Astronomy & Celestial Mechanics
the sky, computed
Concept

K-correction — where it appears

The correction that converts a magnitude measured through a fixed filter into the magnitude the source would have had in its own rest frame. It depends on the source's spectrum, which is usually what the photometry was meant to determine.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Four distances to the same galaxy. Four quantities all called "the distance", against redshift, at a Hubble constant of 67.36 km/s/Mpc, a matter density parameter of 0.3153 and a dark-energy parameter of 0.6847. They agree below z ≈ 0.1 and then part company completely. Comoving distance is the separation now, and it is what a map of the universe is drawn in. Luminosity distance is what a brightness gives, and it is larger by (1+z) because the photons arrive both redshifted and spread out in time. Light-travel distance is the age difference times c, and it is bounded by the age of the universe. Angular-diameter distance is what an angle gives, and it is the odd one: it rises, turns over at z = 1.59 where it reaches 1.79 Gpc, and falls thereafter. Past that redshift a galaxy of fixed size looks bigger the further away it is, because the universe it is being seen across was smaller when the light left it. At z = 10 the four differ by a factor of 121 between the largest and the smallest, so a sentence quoting a cosmological distance without saying which one has not given a number.

Four distances to the same galaxy

Inside the Local Group the word "distance" has one meaning. Past a redshift of about a tenth it has four, they disagree by factors of a hundred by the time the light is old, and one of them stops increasing and starts coming back.

cosmology · Distance ladder Four spectra, and 3.9 magnitudes between them at the same redshift. The K-correction — the magnitude that has to be added to compare a redshifted object with a nearby one through the same filter — against redshift, for four power-law spectra. At zero redshift every correction is zero by construction. Beyond that they diverge, because a filter at a fixed observed wavelength samples a different part of the source's own spectrum at every redshift, and how much flux is there depends on the spectrum. A flat spectrum needs no correction at all at any redshift, and the two extremes drawn differ by 3.9 magnitudes by z = 1.2. The circularity is the point: applying the correction requires the spectrum, and the spectrum is what a magnitude is being used to constrain. The dashed line is the way out — observe in a band chosen so that it lands on the rest-frame band of interest, and the spectral term cancels, leaving only the bandwidth stretch.

A magnitude in a band the source never had

A filter passes light at a fixed observed wavelength, and a redshifted source emitted that light at a shorter one. Comparing a distant galaxy with a nearby one through the same filter therefore compares two different parts of two spectra — and the correction between them needs the spectrum, which is what the magnitude was going to be used to find out.

starlight · Magnitudes

Named alongside it

The objects these essays reach for when they reach for this one.

Luminosity distanceAngular-diameter distanceBandpassBandwidth stretchCircular inferenceComoving distanceCosmological distancesCross filter photometryDistance dualityLight-travel timeLookback timeProper distance

All concepts