The redshift distribution of type Ia supernovae: Constraints on progenitors and cosmic star formation history

We use the redshift distribution of type la supernovae (SNe) discovered by the Supernova Cosmology Project to constrain the star formation history (SFH) of the Universe and SN la progenitor models. Given some of the recent determinations of the SFH, the observed SN la redshift distribution indicates a long (≳1 h^-1 Gyr) mean delay time between the formation of a stellar population and the explosion of some of its members as SNe la. For example, if the SFH of Madau et al. is assumed, the delay time τ is constrained to be τ ≥ 1.7(τ ≥ 0.7) h^-1 Gyr at the 95 per cent (99 per cent) confidence level (CL). SFHs that rise at high redshift, similar to those advocated by Lanzetta et al., are inconsistent with the data at the 95 per cent CL unless τ > 2.5 h^-1 Gyr. Long time-delays disfavour progenitor models such as edge-lit detonation of a white dwarf accreting from a giant donor, and the carbon core ignition of a white dwarf passing the Chandrasekhar mass due to accretion from a subgiant. The SN la delay may be shorter, thereby relaxing some of these constraints, if the field star formation rate falls, between z = 1 and the present, less sharply than implied, e.g. by the original Madau plot. We show that the discovery of larger samples of high-z SNe Ia by forthcoming observational projects should yield strong constraints on the progenitor models and the SFH. In a companion paper, we demonstrate that if SNe la produce most of the iron in galaxy clusters, and the stars in clusters formed at z ∼ 2, the SN la delay time must be lower than 2 Gyr. If so, then the SFH of Lanzetta et al. will be ruled out by the data presented here.