Galaxy number counts in the hubble deep field as a strong constraint on a hierarchical galaxy formation model

Number counts of galaxies are reanalyzed using a semianalytic model (SAM) o f galaxy formation based on the hierarchical clustering scenario. We have d etermined the astrophysical parameters in the SAM that reproduce observatio ns of nearby galaxies and used them to predict the number counts and redshi fts of faint galaxies for three cosmological models: (1) the standard cold dark matter (CDM) universe, (2) a low-density flat universe with nonzero co smological constant, and (3) a low-density open universe with zero cosmolog ical constant. The novelty of our SAM analysis is the inclusion of selectio n effects arising from the cosmological dimming of the surface brightness o f high-redshift galaxies and also from the absorption of visible light by i nternal dust and intergalactic H I clouds. Contrary to previous SAM analyse s that do not take into account such selection effects, we find from compar ison with observed counts and redshifts of faint galaxies in the Hubble Dee p Field (HDF) that the standard CDM universe is not preferred, and a low-de nsity universe either with or without a cosmological constant is favorable, as suggested by other recent studies. Moreover, we find that a simple pres cription for the timescale of star formation (SF), being proportional to th e dynamical timescale of the formation of the galactic disk, is unable to r eproduce the observed number-redshift relation for HDF galaxies, and that t he SF timescale should be nearly independent of redshift, as suggested by o ther SAM analyses for the formation of quasars and the evolution of damped Ly alpha systems.