Do spectra improve distance measurements of Type Ia supernovae?

We investigate the use of a wide variety of spectroscopic measurements to determine distances to low-redshift Type Ia supernovae (SN Ia) in the Hubble flow observed through the CfA Supernova Program. We consider linear models for predicting distances to SN Ia using light-curve width and color parameters (determined using the SALT2 light-curve fitter) and a spectroscopic indicator, and evaluate the resulting Hubble diagram scatter using a cross-validation procedure. We confirm the ability of spectral flux ratios alone at maximum light to reduce the scatter of Hubble residuals by similar to 10% [weighted rms, or WRMS = 0.189 +/- 0.026 mag for the flux ratio R(6630/4400)] with respect to the standard combination of light-curve width and color, for which WRMS = 0.204 +/- 0.029 mag. When used in combination with the SALT2 color parameter, the color-corrected flux ratio R-c(6420/5290) at maximum light leads to an even lower scatter (WRMS = 0.175 +/- 0.025 mag), although the improvement has low statistical significance (<2 sigma) given the size of our sample (26 SN Ia). We highlight the importance of an accurate relative flux calibration and the failure of this method for highly-reddened objects. Comparison with synthetic spectra from 2D delayed-detonation explosion models shows that the correlation of R(6630/4400) with SN Ia absolute magnitudes can be largely attributed to intrinsic color variations and not to reddening by dust in the host galaxy. We consider flux ratios at other ages, as well as the use of pairs of flux ratios, revealing the presence of small-scale intrinsic spectroscopic variations in the iron-group-dominated absorption features around similar to 4300 angstrom and similar to 4800 angstrom. The best flux ratio overall is the color-corrected R-c(4610/4260) at t = -2.5 d from maximum light, which leads to similar to 30% lower scatter (WRMS = 0.143 +/- 0.020 mag) with respect to the standard combination of light-curve width and color, at similar to 2 sigma significance. We examine other spectroscopic indicators related to line-profile morphology (absorption velocity, pseudo-equivalent width etc.), but none appear to lead to a significant improvement over the standard light-curve width and color parameters. We discuss the use of spectra in measuring more precise distances to SN Ia and the implications for future surveys which seek to determine the properties of dark energy.