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Type Ia Supernova Distance Modulus Bias and Dispersion From K-correction Errors: A Direct Measurement Using Lightcurve Fits to Observed Spectral Time Series

We estimate systematic errors due to K-corrections in standard photometric analyses of high redshift Type Ia supernovae. Errors due to K-correction occur when the spectral template model underlying the lightcurve fitter poorly represents the actual supernova spectral energy distribution, meaning that the distance modulus cannot be recovered accurately. In order to quantify this effect, synthetic photometry is performed on artificially redshifted spectrophotometric data from 119 low-redshift supernovae from the Nearby Supernova Factory, and the resulting lightcurves are fit with a conventional lightcurve fitter. We measure the variation in the standardized magnitude that would be fit for a given supernova if located at a range of redshifts and observed with various filter sets corresponding to current and future supernova surveys. We find significant variation in the measurements of the same supernovae placed at different redshifts regardless of filters used, which causes dispersion greater than $\sim0.05$ mag for measurements of photometry using the Sloan-like filters and a bias that corresponds to a $0.03$ shift in $w$ when applied to an outside data set. To test the result of a shift in supernova population or environment at higher redshifts, we repeat our calculations with the addition of a reweighting of the supernovae as a function of redshift and find that this strongly affects the results and would have repercussions for cosmology. We discuss possible methods to reduce the contribution of the K-correction bias and uncertainty.