Using Spectral Flux Ratios to Standardize SN Ia Luminosities
  We present a new method to standardize Type Ia supernova (SN Ia) luminosities
to ~<0.13 magnitudes using flux ratios from a single flux-calibrated spectrum
per SN. Using Nearby Supernova Factory spectrophotomery of 58 SNe Ia, we
performed an unbiased search for flux ratios which correlate with SN Ia
luminosity. After developing the method and selecting the best ratios from a
training sample, we verified the results on a separate validation sample and
with data from the literature. We identified multiple flux ratios whose
correlations with luminosity are stronger than those of light curve shape and
color, previously identified spectral feature ratios, or equivalent width
measurements. In particular, the flux ratio R(642/443) = F(642 nm) / F(443 nm)
has a correlation of 0.95 with SN Ia absolute magnitudes. Using this single
ratio as a correction factor produces a Hubble diagram with a residual scatter
standard deviation of 0.125 +- 0.011 mag, compared with 0.161 +- 0.015 mag when
fit with the SALT2 light curve shape and color parameters x1 and c. The ratio
R(642/443) is an effective correction factor for both extrinsic dust reddening
and instrinsic variations such as those of SN 1991T-like and SN 1999aa-like
SNe. When combined with broad-band color measurements, spectral flux ratios can
standardize SN Ia magnitudes to ~0.12 mag. These are the first spectral metrics
that improve over the standard normalization methods based upon light curve
shape and color and they provide among the lowest scatter Hubble diagrams ever
published.
