The history of star formation in a Λ cold dark matter universe

Employing hydrodynamic simulations of structure formation in a Lambda cold dark matter cosmology, we study the history of cosmic star formation from the 'dark ages' at redshift z similar to 20 to the present. In addition to gravity and ordinary hydrodynamics, our model includes radiative heating and cooling of gas, star formation, supernova feedback and galactic winds. By making use of a comprehensive set of simulations on interlocking scales and epochs, we demonstrate numerical convergence of our results on all relevant halo mass scales, ranging from 10(8) to 10(15) h(-1) M-.. The predicted density of cosmic star formation, , is broadly consistent with measurements, given the observational uncertainty. From the present epoch, gradually rises by approximately a factor of 10 to a peak at z similar to 5-6, which is beyond the redshift range where it has been estimated observationally. In our model, fully 50 per cent of the stars are predicted to have formed by redshift z similar or equal to 2.14, and are thus older than 10.4 Gyr, while only 25 per cent form at redshifts lower than z similar or equal to 1. The mean age of all stars at the present is approximately 9 Gyr. Our model predicts a total stellar density at z = 0 of Omega(star) = 0.004, corresponding to approximately 10 per cent of all baryons being locked up in long-lived stars, in agreement with recent determinations of the luminosity density of the Universe. We determine the 'multiplicity function of cosmic star formation' as a function of redshift; i.e. the distribution of star formation with respect to halo mass. At redshifts around z similar or equal to 10, star formation occurs preferentially in haloes of mass >10(8) -10(10) h(-1) M-., while at lower redshifts, the dominant contribution to comes from progressively more massive haloes. Integrating over time, we find that approximately 50 per cent of all stars formed in haloes less massive than 10(11.5) h(-1) M-., with nearly equal contributions per logarithmic mass interval in the range 10(10) -10(13.5) h(-1) M-., making up similar to70 per cent of the total. We also briefly examine possible implications of our predicted star formation history for reionization of hydrogen in the Universe. According to our model, the stellar contribution to the ionizing background is expected to rise for redshifts z > 3, at least up to redshift z similar to 5, in accord with estimates from simultaneous measurements of the H and He opacities of the Lyman-alpha forest. This suggests that the ultraviolet background will be dominated by stars for z > 4, provided that there are not significantly more quasars at high z than are presently known. We measure the clumping factor of the gas from the simulations and estimate the growth of cosmic H ii regions, assuming a range of escape fractions for ionizing photons. We find that the star formation rate predicted by the simulations is sufficient to account for hydrogen reionization by z similar to 6, but only if a high escape fraction close to unity is assumed.