Luminosity distance ''D_L'' is defined in terms of the relationship between the

absolute magnitude Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse Logarithmic scale, logarithmic Magnitude (astronomy), astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent mag ...

''M'' and

apparent magnitude Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's li ...

''m'' of an astronomical object. :

M = m - 5 \log_\!\,

which gives: :

D_L = 10^

where ''D_L'' is measured in

parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...

s. For nearby objects (say, in the

Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...

) the luminosity distance gives a good approximation to the natural notion of distance in

Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics ther ...

. The relation is less clear for distant objects like

quasar A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...

s far beyond the

since the apparent magnitude is affected by

spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...

curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonic ...

redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in f ...

, and

time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...

. Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account. The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance. Another way to express the luminosity distance is through the flux-luminosity relationship, :

F = \frac

where is

flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

(W·m⁻²), and is

luminosity Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a st ...

(W). From this the luminosity distance (in meters) can be expressed as: :

D_L = \sqrt

The luminosity distance is related to the "comoving transverse distance"

D_M

by :

D_L = (1 + z) D_M

and with the

angular diameter distance In astronomy, angular diameter distance is a distance defined in terms of an object's physical size, x, and its angular size, \theta, as viewed from Earth: d_A= \frac Cosmology dependence The angular diameter distance depends on the assumed cos ...

D_A

by the

Etherington's reciprocity theorem The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular diameter distance. The equation is as follows: d_L=(1+z)^2 d_A, where z is the redshift, d_L is the luminosity dista ...

: :

D_L = (1 + z)^2 D_A

where ''z'' is the

D_M

is a factor that allows calculation of the

comoving distance In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''Proper distance'' roughly corresponds to where a distant object would be at a spec ...

between two objects with the same redshift but at different positions of the sky; if the two objects are separated by an angle

\delta \theta

, the comoving distance between them would be

D_M \delta \theta

. In a spatially flat universe, the comoving transverse distance

D_M

is exactly equal to the radial comoving distance

D_C

, i.e. the comoving distance from ourselves to the object.

Notes

{{reflist

External links

Ned Wright's Javascript Cosmology Calculator

iCosmos: Cosmology Calculator (With Graph Generation )
Observational astronomy Physical quantities

See also

Notes

External links