Resolving the Helium Lyman-$\alpha$ Forest: Mapping Intergalactic Gas and Ionizing Radiation at $z\approx 3$

We present a new, high resolution HST/GHRS spectrum of quasar Q0302-003, and use the HeII Lyman-$\alpha$ absorption, together with a high resolution Keck spectrum of the HI Lyman-$\alpha$ forest, to probe the distribution and ionization state of foreground gas just below the quasar redshift $z\approx 3.3$. The main new conclusions from the current data are: 1. The HeII Lyman-$\alpha$ forest is detected; 2. The ``diffuse'' (redshift-space-filling) medium is also detected, and must have a low density ($\Omega\le 0.01 (h/0.7)^{-3/2}$) consistent with standard primordial nucleosynthesis and models of early gas collapse into protogalaxies; 3. The intergalactic ionizing spectrum is soft ($\eta\ge 100$), although the intergalactic helium is probably mostly doubly ionized by $z=3.3$; 4. The helium abundance is within a factor of a few of standard Big Bang predictions, over a large volume of space at high redshift.