ZTF SN~Ia DR2: Cosmology-independent constraints on Type Ia supernova standardisation from supernova siblings

Understanding Type Ia supernovae (SNe~Ia) and the empirical standardisation relations that make them excellent distance indicators is vital to improving cosmological constraints. SN~Ia ``siblings", i.e. two or more SNe~Ia in the same host or parent galaxy offer a unique way to infer the standardisation relations and their diversity across the population. We analyse a sample of 25 SN~Ia pairs, observed homogeneously by the Zwicky Transient Factory (ZTF) to infer the SNe~Ia light curve width-luminosity and colour-luminosity parameters α and β. Using the pairwise constraints from siblings, allowing for a diversity in the standardisation relations, we find α = 0.218 ± 0.055 and β = 3.084 ± 0.312, respectively, with a dispersion in α and β of ≤ 0.195 and ≤ 0.923, respectively, at 95$%$ C.L. While the median dispersion is large, the values within ~ 1 σ are consistent with no dispersion. Hence, fitting for a single global standardisation relation, we find α = 0.228 ± 0.029 and β = 3.160 ± 0.191. We find a very small intrinsic scatter of the siblings sample σᵢₙₜ ≤ 0.10 at 95% C.L. compared to σᵢₙₜ = 0.22 ± 0.04 when computing the scatter using the Hubble residuals without comparing them as siblings. Splitting the sample based on host galaxy stellar mass, we find that SNe~Ia in both subsamples have consistent α and β. The β value is consistent with the value for the cosmological sample. However, we find a higher α by ~ 2.5 - 3.5 σ. The high α is driven by low x₁ pairs, potentially suggesting that the slow and fast declining SN~Ia have different slopes of the width-luminosity relation. We can confirm or refute this with increased statistics from near future time-domain surveys. (abridged)