2005ApJ...630..875K

We analyze the confining effect of cloud collapse on an expanding supernova shock front. We solve the differential equation for the forces on the shock front due to ram pressure, supernova energy, and gravity. We find that the expansion of the shock front is slowed and in fact reversed by the collapsing cloud. Including radiative losses and a potential time lag between supernova explosion and cloud collapse shows that the expansion is reversed at smaller distances, compared to the nonradiative case. We also consider the case of multiple supernova explosions at the center of a collapsing cloud. For instance, if we scale our self-similar solution to a single supernova of energy 10⁵¹ ergs occurring when a cloud of initial density 10² H/cm3 has collapsed by 50%, we find that the shock front is confined to ∼15 pc in ∼1 Myr. Our calculations are pertinent to the observed unusually compact nonthermal radio emission in blue compact dwarf galaxies (BCDs). More generally, we demonstrate the potential of a collapsing cloud to confine supernovae, thereby explaining how dwarf galaxies would exist beyond their first generation of star formation.