We examine, in some detail, the thermal history of metal-free gas overtaken by radiative shocks with velocities characteristic of gravitationally induced motions inside a typical protogalaxy. This is relevant to suggestions that globular clusters formed within protogalaxies in the compressed gas resulting from such shocks or from a thermal instability. We have solved the hydrodynamical equations, along with the rate equations for nonequilibrium ionization, recombination, molecular formation and dissociation, and the equations of radiative transfer for steady state shocks of velocity 300 km s-1 in a gas of preshock density 0.1-1 cm-3. Our calculations include external sources of UV and soft X-ray radiation such as might be present within a protogalaxy. Specifically, we consider massive young stars and an active galactic nucleus. In the absence of these-sources, enough molecular hydrogen is produced behind the shocks once the gas temperature drops to 104 K to cool the compressed gas rapidly from 104 to 102 K. However, when the total luminosity of the sources exceeds a few times 1044 ergs s-1 in the case of AGN's or a few times 1045 ergs s-1 for early-type stars, the formation of H2 behind these shocks is suppressed, and the cooling time of the gas at 104 K is longer than its internal free-fall time. This ensures that the Jeans mass in the radiatively cooled postshock layer is of the same order of magnitude as the masses of globular clusters. The star formation rate implied by an ordinary stellar origin for the UV field required to imprint such a characteristic mass is marginally consistent with constraints based on the abundances of heavy elements in the spheroidal components of galaxies. We suggest that the formation of globular clusters is a threshold effect with the intensity of the UV/soft X-ray field in a protogalaxy as the controlling factor.
