K correction

{{Short description|Formula for measuring astronomical objects}}

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),{{cite journal|last=Wirtz|first=V.C.|date=1918|title=Über die Bewegungen der Nebelflecke|url=https://zenodo.org/record/1424916|journal=Astronomische Nachrichten|volume=206|issue=13|pages=109–116|bibcode=1918AN....206..109W|doi=10.1002/asna.19182061302}} 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 $K$ 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.{{cite journal | title=Effects of Red Shifts on the Distribution of Nebulae | authorlink=Edwin Hubble | first=Edwin | last=Hubble | date=1936 | journal=Astrophysical Journal | volume=84 | pages=517–554 | doi=10.1086/143782 | bibcode=1936ApJ....84..517H| pmc=}} {{cite journal|last1=Kinney|first1=Anne|last2=Calzetti|first2=Daniela|author2-link=Daniela Calzetti|last3=Bohlin|first3=Ralph C.|last4=McQuade|first4=Kerry|last5=Storchi-Bergmann|first5=Thaisa|last6=Schmitt|first6=Henrique R.|date=1996|title=Template ultraviolet spectra to near-infrared spectra of star-forming galaxies and their application to K-corrections|url=https://lume.ufrgs.br/bitstream/10183/108772/1/000177101.pdf|journal=Astrophysical Journal|volume=467|pages=38–60|bibcode=1996ApJ...467...38K|doi=10.1086/177583|hdl-access=free|hdl=10183/108772}}

The K-correction can be defined as follows

:$M\; =\; m\; -\; 5\; (\backslash log\_\{10\}\{D\_L\}\; -\; 1)\; -\; K\_\{Corr\}\backslash !\backslash ,$

I.E. the adjustment to the standard relationship between absolute and apparent magnitude required to correct for the redshift effect.{{cite arXiv|last=Hogg|first=David|title=The K Correction|eprint=astro-ph/0210394|year=2002}} 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.{{cite journal|arxiv=astro-ph/0606170|title=K-corrections and filter transformations in the ultraviolet, optical, and near infrared|journal=The Astronomical Journal|volume=133|issue=2|pages=734–754|bibcode=2007AJ....133..734B|last1=Blanton|first1=Michael R.|last2=Roweis|first2=Sam|date=2007|doi=10.1086/510127|s2cid=18561804 }} 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.{{cite journal|arxiv=1002.2360|title=Analytical approximations of K-corrections in optical and near-infrared bands|journal=Monthly Notices of the Royal Astronomical Society|volume=405|issue=3|pages=1409|bibcode=2010MNRAS.405.1409C|last1=Chilingarian|first1=Igor V.|last2=Melchior|first2=Anne-Laure|last3=Zolotukhin|first3=Ivan Yu.|date=2010|doi=10.1111/j.1365-2966.2010.16506.x|doi-access=free |s2cid=56310457 }} This approach is implemented in the K corrections calculator web-service.{{cite web|url=http://kcor.sai.msu.ru|title=K-corrections calculator}}