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 $K$ to represent the reduction factor in magnitude due to this effect. Yet Kinney et al., in footnote 7 on page 48 of their article, note an earlier origin from Carl Wilhelm Wirtz (1918), who referred to the correction as a Konstante (German for "constant"), hence K-correction.

The K-correction can be defined as follows

$M = m - 5 (\log_{10}{D_L} - 1) - K_{Corr}\!\,$

I.E. the adjustment to the standard relationship between absolute and apparent magnitude required to correct for the redshift effect.

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 can be precisely approximated using two-dimensional polynomials as functions of a redshift and one observed color. This approach is implemented in the K corrections calculator web-service.

External links

• K Correction plots