A Criterion for Photoionization of Pregalactic Clouds Exposed to Diffuse Ultraviolet Background Radiation
Tajiri, Yukiko, & Umemura, Masayuki
To elucidate the permeation of cosmic ultraviolet (UV) background radiation into a pregalactic cloud and the subsequent ionization, the frequency-dependent radiative transfer equation is solved, coupled with the ionization process, for a spherical top-hat cloud composed of pure hydrogen. The calculations properly involve scattering processes of ionizing photons that originate from radiative recombination. 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. Quantitatively, the self-shielding is prominent above a critical number density of hydrogen, which is given by n$_crit$ = 1.4 × 10$^-2$ cm$^-3$ (M/10$^8$ M$_solar$)$^-1/5$I$^3/5$$_21$ for 10$^4$ K gas, where M is the cloud mass and the UV background intensity is assumed to be I$_\ensuremathν$ = 10$^-21$I$_21$(\en suremathν/\ensuremathν$_L$)$^-1$ ergs cm$^-2$ s$^-1$ sr$^-1$ Hz$^-1$, with \ensuremathν$_L$ being the Lyman limit frequency. The weak dependence of n$_crit$ upon the mass is worth noting. The corresponding critical optical depth (\ensuremathτ$_crit$) turns out to be independent of either M or I$_21$, which is \ensuremathτ$_crit$ = 2.4 for 10$^4$ K gas. The present analysis reveals that the Strömgren 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 when one considers the biasing by photoionization against low-mass galaxy formation.