The volumetric rate of normal type Ia supernovae in the local universe discovered by the Palomar Transient Factory

We present the volumetric rate of normal type Ia supernovae (SNe Ia) discovered by the Palomar Transient Factory (PTF). Using strict data-quality cuts, and considering only periods when the PTF maintained a regular cadence, PTF discovered 90 SNe Ia at $z\le0.09$ in a well-controlled sample over three years of operation (2010-2012). We use this to calculate the volumetric rate of SN Ia events by comparing this sample to simulations of hundreds of millions of SN Ia light curves produced in statistically representative realisations of the PTF survey. This quantifies the recovery efficiency of each PTF SN Ia event, and thus the relative weighting of each event. From this, the volumetric SN Ia rate was found to be $r_v=2.43\pm0.29\,\text{(stat)}_{-0.19}^{+0.33}\text{(sys)}\times10^{-5}\,\text{SNe yr}^{-1}\,\text{Mpc}^{-3}\, h_{70}^{3}$. This represents the most precise local measurement of the SN Ia rate. We fit a simple SN Ia delay-time distribution model, $\propto\mathrm{t}^{-\beta}$, to our PTF rate measurement combined with a literature sample of rate measurements from surveys at higher-redshifts. We find $\beta{\sim}1$, consistent with a progenitor channel governed by the gravitational in-spiral of binary white dwarfs.