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.
