Observations of quasar absorption line systems reveal that the z = 3 intergalactic medium ( IGM ) is polluted by heavy elements down to H I optical depths \tau _ { HI } \ll 10 .
What is not yet clear , however , is what fraction of the volume needs to be enriched by metals and whether it suffices to enrich only regions close to galaxies in order to reproduce the observations .
We use gas density fields derived from large cosmological simulations , together with synthetic quasar spectra and imposed , model metal distributions to investigate what enrichment patterns can reproduce the observed median optical depth of C IV as a function of \tau _ { HI } .
Our models can only satisfy the observational constraints if the z = 3 IGM was primarily enriched by galaxies that reside in low-mass ( m _ { tot } < 10 ^ { 10 } { M } _ { \odot } ) haloes that can eject metals out to distances \ga 10 ^ { 2 } kpc .
Galaxies in more massive haloes can not possibly account for the observations as they are too rare for their outflows to cover a sufficiently large fraction of the volume .
Galaxies need to enrich gas out to distances that are much greater than the virial radii of their host haloes .
Assuming the metals to be well mixed on small scales , our modeling requires that the fractions of the simulated volume and baryonic mass that are polluted with metals are , respectively , > 10 \% and > 50 \% in order to match observations .