Abstract

We investigate the extent to which the characteristic masses and sizes of galaxies (and clusters) are determined by processes occurring at the epoch when the pregalactic material has stopped expanding with the background Universe but has not yet fragmented into stars. Unless pregalactic clouds collapse in an exceedingly homogeneous fashion, their kinetic energy of infall will be thermalized via shocks before the contraction has proceeded by more than a factor ~ 2. What happens next depends on the relative value of the cooling and collapse timescales. Masses in the range |$10^{10} - 10^{12} M_{\odot}$| cool so efficiently that they always collapse at the free-fall rate, and probably quickly fragment into stars. Larger masses, however, may experience a quasistatic contraction phase; and go into free fall (and fragment) only after their radii fall below a critical value rbc. For masses ⪢ |$10^{12} M_{\odot}, r_\text{bc}$| has a mass-independent value ~ 75 kpc. We argue that this characteristic mass and radius may indeed be crucial determinants of the properties of galaxies, and discuss various complications that should be included in more refined calculations. Large masses ( ~ 1014M⊙) which recollapse at recent epochs may be unable to cool at all; and there is no reason why galaxies of characteristic radii |$\lesssim r_\text{bc}$| should not still be forming at small redshifts. The typical giant galaxies which dominate the luminosity function must have formed at a relatively recent epoch |$z \lesssim 10.$| Opacity effects in collapsing protogalaxies are briefly discussed, the possibility that trapped Lyman a may inhibit fragmentation being the only important one. The effects of mass-dependent dissipation on clustering and the covariance function are outlined.