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.
