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Instabilities in the Ionization Zones Around the First Stars

We consider the evolution of the ionization zone around Population III stars with $M_*\sim 25-200 M_\odot$ in protogalaxies with $M\sim 10^7 M_\odot$ at redshifts $z = 12$, assuming that the dark matter profile is a modified isothermal sphere. We study the conditions for the growth of instabilities in the ionization zones. The Rayleigh-Taylor and thermal instabilities develop efficiently in the ionization zones around 25-40 $M_\odot$ stars, while this efficiency is lower for stars with $\sim 120 M_\odot$. For more massive stars ($\sim 200 M_\odot$), the flux of ionizing photons is strong enough to considerably reduce the gas density in the ionization zone, and the typical lifetimes of stars ($\sim 2$ Myr) are insufficient for the growth of instabilities. The gas in a protogalaxy with $M\sim 10^7 M_\odot$ with a 200 $M_\odot$ central star is completely ionized by the end of the star's lifetime; in the case of a 120 $M_\odot$ central star, only one-third of the total mass of gas is ionized. Thus, ionizing photons from stars with $M_*\simlt 120 M_\odot$ cannot leave protogalaxies with $M\simgt 10^7 M_\odot$. If the masses of the central stars are 25 and 40 $M_\odot$, the gas in protogalaxies of this mass remains essentially neutral. We discuss the consequences of the evolution of the ionization zones for the propagation of the envelope after the supernova explosions of the stars and the efficiency of enrichment of the intergalactic medium in heavy elements.