Projected distances to host galaxy reduce SNIa dispersion

We use multi-band imagery data from the Sloan Digital Sky Survey (SDSS) to measure projected distances of 302 supernova type Ia (SNIa) from the centre of their host galaxies, normalized to the galaxy's brightness scale length, with a Bayesian approach. We test the hypothesis that SNIas further away from the centre of their host galaxy are less subject to dust contamination (as the dust column density in their environment is maller) and/or come from a more homogeneous environment. Using the Mann-Whitney U test, we find a statistically significant difference in the observed colour correction distribution between SNIas that are near and those that are far from the centre of their host. The local p-value is 3 x 10^{-3}, which is significant at the 5 per cent level after look-elsewhere effect correction. We estimate the residual scatter of the two subgroups to be 0.073 +/- 0.018 for the far SNIas, compared to 0.114 +/-0.009 for the near SNIas -- an improvement of 30 per cent, albeit with a low statistical significance of 2sigma. This confirms the importance of host galaxy properties in correctly interpreting SNIa observations for cosmological inference.