We study the physical properties of a homogeneous sample of 157 optically-thick absorption line systems at redshifts \sim 1.8 - 4.4 , selected from a high-dispersion spectroscopic survey of Lyman limit systems ( LLSs ) .
By means of multiple ionisation models and Bayesian techniques , we derive the posterior probability distribution functions for the density , metallicity , temperature , and dust content of the absorbing gas .
We find that z > 2 LLSs are highly ionised with ionisation parameters between -3 \lesssim \log U \lesssim - 2 , depending on the H I column density .
LLSs are characterised by low temperatures ( T < 5 \times 10 ^ { 4 } ~ { } K ) and reside in dust-poor environments .
Between z \sim 2.5 - 3.5 , \sim 80 \% of the LLSs have physical densities between n _ { H } \sim 10 ^ { -3.5 } -10 ^ { -2 } ~ { } cm ^ { -3 } for the assumed UV background , but we caution that a degeneracy between the ionisation parameter and the intensity of the radiation field prevents robust inference on the density and sizes of LLSs .
Conversely , metallicity estimates are less sensitive to the assumptions behind ionisation corrections .
LLSs at z > 2 are characterised by a broad unimodal distribution over > 4 orders of magnitude , with a peak at \log Z / Z _ { \odot } \sim - 2 .
LLSs are metal poor , significantly less enriched than DLAs , with \sim 70 \% of the metallicity PDF below \log Z / Z _ { \odot } \leq - 1.5 .
The median metallicity of super LLSs with \log N _ { HI } \geq 19 rapidly evolves with redshift , with a ten-fold increase between z \sim 2.1 - 3.6 ( \sim 1.5 Gyr ) .
Based on this sample , we find that LLSs at z = 2.5 - 3.5 account for \sim 15 \% of all the metals produced by UV-selected galaxies .
The implications for theories of cold gas accretion and metal ejection from galaxies are also discussed .