The observed delay-time distribution ( DTD ) of Type-Ia supernovae ( SNe Ia ) is a valuable probe of SN Ia progenitors and physics , and of the role of SNe Ia in cosmic metal enrichment .
The SN Ia rate in galaxy clusters as a function of cluster redshift is an almost-direct measure of the DTD , but current estimates have been limited out to a mean redshift \langle z \rangle = 1.1 , corresponding to time delays , after cluster star-formation , of \gtrsim 3.2 Gyr .
We analyze data from a Hubble Space Telescope monitoring project of 12 galaxy clusters at z = 1.13 - 1.75 , where we discover 29 SNe , and present their multi-band light curves .
Based on the SN photometry and the apparent host galaxies , we assess cluster membership and SN type , finding 11 cases that are likely SNe Ia in cluster galaxies and 4 more cases which are possible but not certain cluster SNe Ia .
We conduct simulations to estimate the SN detection efficiency , the experiment ’ s completeness , and the photometric errors , and perform photometry of the cluster galaxies to derive the cluster stellar masses .
With this input , we obtain a mean \langle z \rangle = 1.35 cluster rest-frame SN Ia rate per unit formed stellar mass of R _ { Ia,m* } = 2.6 ^ { +3.2 } _ { -1.5 } \times 10 ^ { -13 } { ~ { } yr } ^ { -1 } { M } _ { \odot } ^ { % -1 } .
Separating the cluster sample into high- z and low- z bins , the rates are 2.2 ^ { +2.6 } _ { -1.3 } \times 10 ^ { -13 } { ~ { } yr } ^ { -1 } { M } _ { \odot } ^ { -1 } at \langle z \rangle = 1.25 , and 3.5 ^ { +6.6 } _ { -2.8 } \times 10 ^ { -13 } { ~ { } yr } ^ { -1 } { M } _ { \odot } ^ { -1 } at \langle z \rangle = 1.58 .
Combining our results with previous cluster SN Ia rates , we fit the DTD , now down to delays of 1.5 Gyr , with a power-law dependence , t ^ { \alpha } , with \alpha = -1.30 ^ { +0.23 } _ { -0.16 } .
We confirm previous indications for a SN Ia production efficiency that is several times higher in galaxy clusters than in the field , perhaps caused by a peculiar stellar initial mass function in clusters , or by a higher incidence of binaries that will evolve into SNe Ia .