K correction converts measurements of

astronomical Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxi ...

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). Because astronomical observations often measure through a single

filter Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component tha ...

or bandpass, observers only measure a fraction of the total

spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...

, 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

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...

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 dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to identi ...

Carl Wilhelm Wirtz Carl Wilhelm Wirtz (24 August 1876 in Krefeld – 18 February 1939 in Hamburg) was an astronomer who spent his time between the Kiel Observatory in Germany and the Observatory of Strasbourg, France. He is known for statistically showing the exis ...

(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, 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 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. F ...

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 sed ("stream editor") is a Unix utility that parses and transforms text, using a simple, compact programming language. It was developed from 1973 to 1974 by Lee E. McMahon of Bell Labs, and is available today for most operating systems. sed w ...

), K corrections then can be computed by fitting it against a theoretical or empirical

template. 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

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example ...

s as functions of a redshift and one observed

color Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are assoc ...

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

References

External links

Basic concept of obtaining K corrections
* {{DEFAULTSORT:K Correction Astrophysics Doppler effects