The Hubble Space Telescope Cluster Supernova Survey: II. The Type Ia
  Supernova Rate in High-Redshift Galaxy Clusters
  We report a measurement of the Type Ia supernova (SN Ia) rate in galaxy
clusters at 0.9 < z < 1.45 from the Hubble Space Telescope (HST) Cluster
Supernova Survey. This is the first cluster SN Ia rate measurement with
detected z > 0.9 SNe. Finding 8 +/- 1 cluster SNe Ia, we determine a SN Ia rate
of 0.50 +0.23-0.19 (stat) +0.10-0.09 (sys) SNuB (SNuB = 10^-12 SNe L_{sun,B}^-1
yr^-1). In units of stellar mass, this translates to 0.36 +0.16-0.13 (stat)
+0.07-0.06 (sys) SNuM (SNuM = 10^-12 SNe M_sun^-1 yr^-1). This represents a
factor of approximately 5 +/- 2 increase over measurements of the cluster rate
at z < 0.2. We parameterize the late-time SN Ia delay time distribution with a
power law (proportional to t^s). Under the assumption of a cluster formation
redshift of z_f = 3, our rate measurement in combination with lower-redshift
cluster SN Ia rates constrains s = -1.41 +0.47/-0.40, consistent with
measurements of the delay time distribution in the field. This measurement is
generally consistent with expectations for the "double degenerate" scenario and
inconsistent with some models for the "single degenerate" scenario predicting a
steeper delay time distribution at large delay times. We check for
environmental dependence and the influence of younger stellar populations by
calculating the rate specifically in cluster red-sequence galaxies and in
morphologically early-type galaxies, finding results similar to the full
cluster rate. Finally, the upper limit of one host-less cluster SN Ia detected
in the survey implies that the fraction of stars in the intra-cluster medium is
less than 0.47 (95% confidence), consistent with measurements at lower
redshifts.
