SNIa Host Galaxy Properties and the Dust Extinction Distribution
  Supernovae Type Ia display a complex relation with their host galaxies. An
important prior to the fit of the supernovae's lightcurve is the distribution
of host galaxy extinction values that can be encountered. The SDSS-SN project
has published light curve fits using both MLCS2k2 and SALT2. We use the former
fits extinction parameter ($A_V$) to map this distribution of extinction
values.
  We explore the dependence of this distribution on four observables; the
inclination of the host galaxy disk, radial position of the supernova, redshift
of the supernova and host, and the level of star-formation in the host galaxy.
The distribution of $A_V$ values encountered by supernovae is typically
characterised by: $\rm N_0 ~ e^{-A_V/\tau}$, with $\tau$= 0.4 or 0.33.
  We find that the inclination correction using an infinitely thin disk for the
SNIa is sufficient, resulting in similar exponential $A_V$ distributions for
high- and low-inclination disks. The $A_V$ distribution also depends on the
radial position in the disk, consistent with previous results on the
transparency of spiral disks. The distribution of $A_V$ values narrows with
increased star-formation, possibly due to the destruction or dispersion of the
dusty ISM by stellar winds prior to the ignition of the supernova.
  In future supernova searches, certainly the inclination of the host galaxy
disk, should be considered in the construction of the \av \ prior with
$\tau=0.4/cos(i)$ as the most likely prior in each individual host galaxy's
case.
