We investigate the physical mechanisms that shape the luminosity function of galaxies in hierarchical clustering models. Beginning with the mass function of dark matter halos in the ΛCDM (Λ cold dark matter) cosmology, we show, in incremental steps, how gas cooling, photoionization at high redshift, feedback processes, galaxy merging, and thermal conduction affect the shape of the luminosity function. We consider three processes whereby supernovae and stellar wind energy can affect the forming galaxy: (1) the reheating of cold disk gas to the halo temperature; (2) expansion of the hot, diffuse halo gas; and (3) complete expulsion of cold disk gas from the halo. We demonstrate that while feedback of form 1 is able to flatten the faint end of the galaxy luminosity function, this process alone does not produce the sharp cutoff observed at large luminosities. Feedback of form 2 is also unable to solve the problem at the bright end of the luminosity function. The relative paucity of very bright galaxies can only be explained if cooling in massive halos is strongly suppressed. This might happen if thermal conduction near the centers of halos is very efficient, or if a substantial amount of gas is expelled from halos by process 3 above. Conduction is a promising mechanism, but an uncomfortably high efficiency is required to suppress cooling to the desired level. If, instead, superwinds are responsible for the lack of bright galaxies, then the total energy budget required to obtain a good match to the galaxy luminosity function greatly exceeds the energy available from supernova explosions. The mechanism is only viable if the formation of central supermassive black holes and the associated energy generation play a crucial role in limiting the amount of stars that form in the host galaxy. The models that best reproduce the galaxy luminosity function also give reasonable approximations to the Tully-Fisher relation and the galaxy autocorrelation function.
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