ZTF SN Ia DR2: Colour standardisation of Type Ia Supernovae and its dependence on environment

As type Ia supernova (SN Ia) cosmology transitions from a statistics-dominated to a systematics-dominated era, it is crucial to understand the remaining unexplained uncertainties that affect their luminosity, such as those stemming from astrophysical biases. SNe Ia are standardisable candles whose absolute magnitude reaches a scatter of 0.15 mag when empirical correlations with their light-curve stretch and colour and with their environment are accounted for. We investigate the dependence of the standardisation process of SNe Ia on the astrophysical environment, focusing on colour standardisation. We used the volume-limited ZTF SN Ia DR2 sample, which offers unprecedented statistics for the low-redshift ($z < 0.06$) range. We first studied the colour distribution, to then select a dustless subsample of objects. We then examined the colour-residual relation and its associated parameter $\beta$. Finally, we investigated the colour dependence of the environment-dependent magnitude offsets (steps) to separate their intrinsic and extrinsic components. Our sample of nearly 1,000 SNe probes the red tail of the colour distribution up to $c = 0.8$. The dustless sample exhibits a significantly shorter red tail ($4.3\sigma$) than the whole sample, but the distributions around $c\sim0$ are similar for both samples. This suggests that the reddening above $c\geq0.2$ is dominated by interstellar dust absorption of the host. The colour-residual relation is linear with SN colour. We found indications of a potential evolution of $\beta$ with the stellar host mass, with $\beta\sim3.6$ for low-mass galaxies, compared to $\beta=3.05\pm0.06$ for the full sample. Finally, in contrast to recent claims from the literature, we found no evolution of steps as a function of SN colour. This suggests that dust may not be the dominating mechanism for the dependence on the environment of the magnitude of SNe Ia.