Evolution of the First Supernovae in Protogalaxies: Dynamics of Mixing of Heavy Elements

The paper considers the evolution of the supernova envelopes produced by Population III stars with masses of $M_*\sim 25-200 M_\odot$ located in non-rotating protogalaxies with masses of $M\sim 10^7 M_\odot$ at redshifts $z=12$, with dark-matter density profiles in the form of modified isothermal spheres. The supernova explosion occurs in the ionization zone formed by a single parent star. The properties of the distribution of heavy elements (metals) produced by the parent star are investigated, as well as the efficiency with which they are mixed with the primordial gas in the supernova envelope. In supernovae with high energies ($E\simgt 5\times 10^{52}$ erg), an appreciable fraction of the gas can be ejected from the protogalaxy, but nearly all the heavy elements remain in the protogalaxy. In explosions with lower energies ($E\simlt 3\times 10^{52}$ erg), essentially no gas and heavy elements are lost from the protogalaxy: during the first one to threemillion years, the gas and heavy elements are actively carried from the central region of the protogalaxy ($r\sim 0.1 r_{vir}$, where $r_{vir}$ is the virial radius of the protogalaxy), but an appreciable fraction of the mass of metals subsequently returns when the hot cavity cools and the envelope collapses. Supernovae with high energies ($E\simgt 5\times 10^{52}$ erg) are characterized by a very low efficiency of mixing of metals; their heavy elements are located in the small volume occupied by the disrupted envelope (in a volume comparable with that of the entire envelope), with most of the metals remaining inside the hot, rarified cavity of the envelope. (abridged)