Evolution in the volumetric type Ia supernova rate from the supernova legacy survey

We present a measurement of the volumetric Type Ia supernova (SN Ia) rate (SNR _Ia) as a function of redshift for the first four years of data from the Canada-France-Hawaii Telescope Supernova Legacy Survey (SNLS). This analysis includes 286 spectroscopically confirmed and more than 400 additional photometrically identified SNe Ia within the redshift range 0.1 ≤ z ≤ 1.1. The volumetric SNR _Ia evolution is consistent with a rise to z 1.0 that follows a power law of the form (1+z) ^α, with α = 2.11 ± 0.28. This evolutionary trend in the SNLS rates is slightly shallower than that of the cosmic star formation history (SFH) over the same redshift range. We combine the SNLS rate measurements with those from other surveys that complement the SNLS redshift range, and fit various simple SN Ia delay-time distribution (DTD) models to the combined data. A simple power-law model for the DTD (i.e., t ^-β) yields values from β = 0.98 ± 0.05 to β = 1.15 ± 0.08 depending on the parameterization of the cosmic SFH. A two-component model, where SNR _Ia is dependent on stellar mass (M _stellar) and star formation rate (SFR) as SNR _Ia(z) = A × M _stellar(z) + B × SFR(z), yields the coefficients A = (1.9 ± 0.1) × 10 ^-14 SNe yr ^-1 M ^-1 _⊙ and B = (3.3 ± 0.2) × 10 ^-4 SNe yr ^-1 (M _⊙ yr ^-1) ^-1. More general two-component models also fit the data well, but single Gaussian or exponential DTDs provide significantly poorer matches. Finally, we split the SNLS sample into two populations by the light-curve width (stretch), and show that the general behavior in the rates of faster-declining SNe Ia (0.8 ≤ s < 1.0) is similar, within our measurement errors, to that of the slower objects (1.0 ≤ s < 1.3) out to z 0.8.