Luminosity distance DL is defined in terms of the relationship between the
absolute magnitudeIn astronomy, absolute magnitude measures a celestial object's intrinsic brightness. To derive the absolute magnitude from the observed apparent magnitude of a celestial object its value is corrected for distance to the observer...
M and
apparent magnitudeThe apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, normalized to the value it would have in the absence of the atmosphere...
m of an astronomical object.
which gives:
where
DL is measured in
parsecThe parsec is a unit of length, equal to just under 31 million million kilometres , or about 3.26 light-years. The parsec measurement unit is used in astronomy and is defined as the length of the adjacent side of an imaginary right triangle in space...
s. For nearby objects (say, in the
Milky WayThe Milky Way, or simply the Galaxy, is the galaxy in which the Solar System is located. It is a barred spiral galaxy that is part of the Local Group of galaxies...
) the luminosity distance gives a good approximation to the natural notion of distance in
Euclidean spaceIn mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions higher dimensions...
.
The relation is less clear for distant objects like
quasarA quasi-stellar radio source is a powerfully energetic and distant galaxy with an active galactic nucleus. Quasars were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than extended...
s far beyond the
Milky WayThe Milky Way, or simply the Galaxy, is the galaxy in which the Solar System is located. It is a barred spiral galaxy that is part of the Local Group of galaxies...
since the apparent magnitude is affected by
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions...
curvatureIn mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
,
redshiftIn physics and astronomy, redshift occurs when electromagnetic radiation—usually visible light—emitted or reflected by an object is shifted towards the red end of the electromagnetic spectrum due to the Doppler effect or other gravitationally-induced effects...
, and
time dilationTime dilation is a phenomenon described by the theory of relativity. It can be illustrated by supposing that two observers are in motion relative to each other, and/or differently situated with regard to nearby gravitational masses. They each carry a clock of identically similar construction and...
.
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Luminosity distance DL is defined in terms of the relationship between the
absolute magnitudeIn astronomy, absolute magnitude measures a celestial object's intrinsic brightness. To derive the absolute magnitude from the observed apparent magnitude of a celestial object its value is corrected for distance to the observer...
M and
apparent magnitudeThe apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, normalized to the value it would have in the absence of the atmosphere...
m of an astronomical object.
which gives:
where
DL is measured in
parsecThe parsec is a unit of length, equal to just under 31 million million kilometres , or about 3.26 light-years. The parsec measurement unit is used in astronomy and is defined as the length of the adjacent side of an imaginary right triangle in space...
s. For nearby objects (say, in the
Milky WayThe Milky Way, or simply the Galaxy, is the galaxy in which the Solar System is located. It is a barred spiral galaxy that is part of the Local Group of galaxies...
) the luminosity distance gives a good approximation to the natural notion of distance in
Euclidean spaceIn mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions higher dimensions...
.
The relation is less clear for distant objects like
quasarA quasi-stellar radio source is a powerfully energetic and distant galaxy with an active galactic nucleus. Quasars were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than extended...
s far beyond the
Milky WayThe Milky Way, or simply the Galaxy, is the galaxy in which the Solar System is located. It is a barred spiral galaxy that is part of the Local Group of galaxies...
since the apparent magnitude is affected by
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions...
curvatureIn mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
,
redshiftIn physics and astronomy, redshift occurs when electromagnetic radiation—usually visible light—emitted or reflected by an object is shifted towards the red end of the electromagnetic spectrum due to the Doppler effect or other gravitationally-induced effects...
, and
time dilationTime dilation is a phenomenon described by the theory of relativity. It can be illustrated by supposing that two observers are in motion relative to each other, and/or differently situated with regard to nearby gravitational masses. They each carry a clock of identically similar construction and...
. Calculating the relation between the luminosity distance and, for example, redshift of an object requires taking all of these factors into account.
Another way to express the luminosity distance is through the flux-luminosity relationship. Since,
where F is flux , and L is Luminosity . From this the luminosity distance can be expressed as:
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