In Paper III of our series, "A Uniform Analysis of the Lyα Forest at z = 0-5," we presented a set of 270 quasar spectra from the archives of the Faint Object Spectrograph (FOS) on the Hubble Space Telescope (HST). A total of 151 of these spectra, yielding 906 lines, are suitable for using the proximity effect signature to measure J(ν0), the mean intensity of the hydrogen-ionizing background radiation field, at low redshift. Using a maximum-likelihood technique and the best estimates possible for each QSO's Lyman limit flux and systemic redshift, we find J(ν0) = 7.6 × 10-23 erg s-1 cm-2 Hz-1 sr-1 at 0.03 z 1.67. This is in good agreement with the mean intensity expected from models of the background which incorporate only the known quasar population. When the sample is divided into two subsamples, consisting of lines with z 1 and z 1, the values of J(ν0) found are 6.5×10-23 erg s-1 cm-2 Hz-1 sr-1, and 1.0×10-22 erg s-1 cm-2 Hz-1 sr-1, respectively, indicating that the mean intensity of the background is evolving over the redshift range of this data set. Relaxing the assumption that the spectral shapes of the sample spectra and the background are identical, the best-fit H I photoionization rates are found to be 6.7 × 10-13 s-1 for all redshifts, and 1.9 × 10-13 and 1.3 × 10-12 s-1 for z 1 and z 1, respectively. The inclusion of blazars, associated absorbers, or damped Lyα absorbers, or the consideration of a ΛCDM cosmology rather than one in which ΩΛ = 0 has no significant effect on the results. The result obtained using radio-loud objects is not significantly different from that found using radio-quiet objects. Allowing for a variable equivalent width threshold gives a consistently larger value of J(ν0) than the constant threshold treatment, though this is found to be sensitive to the inclusion of a small number of weak lines near the QSO emission redshifts. This work confirms that the evolution of the number density of Lyα lines is driven by a decrease in the ionizing background from z ~ 2 to z ~ 0 as well as by the formation of structure in the intergalactic medium.
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