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 and. Using the pairwise constraints from siblings, allowing for a diversity in the standardisation relations, we find = 0. 218 0. 055 and = 3. 084 0. 312, respectively, with a dispersion in and of 0. 195 and 0. 923, respectively, at 95\% C. L. While the median dispersion is large, the values within 1 are consistent with no dispersion. Hence, fitting for a single global standardisation relation, we find = 0. 228 0. 029 and = 3. 160 0. 191. We find a very small intrinsic scatter of the siblings sample ₈₍ₓ 0. 10 at 95\% C. L. compared to ₈₍ₓ = 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 and. The value is consistent with the value for the cosmological sample. However, we find a higher by 2. 5 - 3. 5. The high 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)