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We study the physical properties of a homogeneous sample of 157optically-thick absorption line systems at redshifts ~1.8-4.4, selected from ahigh-dispersion spectroscopic survey of Lyman limit systems (LLSs). By means ofmultiple ionisation models and Bayesian techniques, we derive the posteriorprobability distribution functions for the density, metallicity, temperature,and dust content of the absorbing gas. We find that z>2 LLSs are highly ionisedwith ionisation parameters between -3<log U<-2, depending on the HI columndensity. LLSs are characterised by low temperatures (T<5x10^4 K) and reside indust-poor environments. Between z~2.5-3.5, ~80% of the LLSs have physicaldensities between n(H)~10^-3.5-10^-2 cm^-3 for the assumed UV background, butwe caution that a degeneracy between the ionisation parameter and the intensityof the radiation field prevents robust inference on the density and sizes ofLLSs. Conversely, metallicity estimates are less sensitive to the assumptionsbehind ionisation corrections. LLSs at z>2 are characterised by a broadunimodal distribution over >4 orders of magnitude, with a peak at logZ/Zsun~-2. LLSs are metal poor, significantly less enriched than DLAs, with~70% of the metallicity PDF below log Z/Zsun<-1.5. The median metallicity ofsuper LLSs with log N(HI)>19 rapidly evolves with redshift, with a ten-foldincrease between z~2.1-3.6 (~1.5 Gyr). Based on this sample, we find that LLSsat z=2.5-3.5 account for ~15% of all the metals produced by UV-selectedgalaxies. The implications for theories of cold gas accretion and metalejection from galaxies are also discussed.

The physical properties of z>2 Lyman limit systems: new constraints for feedback and accretion models