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 \leq 0.17 and 27 SN events in 492 maxBCG clusters at 0.1 \leq z \leq 0.3 .
We find values for the cluster SN Ia rate of ( { 0.37 } ^ { +0.17 + 0.01 } _ { -0.12 - 0.01 } ) \mathrm { SNu } r h ^ { 2 } and ( { 0.55 } ^ { +0.13 + 0.02 } _ { -0.11 - 0.01 } ) \mathrm { SNu } r h ^ { 2 } ( \mathrm { SNu } x = 10 ^ { -12 } L _ { x \sun } ^ { -1 } \mathrm { 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 } ^ { +0.18 + 0.01 } _ { -0.12 - 0.01 } ) \mathrm { SNu } r h ^ { 2 } and ( { 0.49 } ^ { +0.15 + 0.02 } _ { -0.11 - 0.01 } ) \mathrm { SNu } r h ^ { 2 } in C4 and maxBCG clusters , respectively .
The SN rate for the brightest cluster galaxies ( BCG ) is found to be ( { 2.04 } ^ { +1.99 + 0.07 } _ { -1.11 - 0.04 } ) \mathrm { SNu } r h ^ { 2 } and ( { 0.36 } ^ { +0.84 + 0.01 } _ { -0.30 - 0.01 } ) \mathrm { SNu } r 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 } ^ { +1.31 + 0.043 } _ { -0.91 - 0.015 } and { 3.02 } ^ { +1.31 + 0.062 } _ { -1.03 - 0.048 } , 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 ^ { +0.15 } _ { -0.14 } ) + ( 0.91 ^ { +0.85 } _ { -0.81 } ) \times z ] \mathrm { SNu } B 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 3 hostless , intra-cluster SNe Ia , we estimate the fraction of cluster SNe that are hostless to be ( 9.4 ^ { +8.3 } _ { -5.1 } ) \% .