THE GAS CONSUMPTION HISTORY TO REDSHIFT 4

Using the observations of the star formation rate (SFR) and H I densities to z similar to 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 similar to 4. We find that closed-box models in which H-2 is not replenished by H I require improbably large increases in rho(H-2) and a decrease in the MGDR with lookback time that is inconsistent with observations. Allowing the rho H-2 used in star formation to be replenished by H I does not alleviate the problem because observations show that there is very little evolution of rho H I(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 constrain the rate at which the extragalactic ionized gas must be converted into H I and ultimately into H-2. The ionized gas inflow rate roughly traces the SFR density: about 1-2 x 10(8)M(circle dot) Gyr(-1) Mpc(-3) from z similar or equal to 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 similar to 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.