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.[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
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]