A Direct Measurement of the Intergalactic Medium Opacity to H I Ionizing Photons

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We present a new method to directly measure the opacity from H i Lyman limit (LL) absorption κ LL along quasar sight lines by the intergalactic medium (IGM). The approach analyzes the average ("stacked") spectrum of an ensemble of quasars at a common redshift to infer the mean free path λ 912 mfp to ionizing radiation. We apply this technique to 1800 quasars at z = 3.50–4.34 drawn from the Sloan Digital Sky Survey (SDSS), giving the most precise measurements on κ LL at any redshift. From z = 3.6 to 4.3, the opacity increases steadily as expected and is well parameterized by λ 912 mfp = λ 0 − b λ ( z − 3.6) with λ 0 = (48.4 ± 2.1) h −1 72 Mpc and b λ = (38.0 ± 5.3) h −1 72 Mpc (proper distance). The relatively high λ 912 mfp values indicate that the incidence of systems which dominate κ LL evolves less strongly at z > 3 than that of the Lyα forest. We infer a mean free path three times higher than some previous estimates, a result which has important implications for the photoionization rate derived from the emissivity of star-forming galaxies and quasars. Finally, our analysis reveals a previously unreported, systematic bias in the SDSS quasar sample related to the survey's color targeting criteria. This bias potentially affects all z ∼ 3 IGM studies using the SDSS database.