Binning is Sinning: Redemption for Hubble Diagram Using Photometrically Classified Type Ia Supernovae

Abstract

Abstract Bayesian Estimation Applied to Multiple Species (BEAMS) is implemented in the BEAMS with Bias Corrections (BBC) framework to produce a redshift-binned Hubble diagram (HD) for Type Ia supernovae (SNe Ia). BBC corrects for selection effects and non–SN Ia contamination, and systematic uncertainties are described by a covariance matrix with dimension matching the number of BBC redshift bins. For spectroscopically confirmed SN Ia samples, a recent “Binning is Sinning” article showed that an unbinned HD and covariance matrix reduces the systematic uncertainty by a factor of ∼1.5 compared to the binned approach. Here we extend their analysis to obtain an unbinned HD for a photometrically identified sample processed with BBC. To test this new method, we simulate and analyze 50 samples corresponding to the Dark Energy Survey (DES) with a low-redshift anchor; the simulation includes SNe Ia, and contaminants from core-collapse SNe and peculiar SNe Ia. The analysis includes systematic uncertainties for calibration and measures the dark energy equation of state parameter (w). Compared to a redshift-binned HD, the unbinned HD with nearly 2000 events results in a smaller systematic uncertainty, in qualitative agreement with BHS21, and averaging results among the 50 samples we find no evidence for a w-bias. To reduce computation time for fitting an unbinned HD with large samples, we propose an HD-rebinning method that defines the HD in bins of redshift, color, and stretch; the rebinned HD results in similar uncertainty as the unbinned case, and shows no evidence for a w-bias.