function of galaxies in halos of different masses, the HI mass function, the redshift evolution of the stellar mass function of galaxies, and the global star formation history. Using posterior predictive checking with the available observational results, we find that the model family (i) predicts a Tully-Fisher relation that is curved; (ii) significantly over predicts the satellite fraction; (iii) vastly over predicts the HI mass function; (iv) predicts high-z stellar mass functions that have too many low mass galaxies and too few high mass ones. and (v) predicts a redshift evolution of the stellar mass density and the star formation history that are in moderate disagreement. These results suggest that some important processes are still missing in the current model family and we discuss a number of possible solutions to solve the discrepancies, such as interactions between galaxies and dark matter halos, tidal stripping, the bimodal accretion of gas, preheating, and a redshift-dependent initial mass function.