  Supernova (SN) rates are potentially powerful diagnostics of metal enrichment
and SN physics, particularly in galaxy clusters with their deep,
metal-retaining potentials and relatively simple star-formation histories. We
have carried out a survey for supernovae (SNe) in galaxy clusters, at a
redshift range 0.5<z<0.9, using the Advanced Camera for Surveys (ACS) on the
Hubble Space Telescope. We reimaged a sample of 15 clusters that were
previously imaged by ACS, thus obtaining two to three epochs per cluster, in
which we discovered five likely cluster SNe, six possible cluster SNe Ia, two
hostless SN candidates, and several background and foreground events. Keck
spectra of the host galaxies were obtained to establish cluster membership. We
conducted detailed efficiency simulations, and measured the stellar
luminosities of the clusters using Subaru images. We derive a cluster SN rate
of 0.35 SNuB +0.17/-0.12 (statistical) \pm0.13 (classification) \pm0.01
(systematic) [where SNuB = SNe (100 yr 10^10 L_B_sun)^-1] and 0.112 SNuM
+0.055/-0.039 (statistical) \pm0.042 (classification) \pm0.005 (systematic)
[where SNuM = SNe (100 yr 10^10 M_sun)^-1]. As in previous measurements of
cluster SN rates, the uncertainties are dominated by small-number statistics.
The SN rate in this redshift bin is consistent with the SN rate in clusters at
lower redshifts (to within the uncertainties), and shows that there is, at
most, only a slight increase of cluster SN rate with increasing redshift. The
low and fairly constant SN Ia rate out to z~1 implies that the bulk of the iron
mass in clusters was already in place by z~1. The recently observed doubling of
iron abundances in the intracluster medium between z=1 and 0, if real, is
likely the result of redistribution of existing iron, rather than new
production of iron.
