- Source: Luminosity distance
Luminosity distance DL is defined in terms of the relationship between the absolute magnitude M and apparent magnitude m of an astronomical object.
M
=
m
−
5
log
10
D
L
10
pc
{\displaystyle M=m-5\log _{10}{\frac {D_{L}}{10\,{\text{pc}}}}\!\,}
which gives:
D
L
=
10
(
m
−
M
)
5
+
1
{\displaystyle D_{L}=10^{{\frac {(m-M)}{5}}+1}}
where DL is measured in parsecs. For nearby objects (say, in the Milky Way) the luminosity distance gives a good approximation to the natural notion of distance in Euclidean space.
The relation is less clear for distant objects like quasars far beyond the Milky Way since the apparent magnitude is affected by spacetime curvature, redshift, and time dilation. 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
=
L
4
π
D
L
2
{\displaystyle F={\frac {L}{4\pi D_{L}^{2}}}}
where F is flux (W·m−2), and L is luminosity (W). From this the luminosity distance (in meters) can be expressed as:
D
L
=
L
4
π
F
{\displaystyle D_{L}={\sqrt {\frac {L}{4\pi F}}}}
The luminosity distance is related to the "comoving transverse distance"
D
M
{\displaystyle D_{M}}
by
D
L
=
(
1
+
z
)
D
M
{\displaystyle D_{L}=(1+z)D_{M}}
and with the angular diameter distance
D
A
{\displaystyle D_{A}}
by the Etherington's reciprocity theorem:
D
L
=
(
1
+
z
)
2
D
A
{\displaystyle D_{L}=(1+z)^{2}D_{A}}
where z is the redshift.
D
M
{\displaystyle D_{M}}
is a factor that allows calculation of the comoving distance between two objects with the same redshift but at different positions of the sky; if the two objects are separated by an angle
δ
θ
{\displaystyle \delta \theta }
, the comoving distance between them would be
D
M
δ
θ
{\displaystyle D_{M}\delta \theta }
. In a spatially flat universe, the comoving transverse distance
D
M
{\displaystyle D_{M}}
is exactly equal to the radial comoving distance
D
C
{\displaystyle D_{C}}
, i.e. the comoving distance from ourselves to the object.
See also
Distance measure
Distance modulus
Notes
External links
Ned Wright's Javascript Cosmology Calculator
iCosmos: Cosmology Calculator (With Graph Generation )
Kata Kunci Pencarian:
- Galaksi Sombrero
- NGC 4993
- NGC 3982
- S Persei
- Bintang
- Zeta Geminorum
- NGC 55
- Messier 58
- Galaksi Pusaran
- Variabel Cepheid
- Luminosity distance
- Luminosity
- Distance measure
- Cosmic distance ladder
- Solar luminosity
- Absolute magnitude
- 3C 273
- List of common astronomy symbols
- Mass–luminosity relation
- Apparent magnitude
