# 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 [math]\displaystyle{ K }[/math] 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

- [math]\displaystyle{ M = m - 5 (\log_{10}{D_L} - 1) - K_{Corr}\!\, }[/math]

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]}

## References

- ↑ Wirtz, V.C. (1918). "Über die Bewegungen der Nebelflecke".
*Astronomische Nachrichten***206**(13): 109–116. doi:10.1002/asna.19182061302. Bibcode: 1918AN....206..109W. https://zenodo.org/record/1424916. - ↑ Hubble, Edwin (1936). "Effects of Red Shifts on the Distribution of Nebulae".
*Astrophysical Journal***84**: 517–554. doi:10.1086/143782. Bibcode: 1936ApJ....84..517H. - ↑ 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. Bibcode: 1996ApJ...467...38K. https://lume.ufrgs.br/bitstream/10183/108772/1/000177101.pdf. - ↑ Hogg, David (2002). "The K Correction". arXiv:astro-ph/0210394.
- ↑ 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. Bibcode: 2007AJ....133..734B. - ↑ 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. Bibcode: 2010MNRAS.405.1409C. - ↑ "K-corrections calculator". http://kcor.sai.msu.ru.

## External links

- Basic concept of obtaining K corrections
- Hogg, David W.; Baldry, Ivan K.; Blanton, Michael R.; Eisenstein, Daniel J. (2002).
*The K correction*. Bibcode: 2002astro.ph.10394H.

Original source: https://en.wikipedia.org/wiki/K correction.
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