Numerical and Analytical Modelling of Galaxy Formation and Evolution

We review recent developments in theoretical studies of galaxy formation and evolution. In combination with new data from HST, Keck and other large telescopes, numerical and semi-analytic modelling is beginning to build up a coherent picture of galaxy formation. We summarize the current status of modelling of various galactic properties such as the structure of dark matter halos, the galaxy luminosity function, the Tully-Fisher relation, the colour-magnitude relation for ellipticals, the gross morphological properties of galaxies and the counts of faint galaxies as a function of magnitude, redshift and morphology. Many of these properties can be explained, at least at some level, within a broad class of CDM cosmologies, but a number of fundamental issues remain unresolved. We use our semi-analytic model of galaxy formation to interpret the evolutionary status of the Lyman-break galaxies at $z\simeq 3-3.5$ recently discovered by Steidel et al. The abundance and global properties of these objects are compatible with model predictions in a variety of CDM cosmologies, including the standard version. All these models predict mild evolution in the distribution of star formation rates which peaks at around $z\simeq 1$, but is never much larger than it is at present. The Steidel et al. Lyman-break galaxies are among the very first objects in which appreciable star formation is taking place; they thus signal the onset of galaxy formation. We present three example evolutionary histories of Lyman-break galaxies which illustrate that these objects are the precursors of present day, normal, bright ellipticals and spirals.