Type Ia supernova Hubble diagrams with host galaxy photometric redshifts

Systematic uncertainties associated to type Ia supernova (SN Ia) Hubble dia-grams from photometrically selected samples using photometric SN host galaxy redshifts are investigated. The host redshift uncertainties and the contamination by core-collapse SNe are both addressed. As a test case, we use the 3-year photometric SN Ia sample of the SuperNova Legacy Survey (SNLS), consisting of 437 objects between 0.1 and 1.05 in redshift with 4.7% contamination. We combine this sample with non-SNLS objects of the spectroscopic sample from the joint analysis (JLA) of the SDSS-II and SNLS collaborations, consisting of 501 objects mostly below 0.4 in redshift. We study two options for the origin of the redshifts of the photometric sample, either provided entirely from the host photometric redshift catalogue used in the selection or a mixed origin where around 75% of the sample can be assigned spectroscopic redshifts from dedicated measurements or external catalogues. Using light curve simulations subject to the same photometric selection as data, we study the impact of photometric redshift uncertainties and contamination on flat ACDM fits to Hubble diagrams from such combined samples. Our primary finding is that photometric redshifts and contamination lead to biased cosmological parameters. The magnitude of the bias is found to be similar for both redshift options. This bias can be largely accounted for if photometric redshift uncertainties and contamination are taken into account when computing the SN magnitude bias correction due to selection effects. To reduce the residual cosmological bias, we explore two methods to propagate redshift uncertainties into the cosmological likelihood computation, either by refitting photometric redshifts along with cosmology or by sampling the redshift resolution function. Redshift refitting fails at correcting the cosmological bias whatever the redshift origin, while sampling slightly reduces it in both cases. Finally, for actual data, we find compatible results with those from the JLA diagram for mixed photometric and spectroscopic redshifts, while the full photometric option is biased upwards, but consistent with JLA when all statistical and systematic uncertainties are included.