A Criterion for Photoionization of Pregalactic Clouds Exposed to Diffuse   Ultraviolet Background Radiation
  To elucidate the permeation of cosmic ultraviolet (UV) background radiation into a pregalactic cloud and subsequent ionization, the frequency-dependent radiative transfer equation is solved, coupled with the ionization process. A spherical top-hat cloud which is composed of pure hydrogen is assumed. As a result, it is shown that the self-shielding, although it is often disregarded in cosmological hydrodynamic simulations, could start to emerge shortly after the maximum expansion stages of density fluctuations. The present analysis reveals that the Stro"mgren approximation leads to overestimation of the photoionization effects. Also, the self-shielded neutral core is no longer sharply separated from surrounding ionized regions; a low but noticeable degree of ionization is caused by high energy photons even in the self-shielded core. The present results may be substantial on considering the biasing by photoionization against low-mass galaxy formation. 
Yukiko Tajiri, Masayuki Umemura