The Dependence of the $A_V$ Prior for SN\,Ia on Host Mass and Disk Inclination

TL;DR

This study investigates how the prior assumptions about host galaxy extinction affect supernova Ia distance measurements, suggesting that more detailed occulting galaxy templates are needed to improve cosmological accuracy.

Contribution

It introduces a method to refine the $A_V$ prior based on host galaxy properties using occulting galaxy pairs, highlighting the importance of detailed templates for better supernova distance estimates.

Findings

Host mass-dependent $A_V$ prior lowers luminosity distances.

Matching by stellar mass is more effective than by radius.

More occulting galaxy templates are needed to reduce scatter.

Abstract

Supernovae type Ia (SNIa) are used as "standard candles" for cosmological distance scales. To fit their light curve shape -- absolute luminosity relation, one needs to assume an intrinsic color and a likelihood of host galaxy extinction or a convolution of these, a color distribution prior. The host galaxy extinction prior is typically assumed to be an exponential drop-off for the current supernova programs ($P(A_V) \propto e^{-A_V/\tau_0}$). We explore the validity of this prior using the distribution of extinction values inferred when two galaxies accidentally overlap (an occulting galaxy pair). We correct the supernova luminosity distances from the SDSS-III Supernova projects (SDSS-SN) by matching the host galaxies to one of three templates from occulting galaxy pairs based on the host galaxy mass and the $A_V$-bias - prior-scale ($\tau_0$) relation from Jha et al. (2007). We find that introducing an $A_V$ prior that depends on host mass results in lowered luminosity distances for the SDSS-SN on average but it does not reduce the scatter in individual measurements. This points, in our view, to the need for many more occulting galaxy templates to match to SNIa host galaxies to rule out this possible source of scatter in the SNIa distance measurements. We match occulting galaxy templates based on both mass and projected radius and we find that one should match by stellar mass first with radius as a secondary consideration. We discuss the caveats of the current approach and our aim is to convince the reader that a library of occulting galaxy pairs observed with HST will provide sufficient priors to improve (optical) SNIa measurements to the next required accuracy in Cosmology.