Flux‐averaging Analysis of Type Ia Supernova Data

Because of flux conservation, flux-averaging {\it justifies} the use of thedistance-redshift relation for a smooth universe in the analysis of type Iasupernova (SN Ia) data. We have combined the SN Ia data from the High-$z$ SNSearch and the Supernova Cosmology Project, and binned the combined data byflux-averaging in redshift intervals of $\Delta z=0.05$ and $\Delta z=0.1$. Wefind 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 notsensitive to the redshift bin size. Flux-averaging leads to less biasedestimates of the cosmological parameters by reducing the bias due to systematiceffects such as weak lensing. Comparison of the data of 18 SNe Ia published by both groups yields a mean SNIa peak absolute magnitude of $M_B=-19.33\pm 0.25$. The internal dispersion ofeach data set is about 0.20 magnitude in the {\it calibrated} SN Ia peakabsolute magnitudes. The difference in analysis techniques introduces anadditional uncertainty of about 0.15 magnitude. If the SNe Ia peak absolute luminosity changes with redshift due toevolution, our ability to measure the cosmological parameters from SN Ia datawill be significantly diminished.Comment: 30 pages including 15 figures. Expanded and final version to appear in ApJ (2000