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 \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 5 \times 10 ^ { 52 } Â 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 \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 3 \times 10 ^ { 52 } Â 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 \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 5 \times 10 ^ { 52 } Â 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 .
At the same time , the efficiency of mixing of heavy elements in less energetic supernovae ( E \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 3 \times 10 ^ { 52 } Â erg ) is appreciably higher .
This comes about due to the disruption of the hot cavity during the collapse of the supernova envelope .
However , even in this case , a clear spatial separation of regions enriched and not enriched in metals is visible .
During the collapse of the supernova envelope , the metallicity of the gas is appreciably higher in the central region ( [ Z ] \sim - 1 to 0 ) than at the periphery ( [ Z ] \sim - 2 to -4 ) of the protogalaxy ; most of the enriched gas has metallicities [ Z ] \sim - 3.5 to -2.5 .
The masses of enriched fragments of the supernova envelope remain appreciably lower than the Jeans mass , except in regions at the center of the protogalaxy upon which the surrounding enriched gas is efficiently accreted .
Consequently , the birth of stars with metallicities close to those characteristic of present-day Galactic stars is very probable in the central region of the protogalaxy .