The detection of a HeII absorption trough in the spectra of three
high-redshift quasars provides new constraints on the spectral shape of the UV
extragalactic background. The relative strengths of the observed flux
decrements at the rest-frame wavelengths of 1216 and 304 A require a relatively
soft radiation field at 4 ryd compared to 1 ryd. If the ionizing metagalactic
flux is dominated by the integrated light from QSOs, and the HeII reionization
of the universe was completed well before z~3, then the UV/soft X-ray spectrum
of individual quasars at these epochs must, once the cosmological filtering'' through material along the line of sight is taken into account, satisfy similar constraints on the average. We model the propagation of AGN-like ionizing radiation through the intergalactic medium using CUBA, a numerical code developed in our prior work. We show that, in order to explain the reported HeII absorption, any thermal component responsible for the soft X-ray
excess’’ observed in the spectra of AGNs at z<0.3 must, at z~3, have a typical
temperature >80 eV, and a luminosity not exceeding 20% of that of the ``UV
bump’'.

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