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Fundamental Plane (elliptical Galaxies)
The fundamental plane is a set of bivariate correlations connecting some of the properties of normal elliptical galaxies. Some correlations have been empirically shown. The fundamental plane is usually expressed as a relationship between the effective radius, average surface brightness and central velocity dispersion of normal elliptical galaxies. Any one of the three parameters may be estimated from the other two, as together they describe a plane that falls within their more general three-dimensional space. Properties correlated also include: color, density (of luminosity, mass, or phase space), luminosity, mass, metallicity, and, to a lesser degree, the shape of their radial surface brightness profiles. Motivation Many characteristics of a galaxy are correlated. For example, as one would expect, a galaxy with a higher luminosity has a larger effective radius. The usefulness of these correlations is when a characteristic that can be determined without prior knowledge of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bivariate Data
In statistics, bivariate data is data on each of two variables, where each value of one of the variables is paired with a value of the other variable. Typically it would be of interest to investigate the possible association between the two variables. The association can be studied via a tabular or graphical display, or via sample statistics which might be used for inference. The method used to investigate the association would depend on the level of measurement of the variable. This association that involves exactly two variables can be termed a bivariate correlation, or bivariate association. For two quantitative variables (interval or ratio in level of measurement) a scatterplot can be used and a correlation coefficient or regression model can be used to quantify the association. For two qualitative variables (nominal or ordinal in level of measurement) a contingency table can be used to view the data, and a measure of association or a test of independence could be used. If ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptical Galaxies
An elliptical galaxy is a type of galaxy with an approximately ellipsoidal shape and a smooth, nearly featureless image. They are one of the four main classes of galaxy described by Edwin Hubble in his Hubble sequence and 1936 work ''The Realm of the Nebulae'', with their intermediate scale disks, a subset of the "early-type" galaxy population. Most elliptical galaxies are composed of older, low-mass stars, with a sparse interstellar medium and minimal star formation activity, and they tend to be surrounded by large numbers of globular clusters. Elliptical galaxies are believed to make up approximately 10–15% of galaxies in the Virgo Supercluster, and they are not the dominant type of galaxy in the universe overall. They are preferentially found close to the centers of galaxy clusters. Elliptical galaxies range in size from dwarf ellipticals with tens of millions of stars, to supergiants of over one hundred trillion stars that dominate their galaxy clusters. Originally, Ed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Radius
Galaxy effective radius or half-light radius (R_e) is the radius at which half of the total light of a galaxy is emitted. This assumes the galaxy has either intrinsic spherical symmetry or is at least circularly symmetric as viewed in the plane of the sky. Alternatively, a half-light contour, or isophote, may be used for spherically and circularly asymmetric objects. R_e is an important length scale in \sqrt R term in de Vaucouleurs law, which characterizes a specific rate at which surface brightness In astronomy, surface brightness (SB) quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on it ... decreases as a function of radius: : I(R) = I_e \cdot e^ where I_e is the surface brightness at R = R_e. At R = 0, : I(R=0) = I_e \cdot e^ \approx 2000 \cdot I_e Thus, the central surface brightness is approximately 2000 \cdot I_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Brightness
In astronomy, surface brightness (SB) quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on its surface luminosity density, i.e., its luminosity emitted per unit surface area. In visible and infrared astronomy, surface brightness is often quoted on a magnitude scale, in magnitudes per square arcsecond (MPSAS) in a particular filter band or photometric system. Measurement of the surface brightnesses of celestial objects is called surface photometry. General description The total magnitude is a measure of the brightness of an extended object such as a nebula, cluster, galaxy or comet. It can be obtained by summing up the luminosity over the area of the object. Alternatively, a photometer can be used by applying apertures or slits of different sizes of diameter. The background light is then subtracted from the measurement to obtain t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Velocity Dispersion
In astronomy, the velocity dispersion (''σ'') is the statistical dispersion of velocity, velocities about the Arithmetic mean, mean velocity for a group of astronomical objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or supercluster. By measuring the radial velocities of the group's members through astronomical spectroscopy, the velocity dispersion of that group can be estimated and used to derive the group's mass from the virial theorem.Collins Dictionary of Astronomy, 2nd Ed.; Harper Collins Publishers; 2000; pp. 444, 449 Radial velocity is found by measuring the Doppler broadening, Doppler width of spectral lines of a collection of objects; the more radial velocities one measures, the more accurately one knows their dispersion. A ''central velocity dispersion'' refers to the σ of the interior regions of an extended object, such as a galaxy or cluster. The relationship between velocity dispersion and matter (or the observed electromagnetic radiation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane (geometry)
In mathematics, a plane is a Euclidean (flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with one of a room's walls, infinitely extended, or they may enjoy an independent existence in their own right, as in the setting of two-dimensional Euclidean geometry. Sometimes the word ''plane'' is used more generally to describe a two-dimensional surface, for example the hyperbolic plane and elliptic plane. When working exclusively in two-dimensional Euclidean space, the definite article is used, so ''the'' plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, often in the plane. Euclidean geometry Euclid set forth the first great landmark of mathematical thought, an axiomatic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 star, galaxy, or other astronomical object. In SI units, luminosity is measured in joules per second, or watts. In astronomy, values for luminosity are often given in the terms of the luminosity of the Sun, ''L''⊙. Luminosity can also be given in terms of the astronomical magnitude system: the absolute bolometric magnitude (''M''bol) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term ''brightness'' in astronomy is generally used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the lumin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empirically
In philosophy, empiricism is an epistemological theory that holds that knowledge or justification comes only or primarily from sensory experience. It is one of several views within epistemology, along with rationalism and skepticism. Empiricism emphasizes the central role of empirical evidence in the formation of ideas, rather than innate ideas or traditions. However, empiricists may argue that traditions (or customs) arise due to relations of previous sensory experiences. Historically, empiricism was associated with the "blank slate" concept (''tabula rasa''), according to which the human mind is "blank" at birth and develops its thoughts only through experience. Empiricism in the philosophy of science emphasizes evidence, especially as discovered in experiments. It is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world rather than resting solely on ''a priori'' reasoning, intuition, or rev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faber–Jackson Relation
The Faber–Jackson relation provided the first empirical power-law relation between the luminosity L and the central stellar velocity dispersion \sigma of elliptical galaxy, and was presented by the astronomers Sandra M. Faber and Robert Earl Jackson in 1976. Their relation can be expressed mathematically as: : L \propto \sigma^ \gamma with the index \gamma approximately equal to 4. In 1962, Rudolph Minkowski had discovered and wrote that a "correlation between velocity dispersion and uminosityexists, 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 the value of \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.Paul L. Schechter (1980)Mass-to-light ratios fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tully–Fisher Relation
In astronomy, the Tully–Fisher relation (TFR) is an empirical relationship between the mass or intrinsic luminosity of a spiral galaxy and its asymptotic rotation velocity or emission line width. It was first published in 1977 by astronomers R. Brent Tully and J. Richard Fisher. The luminosity is calculated by multiplying the galaxy's apparent brightness by 4\pi d^2, where d is its distance from us, and the spectral-line width is measured using long-slit spectroscopy. Several different forms of the TFR exist, depending on which precise measures of mass, luminosity or rotation velocity one takes it to relate. Tully and Fisher used optical luminosity, but subsequent work showed the relation to be tighter when defined using microwave to infrared ( K band) radiation (a good proxy for stellar mass), and even tighter when luminosity is replaced by the galaxy's total baryonic mass (the sum of its mass in stars and gas). This latter form of the relation is known as the baryonic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 is defined as the distance at which 1 au subtends an angle of one arcsecond ( of a degree). This corresponds to astronomical units, i.e. 1\, \mathrm = 1/\tan \left( \ \mathrm \right)\, \mathrm. The nearest star, Proxima Centauri, is about from the Sun. Most stars visible to the naked eye are within a few hundred parsecs of the Sun, with the most distant at a few thousand. The word ''parsec'' is a portmanteau of "parallax of one second" and was coined by the British astronomer Herbert Hall Turner in 1913 to make calculations of astronomical distances from only raw observational data easy for astronomers. Partly for this reason, it is the unit preferred in astronomy and astrophysics, though the light-year remains prominent in popular s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Small-angle Approximation
The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians: : \begin \sin \theta &\approx \theta \\ \cos \theta &\approx 1 - \frac \approx 1\\ \tan \theta &\approx \theta \end These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science. One reason for this is that they can greatly simplify differential equations that do not need to be answered with absolute precision. There are a number of ways to demonstrate the validity of the small-angle approximations. The most direct method is to truncate the Maclaurin series for each of the trigonometric functions. Depending on the order of the approximation, \textstyle \cos \theta is approximated as either 1 or as 1-\frac. Justifications Graphic The accuracy of the approximations can be seen belo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
