The iron mass in galaxy clusters is about 6 times larger than could have been produced by core-collapse supernovae ( SNe ) , assuming the stars in the cluster formed with a standard initial mass function ( IMF ) .
SNe Ia have been proposed as the alternative dominant iron source .
Different SN Ia progenitor models predict different “ delay functions ” , between the formation of a stellar population and the explosion of some of its members as SNe Ia .
We use our previous measurements of the cluster SN Ia rate at high redshift to constrain SN Ia progenitor models and the star-formation epoch in clusters .
The low observed rate of cluster SNe Ia at z \sim 0 - 1 means that , if SNe Ia produced the observed amount of iron , they must have exploded at even higher z .
This puts a > 95 \% upper limit on the mean SN Ia delay time of \tau < 2 Gyr ( < 5 Gyr ) if the stars in clusters formed at z _ { f } < 2 ( z _ { f } < 3 ) , assuming H _ { o } = 70 km s ^ { -1 } Mpc ^ { -1 } .
In a companion paper , we show that , for some current versions of cosmic ( field ) star formation history ( SFH ) , observations of field SNe Ia place a lower bound on the delay time , \tau > 3 Gyr .
If these SFHs are confirmed , the entire range of \tau will be ruled out .
Cluster enrichment by core-collapse SNe from a top-heavy IMF will then remain the only viable option .