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

TL;DR

This paper develops formulae to quantify how $K$-corrections contribute to uncertainty in galaxy luminosity measurements, aiding in selecting optimal flux measurements for accurate luminosity estimation.

Contribution

It introduces a Gaussian approximation framework for assessing $K$-correction uncertainties and provides galaxy SED models based on empirical templates and data.

Findings

Derived formulas for $K$-correction uncertainty estimation

Provided SED mean and covariance approximations for galaxy subclasses

Applied models to real galaxy data from multiple surveys

Abstract

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.