K correction
Encyclopedia
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 wavelength
s (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
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 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 polynomial
s as functions of a redshift
and one observed color
. This approach is implemented in the K corrections calculator web-service.
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
object's magnitude
Magnitude (astronomy)
Magnitude is the logarithmic measure of the brightness of an object, in astronomy, measured in a specific wavelength or passband, usually in optical or near-infrared wavelengths.-Background:...
(or equivalently, its flux
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
) that allows a measurement of a quantity of light from an object at a redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
z to be converted to an equivalent measurement in the rest frame
Rest frame
In special relativity the rest frame of a particle is the coordinate system in which the particle is at rest.The rest frame of compound objects is taken to be the frame of reference in which the average momentum of the particles which make up the substance is zero In special relativity the rest...
of the object. If one could measure all the light from an object at all wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s (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
Filter (optics)
Optical filters are devices which selectively transmit light of different wavelengths, usually implemented as plane glass or plastic devices in the optical path which are either dyed in the mass or have interference coatings....
or a single bandpass only sees a fraction of the total spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...
, 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
Edwin Hubble
Edwin Powell Hubble was an American astronomer who profoundly changed the understanding of the universe by confirming the existence of galaxies other than the Milky Way - our own galaxy...
, who supposedly arbitrarily chose
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 WirtzCarl Wilhelm Wirtz
Carl Wilhelm Wirtz was an astronomer who spent his time between Germany and the Observatory of Strasbourg....
(1918), who referred to the correction as a Konstante (German for "constant"), hence K-correction.
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
Photometry (astronomy)
Photometry is a technique of astronomy concerned with measuring the flux, or intensity of an astronomical object's electromagnetic radiation...
measurements are available for a given object thus defining its spectral energy distribution (SED
Spectral Energy Distribution
A spectral energy distribution is a plot of brightness or flux density versus frequency or wavelength of light. It is used in many branches of astronomy to characterize astronomical sources. For example, in radio astronomy, an SED with a negative spectral index around −0.7 would indicate a...
), K corrections then can be computed by fitting
Curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function...
it against a theoretical or empirical SED
Spectral Energy Distribution
A spectral energy distribution is a plot of brightness or flux density versus frequency or wavelength of light. It is used in many branches of astronomy to characterize astronomical sources. For example, in radio astronomy, an SED with a negative spectral index around −0.7 would indicate a...
template. It has been shown, that K corrections in many frequently used broad-band filters for low-redshift galaxies
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
can be precisely approximated using two-dimensional polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
s as functions of a redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
and one observed color
Color index
In astronomy, the color index is a simple numerical expression that determines the color of an object, which in the case of a star gives its temperature...
. This approach is implemented in the K corrections calculator web-service.