Inferring the delay time distribution of type Ia supernovae with CAALAM I: SED modelling choices and their effect on the delay time distribution
A delay time distribution (DTD) quantifies the lag between progenitor formation and the subsequent explosive event. The DTD for a sample of Type Ia supernovae (SNe Ia) from a survey can be modelled through relative rates and the star formation histories (SFH) of all individual galaxies. Modern wide-field surveys require computationally efficient methods to model the DTD without modelling large samples of non-host galaxies. We model the DTD for a volume limited sample from SNe Ia from the Zwicky Transient Facility. The aim is to study the effect of varying SED modelling assumptions, including stellar templates, dust attenuation, SFH models, and photometric coverage. We present a new modelling framework, the Conditional Astral Ancestry Latency Analysis Machine (CAALAM), to infer the DTD of a sample of SNe Ia from the posterior of their host galaxy SFH. A model consisting of a standard stellar template, a non-parametric SFH and a flexible dust attenuation law, is favoured by the data and predicts a non-parametric DTD peaking at 100-330 Myr. When modelled as a power law, the DTD has a characteristic exponent of $-1.30 \pm 0.04$. The exponent is sensitive to dust attenuation, photometry, or SFH. When the DTD is convolved with the SFHs of the host galaxies, we find a bimodal progenitor age distribution, with $\sim60\%$ of progenitors with ages around 1.1-3.6 Gyr and the remaining progenitors older than 3.6 Gyr. We show a correspondence between the modes of the distributions of SN Ia light curve stretch and the progenitor ages. Our inferred DTD implies that most SNe Ia ($\sim 60\%$) occur promptly within 330 Myr of progenitor formation. However, the implied progenitor ages from the DTD convolved with the SFHs from our sample are significantly older. This suggests that the DTD might be a mixture of a prompt and an extended progenitor channel.