# K correction

K correction is a correction to an astronomical object's magnitude (or equivalently, its flux) that allows a measurement of a quantity of light from an object at a redshift z to be converted to an equivalent measurement in the rest frame of the object. If one could measure all the light from an object at all wavelengths (a bolometric flux), a K correction would not be required. If one measures the light emitted in an emission line, a K-correction is not required. The need for a K-correction arises because an astronomical measurement through a single filter or a single bandpass only sees a fraction of the total spectrum, redshifted into the frame of the observer. So if the observer wants to compare the measurements through a red filter of objects at different redshifts, the observer will have to apply estimates of the K corrections to these measurements to make a comparison.

One 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 effect.[1] Yet Kinney et al., in footnote 7 on page 48 of their article,[2] note an earlier origin from Carl Wilhelm Wirtz (1918),[3] who referred to the correction as a Konstante (German for "constant"), hence K-correction.

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. ^ Hubble, Edwin (1936). "Effects of Red Shifts on the Distribution of Nebulae". Astrophysical Journal. 84: 517–554. Bibcode:1936ApJ....84..517H. doi:10.1086/143782.
2. ^ 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. Bibcode:1996ApJ...467...38K. doi:10.1086/177583.
3. ^ Wirtz, V.C. (1918). "Über die Bewegungen der Nebelflecke". Astronomische Nachrichten. 206 (13): 109. Bibcode:1918AN....206..109W. doi:10.1002/asna.19182061302.
4. ^ Hogg, David. "The K Correction".
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. arXiv:. Bibcode:2007AJ....133..734B. doi:10.1086/510127.
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: 1409. arXiv:. Bibcode:2010MNRAS.405.1409C. doi:10.1111/j.1365-2966.2010.16506.x.
7. ^