Galaxy formation through hierarchical clustering

We develop analytic methods for studying the formation of galaxies by gas condensation within massive dark halos. Our scheme applies to cosmogonies where structure grows through hierarchical clustering of a mixture of gas and dissipationless dark matter. It is an elaboration of the ideas of White & Rees. We adopt the simplest models consistent with our current understanding of N-body work on dissipationless clustering, and of numerical and analytic work on gas evolution and cooling. We also employ standard models for the evolution of stellar populations, and construct new models for the way star formation heats and enriches the surrounding gas. Although our approach is phenomenological, we avoid assumptions which have no clear physical basis. Our methods allow us to predict star formation as a function of location and time, and so the following properties of the galaxy population: current star formation rates and halo X-ray luminosities; current luminosity functions both for galaxies and for virialized systems; relations between present luminosity, circular velocity, metallicity, and stellar or total M/L ratio; the history of the OB star contribution to the metagalactic ionizing flux; and the distribution of faint blue (star-forming) galaxies in both apparent magnitude and redshift. In this paper we give detailed results only for a cold dark matter universe with {OMEGA}=1 and H_0_=50 km s^-1^ Mpc^-1^, although our methods are easily applied to other models. Even for this case, predictions depend strongly on the mean baryon density, on the fluctuation amplitude, on the models for heating and metal enrichment by massive stars, and on the initial mass function with which stars form. Our most successful models require a large baryon fraction ({OMEGA}_b_/{OMEGA} ~> 0.1) and efficient heating and enrichment of halo gas. They then approximately reproduce the characteristic luminosities of galaxies and of galaxy clusters, the observed relations between galaxy properties and the kind of bias needed to reconcile {OMEGA} = 1 with the observed kinematics of galaxy clustering. However, the amplitude of this bias is too small, and additional sources of bias must be invoked. Our luminosity functions contain significantly more faint galaxies than are observed. This is a serious discrepancy which may be alleviated by starbursts in dwarf galaxies, by selective merging of such systems, and by observational selection against low surface brightness dwarfs. Successful models form their stars late, typically more than half of them since z = 1, making the epoch of galaxy formation easily accessible to observation.