A Uniform Analysis of the Lyα Forest at z = 0–5. II. Measuring the Mean Intensity of the Extragalactic Ionizing Background Using the Proximity Effect

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Moderate-resolution data for 40 quasi-stellar objects (QSOs) at z ≈ 2 were combined with spectra of comparable resolution of 59 QSOs with redshifts greater than 1.7 found in the literature to form a large, homogeneous sample of moderate-resolution (~1 A) QSO spectra. These spectra were presented and the statistics of the Lyα forest were discussed in Paper I. In this analysis, we demonstrate that a proximity effect is present in the data; i.e., there exists a significant (5.5 σ) deficit of lines at zabs ≈ zem. Within 1.5 h-1 Mpc of the QSO emission redshift, the significance does depend on QSO luminosity, in accordance with the theory that this effect is caused by enhanced ionization of hydrogen in the vicinity of the QSO from UV photons from the QSO itself. The photoionization model of Bajtlik, Duncan, & Ostriker permits an estimate of the mean intensity of the extragalactic background radiation at the Lyman limit. We compare the results of this standard analysis with those obtained using a maximum likelihood technique. If the spectrum of the background is assumed to be identical to that of each individual QSO, and if this background is assumed to be constant over the redshift range 1.7 < z < 3.8, then the best-fit value for J(ν0) is found to be 1.4 × 10-21 ergs s-1 cm-2 Hz-1 sr-1, using QSO redshifts based on the Lyα emission line. Systemic QSO redshifts based on the [O III] λ5007 emission line for 19 objects in our sample show an average redshift of ~400 km s-1 with respect to Lyα emission. Using redshifts based on [O III] or Mg II for the 35 objects for which they are measured and adding 400 km s-1 to the remaining QSO Lyα redshifts gives a lower value of J(ν0), 7.0 × 10-22 ergs s-1 cm-2 Hz-1 sr-1. This value is in reasonable agreement with the predictions of various models of the ionizing background based on the integrated quasar luminosity function. Allowing for the fact that individual QSOs have different spectral indices that may also be different from that of the background, we use the standard methods to solve for the H I photoionization rate, Γ, and the parameters describing its evolution with redshift. The best-fit value for the H I ionization rate we derive is 1.9 × 10-12 s-1, in good agreement with models of the background that incorporate QSOs only. Finally, we use simulated Lyα forest spectra including the proximity effect to investigate curve-of-growth effects in the photoionization model used in the analysis. We find that the presence of lines on the saturated part of the curve of growth could cause our estimates of the background intensity to be overestimated by a factor of 2-3. This large absorption-line sample and these techniques for measuring the background and understanding the systematics involved allow us to place what we believe are the firmest limits on the background at these redshifts.