Numerical Simulations of Galaxy Formation

On the face of it, the combined numerical N-body and hydrodynamic simulations of galaxy formation implement physical collapse models most accurately (e.g. Thomas et al. 1998) and so ought to give the most reliable results. Unfortunately, they are hampered by a number of problems. First, there is our ignorance of what controls star formation. Since the stars endow galaxies with many of their observed properties, the process of star formation is critical to galaxy formation. Yet, we do not know what governs the rate of star formation or the initial mass function. This makes the handling of star formation equally uncertain in all models, so that numerical accuracy is not the advantage that it might be.

The other problems of the full numerical simulations are largely artifacts of limits on computing resources which limit the resolution of the simulations (e.g. Weinberg, Hernquist & Katz 1997). Ways have been found around most such problems, but they raise the issue that some problems have yet to be identified. An example of a problem that is not widely known is the excessive radiative cooling in shocks in numerical simulations (Maguire 1996). This arises because the numerically simulated shocks are orders of magnitude thicker than the real ones, keeping gas at intermediate temperatures, where the cooling rate is high, for much longer than in the real shocks. The effect is that some numerically simulated collapses produce considerably less hot gas than they should. This effect is greatest when the cooling time of the shocked gas is comparable to the dynamical time, that is, in the collapse of ``normal'' protogalaxies (Rees & Ostriker 1977).

A popular alternative to the full numerical models are the semi-analytical models (White & Frenk 1991; Kauffmann, White & Guiderdoni 1994; Baugh, Cole & Frenk 1996; Nulsen & Fabian 1997; Somerville & Primack 1998). In these models the collapse hierarchy is usually simulated using some form of Press-Schechter theory and the outcomes of individual collapses are determined from heuristic arguments. Because they require relatively little computation, the semi-analytical models make it easy to test large ranges of parameters (e.g. to test models of star formation). In principle, a galaxy formation model should account for everything we see, but in practice, the models try to account for the overall properties of galaxies. Semi-analytical models have had some success, but in many respects their treatment of collapses is based weakly on physical models. Furthermore, different collapse models can account for many of the same data. It is likely to be some time before we can say that we have a definitive model for the details of galaxy formation.

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