A DEFINITIVE SURVEY FOR LYMAN LIMIT SYSTEMS AT z ∼ 3.5 WITH THE SLOAN DIGITAL SKY SURVEY

ABSTRACT We perform a semi-automated survey for τ 912 ⩾ 2 Lyman limit systems (LLSs) in quasar spectra from the Sloan Digital Sky Survey, Data Release 7. From a starting sample of 2473 quasars with z em = 3.6–5.0, we analyze 429 spectra meeting strict selection criteria for a total redshift path Δ z = 93.8 and identify 190 intervening systems at z LLS ⩾ 3.3. The incidence of τ 912 ⩾ 2 LLSs per unit redshift, ℓ τ⩾2 ( z ), is well described by a single power law at these redshifts: , with z * ≡ 3.7, C LLS = 1.9 ± 0.2, and γ LLS = 5.1 ± 1.5 (68% c.l.). These values are systematically lower than previous estimates (especially at z < 4) but are consistent with recent measurements of the mean free path to ionizing radiation. Extrapolations of this power law to z = 0 are inconsistent with previous estimations of ℓ( z ) at z < 1 and may indicate a break at z ≈ 2, similar to that observed for the Lyα forest. Our results also indicate that the systems giving rise to LLS absorption decrease by ≈50% in comoving number density and/or physical size from z = 4 to 3.3, perhaps due to an enhanced extragalactic ultraviolet background. The observations place an integral constraint on the H i frequency distribution f ( N H i , X ) and indicate that the power-law slope is likely shallower than β = −1 at . Including other constraints on f ( N H i , X ) from the literature, we infer that β is steeper than β = −1.7 at , implying at least two inflections in f ( N H i , X ). We also perform a survey for proximate LLSs (PLLSs) and find that ℓ PLLS ( z ) is systematically lower (≈25%) than intervening systems. Finally, we estimate that systematic effects impose an uncertainty of 10%–20% in the ℓ( z ) measurements; these effects may limit the precision of all future surveys.