A Measurement of the Rate of Type Ia Supernovae in Galaxy Clusters from the SDSS-II Supernova Survey

We present measurements of the Type Ia supernova (SN) rate in galaxy clusters based on data from the Sloan Digital Sky Survey-II (SDSS-II) Supernova Survey. The cluster SN Ia rate is determined from 9 SN events in a set of 71 C4 clusters at z <= 0.17 and 27 SN events in 492 maxBCG clusters at 0.1 <= z <= 0.3. We find values for the cluster SN Ia rate of (0.37(-0.12-0.01)(+0.17+0.01)) SNur h(2) and (0.55(-0.11-0.01)(+0.13+0.02)) SNur h(2) (SNux = 10(-12) Lx(circle dot)(-1)yr(-1)) in C4 and maxBCG clusters, respectively, where the quoted errors are statistical and systematic, respectively. The SN rate for early-type galaxies is found to be (0.31(-0.12-0.01)(+0.18+0.01)) SNur h(2) and (0.49(-0.11-0.01)(+0.15+0.02)) SNur h(2) in C4 and maxBCG clusters, respectively. The SN rate for the brightest cluster galaxies (BCG) is found to be (2.04(-1.11-0.04)(+1.99+0.07)) SNur h(2) and (0.36(-0.30-0.01)(+0.84+0.01)) SNur h(2) in C4 and maxBCG clusters, respectively. The ratio of the SN Ia rate in cluster early-type galaxies to that of the SN Ia rate in field early-type galaxies is 1.94(-0.91-0.015)(+1.31+0.043) and 3.02(-1.03-0.048)(+1.31+0.062), for C4 and maxBCG clusters, respectively. The SN rate in galaxy clusters as a function of redshift, which probes the late time SN Ia delay distribution, shows only weak dependence on redshift. Combining our current measurements with previous measurements, we fit the cluster SN Ia rate data to a linear function of redshift, and find r(L) =[(0.49(-0.14)(+0.15))+(0.91(-0.81)(+0.85)) x z] SNuB h(2). A comparison of the radial distribution of SNe in cluster to field early-type galaxies shows possible evidence for an enhancement of the SN rate in the cores of cluster early-type galaxies. With an observation of at most three hostless, intra-cluster SNe Ia, we estimate the fraction of cluster SNe that are hostless to be (9.4(-5.1)(+8.3))%.