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The Gas Consumption History to z ~ 4

Using the observations of the star formation rate and HI 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 HI require improbably large increases in rho(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 HI does not alleviate the problem because observations show that there is very little evolution of rho(HI) 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 constrain the rate at which the extraglactic ionized gas must be converted into HI and ultimately into H_2. The ionized gas inflow rate roughly traces the SFRD: about 1 - 2 x 10^8 M_sun Gyr^-1 Mpc^-3 from z ~ 1 - 4, decreasing by about an order of magnitude from z=1 to z=0 with details depending largely on MGDR(t). All models considered require the volume averaged density of rho(H_2) 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, on average, be more molecule rich than they are at the present epoch, which is consistent with observations. These quantitative results, derived solely from observations, agree well with cosmological simulations.