Conventional Type Ia supernova ( SN Ia ) cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape , which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects , resulting in low color-magnitude slopes .
We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of a intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution .
If the intrinsic color-magnitude ( M _ { B } vs . B - V ) slope \beta _ { \text { int } } differs from the host galaxy dust law R _ { B } , this convolution results in a specific curve of mean extinguished absolute magnitude vs. apparent color .
The derivative of this curve smoothly transitions from \beta _ { \text { int } } in the blue tail to R _ { B } in the red tail of the apparent color distribution .
The conventional linear fit approximates this effective curve near the average apparent color , resulting in an apparent slope \beta _ { \text { app } } between \beta _ { \text { int } } and R _ { B } .
We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements , and analyze a dataset of SALT2 optical light curve fits of 248 nearby SN Ia at z < 0.10 .
The conventional linear fit obtains \beta _ { \text { app } } \approx 3 .
Our model finds a \beta _ { \text { int } } = 2.3 \pm 0.3 and a distinct dust law of R _ { B } = 3.8 \pm 0.3 , consistent with the average for Milky Way dust , while correcting a systematic distance bias of \sim 0.10 mag in the tails of the apparent color distribution .
Finally , we extend our model to examine the SN Ia luminosity-host mass dependence in terms of intrinsic and dust components .