Diverse reddening distributions in sight lines to type Ia supernovae

Precise cosmological constraints from type Ia supernovae require adequately accurate corrections for host-galaxy extinction. Modelling these corrections is challenged by the problem of disentangling supernova intrinsic colours from host-galaxy interstellar reddening. The latter is commonly modelled in a probabilistic way assuming an exponential distribution exp(-E(B-V)/\tau) as a universal prior which is applied across all types of supernova host galaxies. We test the robustness of the exponential model and its universality against predictions based on simulating dust and type Ia supernova distributions in host galaxies of different morphological types. We find substantial differences between predicted interstellar reddening in late- and early-type host galaxies, primarily driven by the stellar-to-dust mass ratios. The mean simulated reddening in late-type galaxies matches well those derived from type Ia supernova observations, but it is significantly lower for early-type host galaxies. The reddening distributions exhibit an excess of sight lines with vanishing reddening with respect to the exponential model, although the difference is quite mild for late-type galaxies. On the other hand, the distribution may peak at E(B-V)>0 when considering a population of young type Ia supernovae originating from lower heights within the dust disc. We demonstrate that assuming a universal reddening prior distribution for modeling peak magnitude-colour relation, which is currently a common practice, gives rise to a spurious scatter in the derived extinction properties. It may also bias relative distances between supernovae originating from different host-galaxy populations. The discrepancy between the simulated reddening in average early-type host galaxies and the observed occurrence of reddened supernovae suggests that reddening does not originate from interstellar dust expected in these galaxies.