The missing metals problem -: III.: How many metals are expelled from galaxies?

We revisit the metal budget at z similar or equal to 2, and include the contribution of the intergalactic medium (IGM). Past estimates of the metal budget have indicated that, at redshift z similar or equal to 2.5, 90 per cent of the expected metals were missing. In the first two papers of this series, we have already shown that similar to 30 per cent of the metals are observed in all z similar to 2.5 galaxies detected in current surveys. This fraction could increase to less than or similar to 60 per cent if we extrapolate the faint end of the luminosity function (LF), leaving > 40 per cent of the metals missing. Here, we extend our analysis to the metals outside galaxies (i.e. in the IGM), using (i) observational data and (ii) analytical calculations. Our results for both are strikingly similar. (i) Observationally, we find that, besides the small (5 per cent) contribution of damped Lya absorbers (DLAs), the forest and sub-DLAs contribute substantially to make less than or similar to 30-45 per cent of the metal budget; however, neither of these appear to be sufficient to close the metal budget. The forest accounts for 15-30 per cent depending on the ultraviolet background, and sub-DLAs for greater than or similar to 2 to less than or similar to 17 per cent depending on the ionization fraction. Combining the metals in galaxies and in the IGM, it appears now that > 65 per cent of the metals have been accounted for, and the 'missing metals problem' is substantially eased. (ii) We perform analytical calculations based on the effective yield-mass (y(eff)-V-c) relation, whose deficit for small galaxies is considered as evidence for supernova-driven outflows. As a test of the method, we show that, at z = 0, the calculation self-consistently predicts the total amount of metals expelled from galaxies. At z=2, we find that the method predicts that 25-50 per cent of the metals have been ejected from galaxies into the IGM, consistent with the observations (less than or similar to 35 per cent). The metal ejection is predominantly by L-B < (1/3) L-B* B( z = 2) galaxies, which are responsible for 90 per cent of the metal enrichment, while the 50 percentile is at L similar to (1/10) L-B* B (z = 2). As a consequence, if indeed 50 per cent of the metals have been ejected from galaxies, three to five bursts of star formation are required per galaxy prior to z = 2. The ratio between the mass of metals outside galaxies to those in stars has changed from z = 2 to z = 0; it was 1 : 2 or 1 : 1 and is now 1 : 8 or 1 : 9. This evolution implies that a significant fraction of the IGM metals will cool and fall back into galaxies.