We present a model for the evolution of the galaxy luminosity function, based on a scenario in which galaxies form by hierarchical clustering of a dynamically dominant dark matter component, and in which the rate of star formation is controlled by the frequency of tidal interactions with neighboring galaxies. We apply this to a cosmology with OMEGA = 1, and in which the initial spectrum of density fluctuations is that predicted by the cold dark matter model. The properties of galaxy halos are calculated using the formalism for peaks in a Gaussian density field. The ps in galaxy halos is required to cool before it can form stars and is assumed to collapse dissipatively by a constant factor relative to the halo. Energy injection by supernovae is assumed to drive mass loss from low-mass galaxies. There is no merging of the luminous parts of galaxies. The luminosities and colors of stellar populations are calculated using a spectral evolution model, including the effects of internal extinction. We present results for the present luminosities, colors, mass-to-light ratios, surface brightnesses, and circular velocities of present-day galaxies, and for the numbers, colors and redshifts of the galaxies seen in the faint counts, and make a detailed comparison with the available observational data. For our standard model, we find good fits to the present luminosity function for bright-galaxies and to the surface brightness-luminosity relation, and consistency with the Tully-Fisher relation for spirals. We find a reasonable fit to the galaxy number counts in the B-band over the whole range of magnitudes observed, with the faintest counts being dominated by mass-losing dwarf galaxies at redshifts z approximately 0.2-1. We find consistency with the color distributions at brighter magnitudes, when we include a significant component of extra extinction applied to massive OB stars only. We also obtain satisfactory fits to the redshift distributions of faint galaxies, except for an excess at z less than or similar to 0.1 due to having a steep present luminosity function. Our models are deficient in red bright galaxies at the present day, a problem that could probably be solved by including a modest amount of merging. The faint-end slope predicted for the present-day luminosity function is at least as steep as that found in the Virgo and Fornax clusters and is steeper than that found in the field, in so far as that is known at faint magnitudes. In fact, our model implies that luminous galaxies have not formed in underdense regions because no tidal interactions have occurred to trigger star formation. Instead, there would be dark galaxies, with all their baryons in the form of cool gas. Possible observational counterparts of these gas-rich systems would include Lalpha clouds seen in absorption toward quasars; however, a full discussion of the implications of the present model for the observability of such systems in the field remains to be developed.
