# Astronomy: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, DL 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]

## References

1. Wirtz, V.C. (1918). "Über die Bewegungen der Nebelflecke". Astronomische Nachrichten 206 (13): 109–116. doi:10.1002/asna.19182061302. Bibcode1918AN....206..109W.
2. Hubble, Edwin (1936). "Effects of Red Shifts on the Distribution of Nebulae". Astrophysical Journal 84: 517–554. doi:10.1086/143782. Bibcode1936ApJ....84..517H.
3. Kinney, Anne; Calzetti, Daniela; Bohlin, Ralph C.; McQuade, Kerry; Storchi-Bergmann, Thaisa; Schmitt, Henrique R. (1996). "Template ultraviolet spectra to near-infrared spectra of star-forming galaxies and their application to K-corrections". Astrophysical Journal 467: 38–60. doi:10.1086/177583. Bibcode1996ApJ...467...38K.
4. Hogg, David (2002). "The K Correction". arXiv:astro-ph/0210394.
5. Blanton, Michael R.; Roweis, Sam (2007). "K-corrections and filter transformations in the ultraviolet, optical, and near infrared". The Astronomical Journal 133 (2): 734–754. doi:10.1086/510127. Bibcode2007AJ....133..734B.
6. Chilingarian, Igor V.; Melchior, Anne-Laure; Zolotukhin, Ivan Yu. (2010). "Analytical approximations of K-corrections in optical and near-infrared bands". Monthly Notices of the Royal Astronomical Society 405 (3): 1409. doi:10.1111/j.1365-2966.2010.16506.x. Bibcode2010MNRAS.405.1409C.