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K-corrections and spectral templates of Type Ia supernovae

With the advent of large dedicated Type Ia supernova (SN Ia) surveys, K-corrections of SNe Ia and their uncertainties have become especially important in the determination of cosmological parameters. While K-corrections are largely driven by SN Ia broad-band colors, it is shown here that the diversity in spectral features of SNe Ia can also be important. For an individual observation, the statistical errors from the inhomogeneity in spectral features range from 0.01 (where the observed and rest-frame filters are aligned) to 0.04 (where the observed and rest-frame filters are misaligned). To minimize the systematic errors caused by an assumed SN Ia spectral energy distribution (SED), we outline a prescription for deriving a mean spectral template time series which incorporates a large and heterogeneous sample of observed spectra. We then remove the effects of broad-band colors and measure the remaining uncertainties in the K-corrections associated with the diversity in spectral features. Finally, we present a template spectroscopic sequence near maximum light for further improvement on the K-correction estimate. A library of ~600 observed spectra of ~100 SNe Ia from heterogeneous sources is used for the analysis.