K correction converts measurements of

astronomical Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest include ...

objects into their respective rest frames. The correction acts on that object's observed

magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...

(or equivalently, its

flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications in physics. For transport phe ...

). Because astronomical observations often measure through a single filter or bandpass, observers only measure a fraction of the total

spectrum A spectrum (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...

redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and e ...

ed 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

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

s 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 A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...

. Carl Wilhelm Wirtz (1918), 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 Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects previously ...

, 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. The K-correction can be defined as follows :

M = m - 5 (\log_ - 1) - K_\!\,

I.E. the adjustment to the standard relationship between

absolute Absolute may refer to: Companies * Absolute Entertainment, a video game publisher * Absolute Radio, (formerly Virgin Radio), independent national radio station in the UK * Absolute Software Corporation, specializes in security and data risk ma ...

and apparent magnitude required to correct for the redshift effect. Here, D_L is the

luminosity distance Luminosity distance ''DL'' is defined in terms of the relationship between the absolute magnitude ''M'' and apparent magnitude ''m'' of an astronomical object. : M = m - 5 \log_\!\, which gives: : D_L = 10^ where ''DL'' is measured in parsecs. ...

measured in

parsecs The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (AU), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...

. 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. It has been shown that K corrections in many frequently used broad-band filters for low-redshift

galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar Sys ...

can be precisely approximated using two-dimensional

polynomial In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...

s as functions of a

and one observed

color Color (or colour in English in the Commonwealth of Nations, Commonwealth English; American and British English spelling differences#-our, -or, see spelling differences) is the visual perception based on the electromagnetic spectrum. Though co ...

. This approach is implemented in the K corrections calculator web-service.

References

External links

Basic concept of obtaining K corrections
* {{cite journal, arxiv=astro-ph/0210394, title=The K correction, bibcode = 2002astro.ph.10394H , last1=Hogg, first1=David W., last2=Baldry, first2=Ivan K., last3=Blanton, first3=Michael R., last4=Eisenstein, first4=Daniel J., year=2002 Astrophysics Doppler effects