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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 distance and d_A the angular-diameter distance. History and derivations When Ivor Etherington introduced this equation in 1933, he mentioned that this equation was proposed by Tolman as a way to test a cosmological model. Ellis proposed a proof of this equation in the context of Riemannian geometry. A quote from Ellis: "The core of the reciprocity theorem is the fact that many geometric properties are invariant when the roles of the source and observer in astronomical observations are transposed". This statement is fundamental in the derivation of the reciprocity theorem. Validation from astronomical observations The Etherington's distance-duality equation has been validated from astronomical observations based on the X-ray surface bright ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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_\!\, which gives: : D_L = 10^ 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 = \frac where is flux (W·m−2), and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Candle
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible only for those objects that are "close enough" (within about a thousand parsecs) to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances and methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity. The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 cosmology of the universe. The angular diameter distance to an object at redshift, z , is expressed in terms of the comoving distance, r as: d_A = \frac where S_k(r) is the FLRW coordinate defined as: S_k(r) = \begin \sin \left( \sqrt H_0 r \right)/\left(H_0\sqrt\right) & \Omega_k 0 \end where \Omega_k is the curvature density and H_0 is the value of the Hubble parameter today. In the currently favoured geometric model of our Universe, the "angular diameter distance" of an object is a good approximation to the "real distance", i.e. the proper distance when the light left the object. Angular size redshift relation The angular size redshift relation describes the relation between the angular size observed on the sky of an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ivor Etherington
Ivor Malcolm Haddon Etherington FRSE (8 February 1908 -1 January 1994) was a mathematician who worked initially on general relativity, and later on genetics and introduced genetic algebras. Life He was born in Lewisham in London the son of Annie Margaret and her husband Bruce Etherington, both of whom were Baptist missionaries normally based in Ceylon. His father had died in Ceylon, leaving his mother and two older siblings to return to Britain alone. His mother remarried in 1913 to Edwin Duncombe de Russet, a Baptist minister, but Ivor retained his original name. In 1921 the growing family moved out of London to Thorpe Bay on the Essex coast, where his father then founded the Thorpe Bay School for Boys. In 1922 Ivor was sent back to London to be educated at Mill Hill School. He was later educated at the University of Oxford and continued as a postgraduate at the University of Edinburgh where he received his doctorate. He later became a professor of mathematics at the same unive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemannian Geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture "''Ueber die Hypothesen, welche der Geometrie zu Grunde liegen''" ("On the Hypotheses on which Geometry is Based.") It is a very broad and abstract generalization of the differential geometry of surfaces in R3. Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galaxy Cluster
A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-largest known gravitationally bound structures in the universe after galaxy filaments and were believed to be the largest known structures in the universe until the 1980s, when superclusters were discovered. One of the key features of clusters is the intracluster medium (ICM). The ICM consists of heated gas between the galaxies and has a peak temperature between 2–15 keV that is dependent on the total mass of the cluster. Galaxy clusters should not be confused with ''galactic clusters'' (also known as open clusters), which are star clusters ''within'' galaxies, or with globular clusters, which typically orbit galaxies. Small aggregates of galaxies are referred to as galaxy groups rather than clusters of galaxies. The galaxy groups and c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance Measures (cosmology)
Distance measures are used in physical cosmology to give a natural notion of the distance between two objects or events in the universe. They are often used to tie some ''observable'' quantity (such as the luminosity of a distant quasar, the redshift of a distant galaxy, or the angular size of the acoustic peaks in the cosmic microwave background (CMB) power spectrum) to another quantity that is not ''directly'' observable, but is more convenient for calculations (such as the comoving coordinates of the quasar, galaxy, etc.). The distance measures discussed here all reduce to the common notion of Euclidean distance at low redshift. In accord with our present understanding of cosmology, these measures are calculated within the context of general relativity, where the Friedmann–Lemaître–Robertson–Walker solution is used to describe the universe. Overview There are a few different definitions of "distance" in cosmology which are all asymptotic one to another for small re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
