Where are the cosmic metals at z ∼ 3?

The global temperature distribution of the cosmic gas-phase oxygen at z similar to 3 is determined by combining high-resolution cosmological simulations of individual protogalactic as well as larger regions with the observed, extinction-corrected, rest-frame V-band galaxy luminosity function. The simulations have been performed with three different stellar initial mass functions (IMFs), a Kroupa (K98), a Salpeter (S) and an Arimoto-Yoshii (AY), spanning a range of a factor of 5 in chemical yield and specific supernova type II energy feedback. Gas-phase oxygen is binned according to T as log(T) less than or similar to 4.0 ('cold'), log(T) similar to 4.5 ('warm') and log(T) similar to 5.0, 5.5, 6.0, 6.5, 7.0 ('hot' phases). Oxygen is found to be distributed over all T phases, in particular for the top-heavy AY IMF. But, at variance with previous works, it is found that for the K98 and S IMFs the cold phase is the most important. For these IMFs it contains 47 and 37 per cent, respectively, of all gas-phase oxygen, mainly at fairly high density, n(H) greater than or similar to 0.1 cm(-3). The implications of this in relation to observational damped Ly alpha absorber studies are discussed. In relation to 'missing metals' it is found that a significant fraction of the oxygen is located in a warm/hot phase that may be very difficult to detect. Moreover, it is found that less than about 20-25 per cent of the cosmic oxygen is associated with galaxies brighter than M-V similar to -22, i.e. the faintest galaxy luminosities probed by current metallicity determinations for Lyman-break galaxies (LBGs). Hence, 75-80 per cent of the oxygen is also in this sense 'missing'. From the LBG-based, lambda similar to 1500 angstrom ultraviolet luminosity density history at z >= 3, we obtain an essentially IMF-independent constraint on the mean oxygen density at z = 3. We compare this to what is obtained from our models, for the three different IMFs. We find that the K98 IMF is strongly excluded, as the chemical yield is simply too small, the Salpeter is marginally excluded, and the AY matches the constraint well. The K98 IMF can only match the data if the lambda similar to 1500 angstrom extinction corrections have been overestimated by factor of similar to 4, which seems highly unlikely. The yields for K98 are also far too small to match the observational data for C-IV. The optimal IMF should have a yield intermediate between the S and AY.