We present a direct measurement of the metallicity distribution function for the high redshift intergalactic medium. We determine the shape of this function using survival statistics, which account for both detections and non-detections of OVI and CIV associated with HI absorption in quasar spectra. Our OVI sample probes the metal content of ~50% of all baryons at z~2.5. We find a median intergalactic abundance of [O,C/H]=-2.82; the differential abundance distribution is approximately lognormal with mean <[C,O/H]>~-2.85 and sigma=0.75 dex. Some 60-70% the Lya forest lines are enriched to observable levels ([O,C/H]>-3.5) while the remaining ~30% of the lines have even lower abundances. Thus we have not detected a universal metallicity floor as has been suggested for some Population III enrichment scenaria. In fact, we argue that the bulk of the intergalactic metals formed later than the first stars that are thought to have triggered reionization. We do not observe a significant trend of decreasing metallicity toward the lower density IGM, at least within regions that would be characterized as filaments in numerical simulations. However, an [O/H] enhancement may be present at somewhat high densities. We estimate that roughly half of all baryons at these redshifts have been enriched to [O/H]>=-3.5. We develop a simple model for the metallicity evolution of the IGM, to estimate the chemical yield of galaxies formed prior to z~2.5. We find that the typical galaxy recycled 0.1-0.4% of its mass back into the IGM as heavy elements in the first 3 Gyr after the Big Bang.
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