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

We perform a semi-automated survey for tau(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 Delta z = 93.8 and identify 190 intervening systems at z(LLS) >= 3.3. The incidence of tau(912) >= 2 LLSs per unit redshift, l(tau >= 2)(z), is well described by a single power law at these redshifts: l(tau >= 2)(z) = C-LLS[(1 + z)/(1 + z(*))](gamma LLS), with z(*) = 3.7, C-LLS = 1.9 +/- 0.2, and (gamma 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 approximate to 2, similar to that observed for the Ly alpha forest. Our results also indicate that the systems giving rise to LLS absorption decrease by approximate to 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-HI, X) and indicate that the power-law slope beta equivalent to d ln f(N-HI, X)/d ln N-HI is likely shallower than beta = -1 at N-HI approximate to 10(18) cm(-2). Including other constraints on f(N-HI, X) from the literature, we infer that beta is steeper than beta = -1.7 at N-HI approximate to 10(15) cm(-2), implying at least two inflections in f(N-HI, X). We also perform a survey for proximate LLSs (PLLSs) and find that l(PLLS)(z) is systematically lower (approximate to 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.