Two-population model of type Ia supernovae and their associations with host galaxies in ZTF DR2

We constrain type Ia supernova intrinsic properties, extinction, and probabilistic supernova-host associations using the volume-limited sample from the Zwicky Transient Factory DR2, the largest selection-free data set of type Ia supernovae to date. We employ Bayesian hierarchical modelling to jointly analyse the distribution of SALT2 light-curve parameters and global host-galaxy properties (stellar mass and rest-frame g-z colour). The adopted model is a mixture of distributions representing two supernova populations corresponding to two distinct modes of the stretch-parameter distribution, and two host-galaxy populations corresponding to two modes in the host-galaxy parameter space (red/massive and blue/less massive). Motivated by observations, high-stretch supernovae are allowed to populate both host-galaxy populations, whereas low-stretch supernovae are assumed to be exclusively associated with the red/massive host-galaxy population. The apparent non-linearity of the supernova magnitude-stretch relation implies a luminosity gap between the supernova populations, with the low-stretch population being Delta MB=0.14+/-0.03 mag brighter at x1=0, and different slopes (Delta alpha=0.064+/-0.023, steeper for the low-stretch population). The mean extinction coefficient is RB=3.89+/-0.29 (consistent with typical Milky Way values) in the blue/less massive host-galaxy population, which contains 68 per cent of high-stretch supernovae, and RB=3.08+/-0.08 in the red/massive host-galaxy population. Host-galaxy step corrections, both in stellar mass and colour, naturally emerge from the way the two supernova populations, characterised by different intrinsic luminosities and exctinctions, are distributed across host-galaxy populations. The adopted framework for modelling supernova populations and supernova-host associations makes host-galaxy step corrections redundant.