K correction

K correction converts measurements of astronomical objects into their respective rest frames. The correction acts on that object's observed magnitude (or equivalently, its flux). Because astronomical observations often measure through a single filter or bandpass, observers only measure a fraction of the total spectrum, redshifted into the frame of the observer. For example, to compare measurements of stars at different redshifts viewed through a red filter, one must estimate K corrections to these measurements in order to make comparisons. If one could measure all wavelengths of light from an object (a bolometric flux), a K correction would not be required, nor would it be required if one could measure the light emitted in an emission line.

Carl Wilhelm Wirtz (1918),^[1] who referred to the correction as a Konstanten k (German for "constant") - correction dealing with the effects of redshift of in his work on Nebula. English-speaking claim for the origin of the term "K correction" is Edwin Hubble, who supposedly arbitrarily chose ${\displaystyle K}$ to represent the reduction factor in magnitude due to this same effect and who may not have been aware / given credit to the earlier work.^{[2] [3]}

The K-correction can be defined as follows

${\displaystyle M=m-5(\log _{10}{D_{L}}-1)-K_{Corr}\!\,}$

I.E. the adjustment to the standard relationship between absolute and apparent magnitude required to correct for the redshift effect.^[4] Here, D_L is the luminosity distance measured in parsecs.

The exact nature of the calculation that needs to be applied in order to perform a K correction depends upon the type of filter used to make the observation and the shape of the object's spectrum. If multi-color photometric measurements are available for a given object thus defining its spectral energy distribution (SED), K corrections then can be computed by fitting it against a theoretical or empirical SED template.^[5] It has been shown that K corrections in many frequently used broad-band filters for low-redshift galaxies can be precisely approximated using two-dimensional polynomials as functions of a redshift and one observed color.^[6] This approach is implemented in the K corrections calculator web-service.^[7]