A comparison of semi-analytic and smoothed particle hydrodynamics galaxy formation

We compare the statistical properties of galaxies found in two different models of hierarchical galaxy formation: the semi-analytic model of Cole et al. and the smoothed particle hydrodynamics (SPH) simulations of Pearce et al. These two techniques model gas processes very differently: by approximate, analytic methods in the case of the semi-analytic model, and by direct numerical integration of the equations of hydrodynamics for a set of discrete particles in the case of SPH. Using a 'stripped-down' version of the semi-analytic model which mimics the resolution of the SPH simulations and excludes physical processes not included in them, we find that the two models produce an ensemble of galaxies with remarkably similar properties, although there are some differences in the gas cooling rates and in the number of galaxies that populate haloes of different mass. The full semi-analytic model, which has effectively no resolution limit and includes a treatment of star formation and supernovae feedback, produces somewhat different (but readily understandable) results. Our comparison demonstrates that, on the whole, SPH simulations and semi-analytic models give similar results for the thermodynamic evolution of cooling gas in cosmological volumes. Agreement is particularly good for the present-day global fractions of hot gas, cold dense (i.e. galactic) gas and uncollapsed gas, for which the SPH and stripped-down semi-analytic calculations differ by at most 25 per cent. In the most massive haloes, the stripped-down semi-analytic model predicts, on the whole, up to 50 per cent less gas in galaxies than is seen in the SPH simulations. The two techniques apportion this cold gas somewhat differently amongst galaxies in a given halo. This difference can be tracked down to the greater cooling rate in massive haloes in the SPH simulation compared with the semi-analytic model. The galaxy correlation functions in the two models agree to better than about 50 per cent over most pair separations and evolve with redshift in very similar ways. Our comparison demonstrates that these different techniques for modelling galaxy formation produce results that are broadly consistent with each other and highlights areas where further study is required.