1. INTRODUCTION

Numerical simulations of large-scale structure have met with great success. However these same simulations fail to account for the observed properties of galaxies. On large scales, ~ 0.01-100 Mpc, the ansatz of cold, weakly interacting dark matter has led to realistic maps of the galaxy distribution, under the assumptions that light traces mass and that the initial conditions are provided by the observed temperature fluctuations in the cosmic microwave background. On smaller scales, light no longer traces mass because of the complexity of galaxy and star formation. Baryon physics must be added to the simulations in order to produce realistic galaxies. It is here that the modelling falls apart.

Theory provides the mass function of dark halos. Observation yields the luminosity function of galaxies, usually fit by a Schechter function. Comparison of the two is at first sight disconcerting. One can calculate the M / L ratio for the two functions to overlap at one point, for a mass M^* corresponding to L_*. Define t_cool = (3/2 nkT) / ((T) n²) and t_dyn = 3 / (32 G )^1/2. For star formation to occur, cooling is essential, and the condition t_cool < t_dyn guarantees cooling in an inhomogeneous galactic halo where gas clouds collide at the virial velocity. One finds that

For a cooling function (T) T, over the relevant temperature range (10⁵ - 10⁷ K), one can take -1/2 for a low metallicity plasma (Gnat & Sternberg 2007). The result is that one finds a characteristic galactic halo mass, in terms of fundamental constants, to be of order 10¹² M. The inferred value of the mass-to-light ratio M / L is similar to that observed for L_* galaxies. This is a success for theory: dissipation provides a key ingredient in understanding the stellar masses of galaxies, at least for the "typical" galaxy. The characteristic galactic mass is understood by the requirement that cooling within a dynamical time is a necessary condition for efficient star formation.

However all studies to date produce too many small galaxies, too many big galaxies in the nearby universe, too few massive galaxies at high redshift, and too many baryons within the galaxy halos. In addition there are structural problems: for example, massive galaxies with thin disks and/or without bulges are missing, and the concentration and cuspiness of cold dark matter is found to be excessive in barred galaxies and in dwarfs. The resolution to all of these difficulties must lie in feedback. There are various flavours of feedback that span the range of processes including reionisation at very high redshift, supernova explosions, tidal stripping and input from active galactic nuclei. All of these effects no doubt have a role, but we shall see that what is missing is a robust theory of star formation as well as adequate numerical resolution to properly model the interactions between baryons, dynamics and dark matter.