The cosmic star formation histories are evaluated for different minimum masses of the initial halo structures , with allowance for realistic gas outflows .
With a minimum halo mass of 10 ^ { 7 } – 10 ^ { 8 } \mathrm { M } _ { \odot } and a moderate outflow efficiency , we reproduce both the current baryon fraction and the early chemical enrichment of the IGM .
The intensity of the formation rate of “ normal ” stars is also well constrained by the observations : it has to be dominated by star formation in elliptical galaxies , except perhaps at very low redshift .
The fraction of baryons in stars is predicted as are also the type Ia and II supernova event rates .
Comparison with SN observations in the redshift range z = 0 - 2 allows us to set strong constraints on the time delay of type Ia supernovae ( a total delay of \sim 4 Gyr is required to fit the data ) , the lower end of the mass range of the progenitors ( 2 - 8 \mathrm { M } _ { \odot } ) and the fraction of white dwarfs that reproduce the type Ia supernova ( about 1 per cent ) .
The intensity in the initial starburst of zero metallicity stars below 270 \mathrm { M _ { \odot } } must be limited in order to avoid premature overenrichment of the IGM .
Only about 10 - 20 % of the metals present in the IGM at z = 0 have been produced by population III stars at very high z .
The remaining 80 - 90 % are ejected later by galaxies forming normal stars , with a maximum outflow efficiency occurring at a redshift of about 5 .
We conclude that 10 ^ { -3 } of the mass in baryons must lie in first massive stars in order to produce enough ionizing photons to allow early reionization of the IGM by z \sim 15 .