2008A&A...489..505V

This paper is motivated by the recent detection of many extremely metal-deficient ([Fe/H]←3) stars in the Milky Way. We numerically explore the chemical, thermal, and dynamical evolution of a shell formed by a high-energy supernova explosion (10⁵³erg) in dwarf protogalaxies with a total (dark matter plus baryonic) mass 10⁷M_☉ at a redshift z=12. We consider two initial configurations for the baryonic matter, one without rotation and the other having the ratio of rotational to gravitational energy β=0.17. The (non-rotating) dark matter halo is described by a quasi-isothermal sphere. This choice is motivated by recently proposed mechanisms for rapid flattening of a central cuspy region in dwarf protogalaxies. We use a finite-difference numerical hydrodynamics code to simulate supernova explosions in dwarf protogalaxies with axial symmetry. The advection is treated using a third-order piecewise parabolic scheme. The heating and cooling processes in the gas are taken into account by solving the rate equations numerically for the main atomic, molecular, and ionic species in the primordial gas. We find that the dynamics of the shell is different in protogalaxies with and those without rotation. For instance, the Rayleigh-Taylor instability in the shell develops faster in protogalaxies without rotation. The fraction of a blown-away baryonic mass is approximately twice as high in models with rotation than in models without rotation. We argue that these differences are caused by different initial gas density profiles in non-rotating and rotating protogalaxies. On the other hand, the chemical evolution of gas in protogalaxies with and without rotation is found to be similar. The relative number densities of molecular hydrogen and HD molecules in the cold gas (T≤10³K) saturate at typical values of 10^–3 and 10^–7, respectively. The saturation times in models with rotation are somewhat longer than in models without rotation. The clumps formed in the fragmented shell move with velocities that are at least twice as high as the escape velocity. The mass of the clumps is ∼0.1-10M_☉, which is lower than the Jeans mass. We conclude that the clumps are pressure supported. A supernova explosion with energy 10⁵³ erg destroys our model protogalaxy. The clumps formed in the fragmented shell are pressure supported. We conclude that protogalaxies with a total mass ∼10⁷M_☉ are unlikely to form stars due to high-energy supernova explosions of the first stars.