  Current numerical studies suggest that the first galaxies formed a few stars
at a time and were enriched only gradually by the first heavy elements.
However, the large box sizes in these models cannot resolve primordial
supernova explosions or the mixing of their metals with ambient gas, which
could result in intervening, prompt generations of low-mass stars. We present
multiscale 1D models of Population III supernovae in cosmological halos that
evolve the blast from its earliest stages as a free expansion. We find that if
the star ionizes the halo, the ejecta strongly interacts with the dense shell
swept up by the H II region, potentially cooling and fragmenting it into clumps
that are unstable to gravitational collapse. If the star fails to ionize the
halo, the explosion propagates metals out to 20 - 40 pc and then collapses,
enriching tens of thousands of solar masses of primordial gas, in contrast to
previous models that suggest such explosions 'fizzle'. Rapid formation of
low-mass stars trapped in the gravitational potential well of the halo appears
to be inevitable in such circumstances. Consequently, it is possible that far
more stars were swept up into the first galaxies, at earlier times and with
distinct chemical signatures, than in present models. Upcoming measurements by
JWST and ALMA may discriminate between these two paradigms.
