Metal Enrichment of The Primordial Interstellar Medium through 3-D Hydrodynamical Evolution of The First Supernova Remnant

The long-term evolution of supernova remnants (SNRs) in the primordial interstellar medium (ISM) with an inhomogeneous structure is calculated to investigate metal enrichment of the primordial gas. For this purpose, we have constructed a parallel 3-D hydrodynamics code incorporating the radiative cooling and self-gravity. The self-gravity and radiative cooling develop the inhomogeneous structure of the ISM from a small perturbation with a power-law spectrum. The resultant density ranges from 0.5 cm$^{-3}$ to 10$^6$ cm $^{-3}$. Calculations for a supernova (SN) with the progenitor mass of 20 solar mass are performed as the first step of a series of our study. It is found from the results that a single SN distributes some of newly synthesized heavy elements into a dense filament of the ISM with densities ranging from 100 to 10$^4$ cm$^{-3}$ depending on where the SN explodes. Thus, the metallicity [Mg/H] of the dense filaments polluted by the SN ejecta becomes $-2.7\pm0.5$. From these filaments, the first Population II stars will form. This value is in accordance with the previous analytical work (Shigeyama & Tsujimoto 1998) with accuracy of $\sim 0.3$ dex.