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]

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

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