The Gas Consumption History to Z ∼ 4

Using the observations of the star formation rate and H I densities to z ∼ 4, with measurements of the Molecular Gas Depletion Rate (MGDR) and local density of H 2 at z = 0, we derive the history of the gas consumption by star formation to z ∼ 4. We find that closed-box models in which H 2 is not replenished by H I require improbably large increases in ρ(H 2) and a decrease in the MGDR with lookback time that is inconsistent with observations. Allowing the H 2 used in star formation to be replenished by H I yields approximately the same solutions as the closed box model since observations show that there is very little evolution of ρ HI (z) from z = 0 to z = 4. We show that to be consistent with observational constraints, star formation on cosmic timescales must be fueled by intergalactic ionized gas, which may come from either accretion of gas through cold, but ionized, flows or from ionized gas associated with accretion of dark matter halos. We derive a lower limit to the rate at which the extraglactic ionized gas must be converted into H I and ultimately into H 2 to be about 1 – 2 ×10 8 M ⊙ Gyr −1 Mpc −3 from z ≃ 1 − 4. Between z = 1 and z = 0 this mass flow rate decreases by about an order of magnitude with details depending largely on MGDR(t). All models considered require the volume averaged density of ρ H2 to increase by a factor of 1.5 – 10 to z ∼ 1.5 over the currently measured value. Because the molecular gas must reside in galaxies, it implies that galaxies at high z must be, on average, more molecule rich than they are at the present epoch.