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 incorporate both detections and non-detections of O vi and C iv absorption , associated with H i lines in high resolution quasar spectra .
The O vi sample ( taken from 7 QSOs at z _ { abs } \sim 2.5 ) contains lines with N _ { { H \mbox { \tiny I } } } \geq 10 ^ { 13.6 } , encompassing \sim 50 \% of all baryons at z \sim 2.5 .
Our survey accounts for \approx 98.8 \% of the C iv mass and \approx 90 \% of the O vi mass in the universe at this epoch .
We find a median intergalactic abundance of [ O,C / H ] = -2.82 ; the differential abundance distribution is approximately lognormal with mean \left < [ C,O / H ] \right > \approx - 2.85 and \sigma = 0.75 dex .
We discuss the sensitivity of these results to the assumed form of the ionizing UV radiation field .
Some \sim 60 - 70 \% of lines in the Ly- \alpha forest are enriched to observable levels of [ O,C / H ] \gtrsim - 3.5 , while the remaining \sim 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 strong 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,C / H ] \gtrsim - 3.5 .
Using a simple “ closed box ” model for the metallicity evolution of the IGM , we estimate the chemical yield of galaxies formed prior to z \sim 2.5 , finding 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 .