Paper detail

Cosmic histories of star formation and reionization: An analysis with a power-law approximation

With a simple power-law approximation of high-redshift ($\gtrsim3.5$) star formation history, i.e., $\dotρ_*(z)\propto [(1+z)/4.5]^{-α}$, we investigate the reionization of intergalactic medium (IGM) and the consequent Thomson scattering optical depth for cosmic microwave background (CMB) photons. A constraint on the evolution index $α$ is derived from the CMB optical depth measured by the {\it Wilkinson Microwave Anisotropy Probe} (WMAP) experiment, which reads $α\approx2.18\lg{\mathscr{N}_γ}-3.89$, where the free parameter $\mathscr{N}_γ$ is the number of the escaped ionizing ultraviolet photons per baryon. Moreover, the redshift for full reionization, $z_f$, can also be expressed as a function of $α$ as well as $\mathscr{N}_γ$. By further taking into account the implication of the Gunn-Peterson trough observations to quasars for the full reionization redshift, i.e., $6\lesssim z_f \lesssim7$, we obtain $0.3\lesssimα\lesssim1.3$ and $80\lesssim\mathscr{N}_γ\lesssim230$. For a typical number of $\sim4000$ of ionizing photons released per baryon of normal stars, the fraction of these photons escaping from the stars, $f_{\rm esc}$, can be constrained to within the range of $(2.0-5.8)%$.