$K$-corrections: an Examination of their Contribution to the Uncertainty of Luminosity Measurements

In this paper we provide formulae that can be used to determine the uncertainty contributed to a measurement by a $K$-correction and, thus, valuable information about which flux measurement will provide the most accurate $K$-corrected luminosity. All of this is done at the level of a Gaussian approximation of the statistics involved, that is, where the galaxies in question can be characterized by a mean spectral energy distribution (SED) and a covariance function (spectral 2-point function). This paper also includes approximations of the SED mean and covariance for galaxies, and the three common subclasses thereof, based on applying the templates from Assef et al. (2010) to the objects in zCOSMOS bright 10k (Lilly et al. 2009) and photometry of the same field from Capak et al. (2007), Sanders et al. (2007), and the AllWISE source catalog.