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>=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 zem=3.6-4.4, we analyze 469 spectra meeting strict seletion criteria for a total redshift path Dz=93.8 and identify 192 intervening systems at z>3.3. The incidence of tau>=2 LLSs per unit redshift, l(z), is well described by a single-power law at these redshifts: l(z) = C_LLS [(1+z)/(1+z_*)]^gamma, with z_*=3.7, C_LLS = 1.9+/-0.2, and gamma = 5.2+/-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 suggest a break at z~2, similar to that observed for the Lya 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 HI frequency distribution f(N_HI,X) and indicate that the power-law slope beta= dln[f(N,X)]/dln[N] is likely shallower than beta = -1 at N_HI=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~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(z)_PLLS 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.