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23-399: With the index γ {\displaystyle \gamma } approximately equal to 4. In 1962, Rudolph Minkowski had discovered and wrote that a "correlation between velocity dispersion and [luminosity] exists, but it is poor" and that "it seems important to extend the observations to more objects, especially at low and medium absolute magnitudes". This was important because

46-541: A Hubble age of around 20 billion years. At the time, many, especially Sandage, believed that the cosmological constant was zero. In such a case, a low Hubble constant is necessary in order for the age of the universe (as opposed to the Hubble age ) to be at least as old as the oldest objects it contains, i.e. ca. 14 billion years. Sandage performed photometric studies of globular clusters , and calculated their age to be at least 25 billion years. This led him to speculate that

69-791: A PhD from the California Institute of Technology ; the German -born Wilson Observatory-based astronomer Walter Baade was his advisor. During this time Sandage was a graduate student assistant to cosmologist Edwin Hubble . He continued Hubble's research program after Hubble died in 1953. In 1952 Baade surprised his fellow astronomers by announcing (at the 1952 Conference of the International Astronomical Union , in Rome) his determination of two separate populations of Cepheid variable stars in

92-452: A galaxy, which is otherwise hard to obtain, by relating it to more easily observable properties of the galaxy. In the case of elliptical galaxies, if one can measure the central stellar velocity dispersion, which can be done relatively easily by using spectroscopy to measure the Doppler shift of light emitted by the stars, then one can obtain an estimate of the true luminosity of the galaxy via

115-407: Is a totally unjustified assumption) to get Using this and combining it with the relation between R {\displaystyle R} and L {\displaystyle L} , this results in and by rewriting the above expression, we finally obtain the relation between luminosity and velocity dispersion: that is Given that massive galaxies originate from homologous merging, and

138-590: Is as a tool for determining distances to external galaxies. The gravitational potential of a mass distribution of radius R {\displaystyle R} and mass M {\displaystyle M} is given by the expression: Where α is a constant depending e.g. on the density profile of the system and G is the gravitational constant . For a constant density, α   = 3 5 {\displaystyle \alpha \ ={\frac {3}{5}}} The kinetic energy is: (Recall σ {\displaystyle \sigma }

161-501: Is the 1-dimensional velocity dispersion. Therefore, 3 σ 2 = V 2 {\displaystyle 3\sigma ^{2}=V^{2}} .) From the virial theorem ( 2 K + U = 0 {\displaystyle 2K+U=0} ) it follows If we assume that the mass to light ratio, M / L {\displaystyle M/L} , is constant, e.g. M ∝ L {\displaystyle M\propto L} we can use this and

184-472: The Andromeda Galaxy , resulted in a doubling of the estimated age of the universe (from 1.8 to 3.6 billion years). Hubble had posited the earlier value; he had considered only the weaker Population II Cepheid variables as standard candles . After Baade's pronouncements, Sandage showed that astronomers' previous assumption, that the brightest stars in galaxies were of approximately equal inherent intensity,

207-474: The National Geographic Society – Palomar Observatory Sky Survey , a photographic atlas of the entire northern sky (and south to declination -22°) down to an apparent magnitude of 22. Together with Albert George Wilson , he co-discovered the near-Earth Apollo asteroid 1620 Geographos in 1951, and he also discovered Planetary Nebula M2-9 . He additionally discovered a correlation between

230-892: The Faber–Jackson relation. This can be compared to the apparent magnitude of the galaxy, which provides an estimate of the distance modulus and, hence, the distance to the galaxy. By combining a galaxy's central velocity dispersion with measurements of its central surface brightness and radius parameter, it is possible to improve the estimate of the galaxy's distance even more. This standard yardstick, or "reduced galaxian radius-parameter", r g {\displaystyle r_{g}} , devised by Gudehus in 1991, can yield distances, free of systematic bias, accurate to about 31%. Rudolph Minkowski Rudolph Minkowski (born Rudolf Leo Bernhard Minkowski / m ɪ ŋ ˈ k ɔː f s k i , - ˈ k ɒ f -/ ; German: [mɪŋˈkɔfski] ; May 28, 1895 – January 4, 1976)

253-431: The above expression to obtain a relation between R {\displaystyle R} and σ 2 {\displaystyle \sigma ^{2}} : Let us introduce the surface brightness, B = L / ( 4 π R 2 ) {\displaystyle B=L/(4\pi R^{2})} and assume this is a constant (which from a fundamental theoretical point of view,

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276-488: The collapse of a proto-galactic gas cloud into our present Milky Way Galaxy. He later defended the paper in 1990. In his 1961 paper "The Ability of the 200-inch Telescope to Discriminate Between Selected World Models," he suggested that the future of observational cosmology would be the search for two parameters: the Hubble constant H 0 and the deceleration parameter q 0 . This paper influenced observational cosmology for at least three decades as it carefully specified

299-608: The core of the so-called Cigar Galaxy . These must have been caused by massive explosions in the core, and they have apparently been occurring for at least 1.5 million years. Sandage was a prolific researcher; during his career he published more than 500 papers. Until his death he continued to be an active researcher at the Carnegie Observatories , still publishing several papers a year. In 1959, Sandage married Mary Connelley, also an astronomer, with whom he had two sons, David and John. In 1983 Sandage announced he had become

322-502: The cosmological distance scale, ranging from calibrators within our own Milky Way Galaxy, to cosmologically distant galaxies. Sandage began working at the Palomar Observatory . In 1958 he published the first good estimate for the Hubble constant , revising Hubble's value of 250 down to 75 km/s/Mpc, which is close to today's accepted value. Later he became the chief advocate of an even lower value, around 50, corresponding to

345-605: The fainter ones from dissipation, the assumption of constant surface brightness can no longer be supported. Empirically, surface brightness exhibits a peak at about M V = − 23 {\displaystyle M_{V}=-23} . The revised relation then becomes for the less massive galaxies, and for the more massive ones. With these revised formulae, the fundamental plane splits into two planes inclined by about 11 degrees to each other. Even first-ranked cluster galaxies do not have constant surface brightness. A claim supporting constant surface brightness

368-551: The luminosity of early-type galaxies and their velocity dispersion , which was later quantified by Faber and Jackson . He won the Bruce Medal in 1961. The lunar crater Minkowski is named after him and his uncle. In the 1940's he created a catalog of nearly 200 planetary nebulae, including Minkowski 2-9 , and a dwarf galaxy near NGC 541 , known as Minkowski's object , is named after him. Allan R. Sandage Allan Rex Sandage (June 18, 1926 – November 13, 2010)

391-415: The types of observational tests that could be performed with a large telescope. He also published two atlases of galaxies, in 1961 and 1981, based on the Hubble classification scheme. In 1962 Sandage studied the possibility of directly measuring the temporal variation of the redshift of extra-galactic sources. This analysis became known as the "Sandage–Loeb test". Sandage discovered jets erupting from

414-446: The universe did not merely expand, but actually expanded and contracted with a period of 80 billion years. The current cosmological estimates of the age of the universe, in contrast, are typically of the order of 14 billion years. As part of his studies concerning the formation of galaxies in the early universe, he co-wrote the paper now referred to as ELS after the authors Olin J. Eggen , Donald Lynden-Bell and Sandage, first describing

437-451: The value of γ {\displaystyle \gamma } depends on the range of galaxy luminosities that is fitted, with a value of 2 for low-luminosity elliptical galaxies discovered by a team led by Roger Davies , and a value of 5 reported by Paul L. Schechter for luminous elliptical galaxies. The Faber–Jackson relation is understood as a projection of the fundamental plane of elliptical galaxies. One of its main uses

460-510: Was a German-American astronomer . Minkowski was the son of Marie Johanna Siegel and physiologist Oskar Minkowski . His uncle was Hermann Minkowski , a mathematician and one of Einstein's teachers in Zürich. Rudolph studied supernovae and, together with Walter Baade , divided them into two classes ( Type I and Type II ) based on their spectral characteristics. He and Baade also found optical counterparts to various radio sources. He headed

483-587: Was an American astronomer . He was Staff Member Emeritus with the Carnegie Observatories in Pasadena, California . He determined the first reasonably accurate values for the Hubble constant and the age of the universe . Sandage was one of the most influential astronomers of the 20th century. He was born in Iowa City, Iowa , United States . He graduated from the University of Illinois in 1948. In 1953 he received

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506-417: Was mistaken in the case of H II regions which he found not to be stars and inherently brighter than the brightest stars in distant galaxies. This resulted in another 1.5-fold increase in the calculated age of the universe, to approximately 5.5 billion years. Throughout the 1950s and well into the 1980s Sandage was regarded as the pre-eminent observational cosmologist , making contributions to all aspects of

529-458: Was presented by astronomer Allan R. Sandage in 1972 based on three logical arguments and his own empirical data. In 1975, Donald Gudehus showed that each of the logical arguments was incorrect and that first-ranked cluster galaxies exhibited a standard deviation of about half a magnitude. Like the Tully–Fisher relation, the Faber–Jackson relation provides a means of estimating the distance to

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