Implications on the Ionizing Background Radiation from HST Heii Gunn-Peterson Test

Recently, Jakobsen et al. reported that the HeII Gunn-Peterson optical depth is greater than 1.7 at $ z=3.3$. When we consider this observation combined with the HI Gunn-Peterson optical depths and the intensity of the UV background at high redshifts, we can put constraints on the spectrum of the UV background and the mass fraction of intergalactic medium. We find that the spectrum must be steep ($\alpha \gsim 3; J_{\nu} \propto \nu^{-\alpha} $) to be consistent with observations, and that the mass fraction of the intergalactic medium must be greater than 0.3 (0.1) in the case $ \alpha=3 (4)$ for baryon density consistent with the primordial nucleosynthesis. We also find that HeII fraction is as low as $10^{-3} \sim 10^{-1} $ even for this steep spectrum.