The reddening law of Type Ia Supernovae: separating intrinsic variability from dust using equivalent widths

We employ 76 type Ia supernovae (SNe Ia) with optical spectrophotometry within 2.5 days of B-band maximum light obtained by the Nearby Supernova Factory to derive the impact of Si and Ca features on the supernovae intrinsic luminosity and determine a dust reddening law. We use the equivalent width of Si II λ4131 in place of the light curve stretch to account for first-order intrinsic luminosity variability. The resulting empirical spectral reddening law exhibits strong features that are associated with Ca II and Si II λ6355. After applying a correction based on the Ca II H&K equivalent width we find a reddening law consistent with a Cardelli extinction law. Using the same input data, we compare this result to synthetic rest-frame UBVRI-like photometry to mimic literature observations. After corrections for signatures correlated with Si II λ4131 and Ca II H&K equivalent widths and introducing an empirical correlation between colors, we determine the dust component in each band. We find a value of the total-to-selective extinction ratio, R v = 2.8 ± 0.3. This agrees with the Milky Way value, in contrast to the low R v values found in most previous analyses. This result suggests that the long-standing controversy in interpreting SN Ia colors and their compatibility with a classical extinction law, which is critical to their use as cosmological probes, can be explained by the treatment of the dispersion in colors, and by the variability of features apparent in SN Ia spectra.