  Within collapsing protogalaxies, thermal instability leads to the formation
of a population of cool fragments which are confined by the pressure of a
residual hot background medium. The critical mass required for the cold clouds
to become gravitationally unstable and to form stars is determined by both
their internal temperature and external pressure. We perform a systematic study
of the cooling properties of low-metallicity clouds, and we determine, for
appropriate ranges of external pressure and metallicity, the minimum
temperature clouds can attain prior to the formation of nearby massive stars.
The intense UV radiation of massive stars would photoionize the clouds and
quench star formation. We also determine the minimum metallicity these clouds
must attain in order to form presently observable Population II stars. Based on
our conclusion that low-mass stars cannot be formed efficiently in a metal
deficient environment, we argue that brown dwarfs are unlikely to be the main
contributors to mass in the Galactic halo.
