Berkeley Supernova Ia Program - III. Spectra near maximum brightness improve the accuracy of derived distances to Type Ia supernovae

In this third paper in a series we compare spectral feature measurements to\nphotometric properties of 108 low-redshift (z < 0.1) Type Ia supernovae (SNe\nIa) with optical spectra within 5 d of maximum brightness. We find the\npseudo-equivalent width (pEW) of the Si II 4000 line to be a good indicator of\nlight-curve width, and the pEWs of the Mg II and Fe II complexes are relatively\ngood proxies for SN colour. We also employ a combination of light-curve\nparameters (specifically the SALT2 stretch and colour parameters x_1 and c,\nrespectively) and spectral measurements to calculate distance moduli. The\nresiduals from these models are then compared to the standard model which uses\nonly light-curve stretch and colour. Our investigations show that a distance\nmodel that uses x_1, c, and the velocity of the Si II 6355 feature does not\nlead to a decrease in the Hubble residuals. We also find that distance models\nwith flux ratios alone or in conjunction with light-curve information rarely\nperform better than the standard (x_1,c) model. However, when adopting a\ndistance model which combines the ratio of fluxes near ~3750 Ang. and ~4550\nAng. with both x_1 and c, the Hubble residuals are decreased by ~10 per cent,\nwhich is found to be significant at about the 2-sigma level. The weighted\nroot-mean-square of the residuals using this model is 0.130 +/- 0.017 mag (as\ncompared with 0.144 +/- 0.019 mag when using the same sample with the standard\nmodel). This Hubble diagram fit has one of the smallest scatters ever published\nand at the highest significance ever seen in such a study. Finally, these\nresults are discussed with regard to how they can improve the cosmological\naccuracy of future, large-scale SN Ia surveys. [Abridged]\n