Testing the consistency of dust laws in SN Ia host galaxies: a BAYESN examination of Foundation DR1

We apply BAYESN, our new hierarchical Bayesian model for the SEDs of Type Ia supernovae (SNe Ia), to analyse the griz light curves of 157 nearby SNe Ia (0.015 < z < 0.08) from the public Foundation Supernova Survey data set. We train a new version of BAYESN, continuous from 0.35 to 0.95 mu m, which we use to model the properties of SNe Ia in the rest-frame z-band, study the properties of dust in their host galaxies, and construct a Hubble diagram of SN Ia distances determined from full griz light curves. Our griz Hubble diagram has a low total RMS of 0.13 mag using BAYESN, compared to 0.16 mag using SALT2. Additionally, we test the consistency of the dust law R-V between low- and high-mass host galaxies by using our model to fit the full time- and wavelength-dependent SEDs of SNe Ia up to moderate reddening (peak apparent B - V less than or similar to 0.3). Splitting the population at the median host mass, we find R-V = 2.84 +/- 0.31 in low-mass hosts, and R-V = 2.58 +/- 0.23 in high-mass hosts, both consistent with the global value of R-V = 2.61 +/- 0.21 that we estimate for the full sample. For all choices of mass split we consider, R-V is consistent across the step within less than or similar to 1.2 sigma. Modelling population distributions of dust laws in low- and high-mass hosts, we find that both subsamples are highly consistent with the full sample's population mean mu(R-V) = 2.70 +/- 0.25 with a 95 per cent upper bound on the population sigma(R-V) < 0.61. The R-V population means are consistent within less than or similar to 1.2 sigma. We find that simultaneous fitting of host-mass-dependent dust properties within our hierarchical model does not account for the conventional mass step.