The Type-Ia Supernova Rate in z < 1 Galaxy Clusters: Implications for Progenitors and the Source of Cluster Iron

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 ~ 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 redshift z<2 (z<3), assuming Ho=70 km/s/Mpc. In a companion paper (astro-ph/0309796), 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.