ABRIDGED 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 $({0.37}^{+0.17+0.01}_{-0.12-0.01}) mathrm{SNu}r h^{2}$ and $({0.55}^{+0.13+0.02}_{-0.11-0.01}) mathrm{SNu}r h^{2}$ ($mathrm{SNu}x = 10^{-12} L_{xsun}^{-1} mathrm{yr}^{-1}$) 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. 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. The SN rate in galaxy clusters as a function of redshift...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... we estimate the fraction of cluster SNe that are hostless to be $(9.4^+8._3-5.1)%$.
We present measurements of the Hubble diagram for 103 Type Ia supernovae (SNe) with redshifts 0.04 < z < 0.42, discovered during the first season (Fall 2005) of the Sloan Digital Sky Survey-II (SDSS-II) Supernova Survey. These data fill in the redshi
ft desert between low- and high-redshift SN Ia surveys. We combine the SDSS-II measurements with new distance estimates for published SN data from the ESSENCE survey, the Supernova Legacy Survey, the Hubble Space Telescope, and a compilation of nearby SN Ia measurements. Combining the SN Hubble diagram with measurements of Baryon Acoustic Oscillations from the SDSS Luminous Red Galaxy sample and with CMB temperature anisotropy measurements from WMAP, we estimate the cosmological parameters w and Omega_M, assuming a spatially flat cosmological model (FwCDM) with constant dark energy equation of state parameter, w. For the FwCDM model and the combined sample of 288 SNe Ia, we find w = -0.76 +- 0.07(stat) +- 0.11(syst), Omega_M = 0.306 +- 0.019(stat) +- 0.023(syst) using MLCS2k2 and w = -0.96 +- 0.06(stat) +- 0.12(syst), Omega_M = 0.265 +- 0.016(stat) +- 0.025(syst) using the SALT-II fitter. We trace the discrepancy between these results to a difference in the rest-frame UV model combined with a different luminosity correction from color variations; these differences mostly affect the distance estimates for the SNLS and HST supernovae. We present detailed discussions of systematic errors for both light-curve methods and find that they both show data-model discrepancies in rest-frame $U$-band. For the SALT-II approach, we also see strong evidence for redshift-dependence of the color-luminosity parameter (beta). Restricting the analysis to the 136 SNe Ia in the Nearby+SDSS-II samples, we find much better agreement between the two analysis methods but with larger uncertainties.
