Flux‐averaging Analysis of Type Ia Supernova Data

Because of flux conservation, flux-averaging {\it justifies} the use of the distance-redshift relation for a smooth universe in the analysis of type Ia supernova (SN Ia) data. We have combined the SN Ia data from the High-$z$ SN Search and the Supernova Cosmology Project, and binned the combined data by flux-averaging in redshift intervals of $\Delta z=0.05$ and $\Delta z=0.1$. We find that the unbinned data yield a Hubble constant of $H_0=65\pm 1 $km$ $s$^{-1} $Mpc$^{-1}$ (statistical error only), a matter density fraction of $\Omega_m=0.7\pm0.4$, and a vacuum energy density fraction of $\Omega_{\Lambda}=1.2\pm0.5$. The binned data for $\Delta z=0.1$ yield $H_0=65\pm 1 $km$ $s$^{-1} $Mpc$^{-1}$ (statistical error only), $\Omega_m=0.3\pm0.6$, and $\Omega_{\Lambda}=0.7\pm0.7$. Our results are not sensitive to the redshift bin size. Flux-averaging leads to less biased estimates of the cosmological parameters by reducing the bias due to systematic effects such as weak lensing. Comparison of the data of 18 SNe Ia published by both groups yields a mean SN Ia peak absolute magnitude of $M_B=-19.33\pm 0.25$. The internal dispersion of each data set is about 0.20 magnitude in the {\it calibrated} SN Ia peak absolute magnitudes. The difference in analysis techniques introduces an additional uncertainty of about 0.15 magnitude. If the SNe Ia peak absolute luminosity changes with redshift due to evolution, our ability to measure the cosmological parameters from SN Ia data will be significantly diminished.Comment: 30 pages including 15 figures. Expanded and final version to appear in ApJ (2000