Abstract
There are mainly two different approaches to measure the cosmic star formation history: direct star formation rate density (SFRD) and stellar mass density rhostar as functions of redshift. Compilations of current observations seem to show a disparity in the two quantities, in the sense that the integral of SFRD is higher than the observed rhostar (after considering gas recycling). Using cosmological smoothed particle hydrodynamics simulations based on the concordance Lambda cold dark matter model, we show that the two quantities become more consistent with each other when we consider the observed galaxy mass limit. The comparison between simulations and (dust corrected) observed cosmic SFRD shows a good agreement, while the observed rhostar is significantly lower than the simulation results. This can be reconciled if the current high-$z$ galaxy surveys are missing faint low-mass galaxies due to their flux limit. Our simulated GSMFs have steep low-mass end slopes of alpha < -2 at z>3, and when these numerous low-mass galaxies are included, the total rhostar matches with the integral of SFRD.
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