The Fluctuating Intergalactic Radiation Field at Redshifts z = 2.3-2.9 from He II and H I Absorption towards HE 2347-4342

We provide an in-depth analysis of the He II and H I absorption in the intergalactic medium (IGM) at redshifts z = 2.3-2.9 toward HE 2347-4342, using spectra from the Far Ultraviolet Spectroscopic Explorer (FUSE) and the Ultraviolet-Visual Echelle Spectrograph (UVES) on the VLT telescope. Following up on our earlier study (Kriss et al. 2001, Science, 293, 1112), we focus here on two major topics: (1) small-scale variability (Delta z = 10^-3) in the ratio eta = N(He II)/N(H I); and (2) an observed correlation of high-eta absorbers (soft radiation fields) with voids in the (H I) Ly-alpha distribution. These effects may reflect fluctuations in the ionizing sources on scales of 1 Mpc, together with radiative transfer through a filamentary IGM whose opacity variations control the penetration of 1-5 ryd radiation over 30-40 Mpc distances. Owing to photon statistics and backgrounds, we can measure optical depths over the ranges 0.1 < tau(HeII) < 2.3 and 0.02 < tau(HI) < 3.9, and reliably determine values of eta = 4 tau(HeII)/tau(HI) over the range 0.1 to 460. Values of eta = 20-200 are consistent with models of photoionization by quasars with observed spectral indices alpha_s = 0-3. Values of eta > 200 may require additional contributions from starburst galaxies, heavily filtered quasar radiation, or density variations. Regions with eta < 30 may indicate the presence of local hard sources. We find that eta is higher in "void" regions, where H I is weak or undetected and 80% of the path length has eta > 100. These voids may be ionized by soft sources (dwarf starbursts) or by QSO radiation softened by escape from the AGN cores or transfer through the "cosmic web". The apparent differences in ionizing spectra may help to explain the 1.45 Gyr lag between the reionization epochs, z(HI) = 6.2 +/-0.2 and z(HeII) = 2.8 +/-0.2.