What appear on a Hertzsprung-Russell diagram?
"which are generally elliptical galaxies. The blue cloud includes most blue galaxies which are generally spirals. In between the two distributions is an underpopulated space known as the green valley which includes a number of red spirals. Unlike the comparable Hertzsprung–Russell diagram for stars, galaxy properties are not necessarily completely determined by their location on the color–magnitude diagram. The diagram also shows considerable evolution through time. The red sequence earlier in evolution of the universe was more constant in color across magnitudes and the blue cloud was not as uniformly distributed but showed sequence progression. New research suggests the green"
"variable stars in the Hertzsprung-Russell diagram. These giant stars are observed to undergo pulsations ranging from weak irregularity, when one can still define an average cycling time or period, (as in most RV Tauri and semiregular variables) to the near absence of repetitiveness in the irregular variables. The W Virginis variables are at the interface; the short period ones are regular and the longer period ones show first relatively regular alternations in the pulsations cycles, followed by the onset of mild irregularity as in the RV Tauri stars into which they gradually morph as their periods get longer. Stellar evolution"
"are located in the Hertzsprung–Russell diagram together with some others observed from the ground. Discoveries were numerous. Let us cite the first detection of solar-like oscillations in stars other than the Sun, the first detection of non-radial oscillations in red giant stars, the detection of solar-like oscillations in massive stars, the discovery of hundreds of frequencies in δ Scuti stars, the spectacular time evolution of the frequency spectrum of a Be (emission lines B) star during an outburst, the first detection of a deviation from a constant period spacing in gravity modes in an SPB (Slowly Pulsating B) star. Interpreting"
"the Hertzsprung–Russell diagram, indicating that is it now generating energy through the thermonuclear fusion of helium at its core. The star has 2.5 times the mass of the Sun and has expanded to 9 times the Sun's radius. As such, it is radiating nearly 46 times the solar luminosity from its outer atmosphere at an effective temperature of 4,864 K. There is a magnitude 9.7 companion star at an angular separation of 1.8″. Most likely the pair form a binary star system. At least one of the stars appears to be a source of X-ray emission. The X-ray band flux"
"sequence curve on the Hertzsprung-Russell diagram for newly formed stars. However, this was challenged, after using the much more accurate parallaxes from the Hipparcos catalogue (ESA, 1997), it was calculated that the stars actually have higher luminosities and so are shifted upwards, crossing them into the main sequence. Most stars will evolve above this curve as they age. ζ has an intermediate level of magnetic activity in its chromosphere with an erratic variability. ζ is more sedate, showing a much lower level of activity with a 10-year cycle. Although the kinematics of this system suggest that they belong to a"
"Main sequence In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell. Stars on this band are known as main-sequence stars or dwarf stars. These are the most numerous true stars in the universe, and include the Earth's Sun. After condensation and ignition of a star, it generates thermal energy in its dense core region through nuclear fusion of hydrogen into helium. During this stage of the star's lifetime, it is"
"Hertzsprung-Russell diagram. These rings are very evenly spaced, suggesting that the mechanism responsible for their formation ejected them at very regular intervals and at very similar speeds. The total mass of the rings is about 0.1 solar masses. The pulsations that formed the rings probably started 15,000 years ago and ceased about years ago, when the formation of the bright central part began (see above). Further out, a large faint halo extends to large distances from the star. The halo again predates the formation of the main nebula. The mass of the halo is estimated as 0.26–0.92 solar masses. Cat's"
"use exploding white dwarfs as standard candles in determining distances. White dwarfs have low luminosity and therefore occupy a strip at the bottom of the Hertzsprung–Russell diagram, a graph of stellar luminosity versus color or temperature. They should not be confused with low-luminosity objects at the low-mass end of the main sequence, such as the hydrogen-fusing red dwarfs, whose cores are supported in part by thermal pressure, or the even lower-temperature brown dwarfs. The relationship between the mass and radius of white dwarfs can be derived using an energy minimization argument. The energy of the white dwarf can be approximated"
"Hofstadter's butterfly In physics, Hofstadter's butterfly is a mathematical object describing the theorised behaviour of electrons in a magnetic field, discovered in 1976 by Douglas Hofstadter. It takes its name from its visual resemblance to a butterfly. It is a fractal structure and as such it shows self-similarity, meaning that small fragments of the structure contain a (distorted) copy of the entire structure. It is one of the rare non-random fractal structures discovered in physics, along with KAM theorem. A central concern in Hofstadter's paper is how the two distinct behaviours predicted for 'rational' and 'irrational' magnetic fields must be"
"Instability strip The unqualified term instability strip usually refers to a region of the Hertzsprung–Russell diagram largely occupied by several related classes of pulsating variable stars: Delta Scuti variables, SX Phoenicis variables, and rapidly oscillating Ap stars (roAps) near the main sequence; RR Lyrae variables where it intersects the horizontal branch; and the Cepheid variables where it crosses the supergiants. RV Tauri variables are also often considered to lie on the instability strip, occupying the area to the right of the brighter Cepheids (at lower temperatures), since their pulsations are attributed to the same mechanism. The instability strip intersects the"
"Hertzsprung–Russell diagram and is of spectral class M5.5. M5.5 means that it falls in the low-mass end of M-type stars. Its absolute visual magnitude, or its visual magnitude as viewed from a distance of , is 15.5. Its total luminosity over all wavelengths is 0.17% that of the Sun, although when observed in the wavelengths of visible light the eye is most sensitive to, it is only 0.0056% as luminous as the Sun. More than 85% of its radiated power is at infrared wavelengths. It has a regular activity cycle of starspots. In 2002, optical interferometry with the Very Large"
"blue variables may be related and show similar short- and long-term spectral and brightness variations with irregular eruptions. Instability strip The unqualified term instability strip usually refers to a region of the Hertzsprung–Russell diagram largely occupied by several related classes of pulsating variable stars: Delta Scuti variables, SX Phoenicis variables, and rapidly oscillating Ap stars (roAps) near the main sequence; RR Lyrae variables where it intersects the horizontal branch; and the Cepheid variables where it crosses the supergiants. RV Tauri variables are also often considered to lie on the instability strip, occupying the area to the right of the brighter"
"sequence lifespan of stars at this point, it becomes possible to estimate the age of the cluster. Main sequence In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell. Stars on this band are known as main-sequence stars or dwarf stars. These are the most numerous true stars in the universe, and include the Earth's Sun. After condensation and ignition of a star, it generates thermal energy in its dense core"
"Henry Norris Russell Prof Henry Norris Russell ForMemRS HFRSE FRAS (October 25, 1877 – February 18, 1957) was an American astronomer who, along with Ejnar Hertzsprung, developed the Hertzsprung–Russell diagram (1910). In 1923, working with Frederick Saunders, he developed Russell–Saunders coupling, which is also known as LS coupling. Russell was born on 25 October 1877, at Oyster Bay, New York, the son of Rev Alexander Gatherer Russell (1845-1911) and his wife, Eliza Hoxie Norris. He studied astronomy at Princeton University, obtaining his B.A. In 1897 and his doctorate in 1899, studying under Charles Augustus Young. From 1903 to 1905, he"
"observes the quantum Hall effect. The integers that appear in the Hall effect are examples of topological quantum numbers. They are known in mathematics as the first Chern numbers and are closely related to Berry's phase. A striking model of much interest in this context is the Azbel–Harper–Hofstadter model whose quantum phase diagram is the Hofstadter butterfly shown in the figure. The vertical axis is the strength of the magnetic field and the horizontal axis is the chemical potential, which fixes the electron density. The colors represent the integer Hall conductances. Warm colors represent positive integers and cold colors negative"
"constant times formula_6. Note that area is 4π(g-1) from the Gauss-Bonnet theorem, so that SR(g) behaves asymptotically as a constant times formula_7. The study of the asymptotic behavior for large genus formula_8 of the systole of hyperbolic surfaces reveals some interesting constants. Thus, Hurwitz surfaces formula_9 defined by a tower of principal congruence subgroups of the (2,3,7) hyperbolic triangle group satisfy the bound resulting from an analysis of the Hurwitz quaternion order. A similar bound holds for more general arithmetic Fuchsian groups. This 2007 result by Mikhail Katz, Mary Schaps, and Uzi Vishne improves an inequality due to Peter Sarnak"
"grouped into those with strong helium lines, termed He-sdO, and those with stronger hydrogen lines, H strong sdO. The He-sdO are fairly rare. Usually nitrogen is enriched and carbon depleted. However there are variations with enhancement in concentration of even numbered elements such as carbon, oxygen, neon, silicon, magnesium or iron. They can be plotted on the Hertzsprung–Russell diagram. They are from two stages in the stellar lifecycle, post–asymptotic giant branch (the luminous sdO), and post–extended horizontal branch compact sdO. The post-AGB stars are expected to be found in planetary nebulas, but only four of the sdO stars are known"
"years, other aspects of analysis on the Heisenberg group have been also studied, like minimal surfaces in the Heisenberg group, the Bernstein problem in the Heisenberg group and curvature flows. CR manifold In mathematics, a CR manifold is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Formally, a CR manifold is a differentiable manifold ""M"" together with a preferred complex distribution ""L"", or in other words a complex subbundle of the complexified tangent bundle formula_1 such that The"
"observations of open and globular clusters. Clusters are also a crucial step in determining the distance scale of the universe. A few of the nearest clusters are close enough for their distances to be measured using parallax. A Hertzsprung–Russell Diagram can be plotted for these clusters which has absolute values known on the luminosity axis. Then, when similar diagram is plotted for a cluster whose distance is not known, the position of the main sequence can be compared to that of the first cluster and the distance estimated. This process is known as main-sequence fitting. Reddening and stellar populations must"
"the Hertzsprung–Russell diagram as that of classical Cepheids. Delta Scuti stars are located at the intersection of the strip with the main sequence. This star is rotating at about 92% of its critical speed, completing 1.12 rotations every day. This is giving the star an oblate spheroid shape with an equatorial bulge that is 24% larger than the polar radius. This shape is causing the polar region to have a higher temperature than the equator: the temperature difference is about 1,000 K. The axis of rotation is inclined about 20° to the line of sight from the Earth. β Cassiopeiae"
"with the first deep photographic photometric studies of globular clusters and were notable for being absent from all open clusters that had been studied up to that time. The horizontal branch is so named because in low-metallicity star collections like globular clusters, HB stars lie along a roughly horizontal line in a Hertzsprung–Russell diagram. After exhausting their core hydrogen, stars leave the main sequence and begin fusion in a hydrogen shell around the helium core and become giants on the red giant branch. In stars with masses up to 2.3 times the mass of the Sun the helium core becomes"
"for many purposes, explicit isomorphisms are unnecessary. Thus, traces of group elements (and hence also translation lengths of hyperbolic elements acting in the upper half-plane, as well as systoles of Fuchsian subgroups) can be calculated by means of the reduced trace in the quaternion algebra, and the formula (2,3,7) triangle group In the theory of Riemann surfaces and hyperbolic geometry, the triangle group (2,3,7) is particularly important. This importance stems from its connection to Hurwitz surfaces, namely Riemann surfaces of genus ""g"" with the largest possible order, 84(""g"" − 1), of its automorphism group. A note on terminology – the"
"in a spacetime diagram which uses Kruskal–Szekeres coordinates (see figure). In this spacetime, it is possible to come up with coordinate systems such that if you pick a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an ""embedding diagram"" depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an ""Einstein-Rosen bridge"" or Schwarzschild wormhole. Depending on where the space-like"
"diagram is a plot of formula_3 (horizontal axis) against formula_10 (vertical axis). The 2½ scale factor is intended to make radial distance from the white point correlate with the Munsell chroma along any one hue radius (i.e., to make the diagram perceptually uniform). For achromatic surfaces, formula_11 and hence formula_12, formula_13. In other words, the white point is at the origin. Constant differences along the chroma dimension did not ""appear"" different by a corresponding amount, so Adams proposed a new class of spaces, which he termed chromatic ""valence"". These spaces have ""nearly equal radial distances for equal changes in Munsell"
"lightest elements. Stellar structure and the Hertzsprung–Russell diagram indicate that the length of the lifetime of a star depends greatly on its initial mass, so that massive stars are very short-lived, and less massive stars are longer-lived. BFH argues that as a star dies, it will enrich the interstellar medium with 'heavy elements' (in this case all elements heavier than lithium, the third element), from which newer stars are formed. This account is consistent with the observed negative correlation between stellar metallicity and red shift. The theory presented by the authors of BFH also described key aspects of the nuclear"
"were probably at the hot end of spectral class A during their main sequence lifetime, similar to Vega. They have now exhausted their core hydrogen and evolved off the main sequence, their outer layers expanding and cooling. Despite the giant luminosity class, the secondary component is very clearly within the Hertzsprung gap on the Hertzsprung–Russell diagram, still expanding and cooling towards the red giant branch, making it a subgiant in evolutionary terms. The more massive primary has already passed through this stage, when it reached a maximum radius of 36 to 38 times that of the Sun. It is now"
"given by the Lie vector fields which obey the relations [""X"",""Y""]=""Z"" and [""X"",""Z""]=[""Y"",""Z""]=0. Being Lie vector fields, these form a left-invariant basis for the group action. The geodesics on the manifold are spirals, projecting down to circles in two dimensions. That is, if is a geodesic curve, then the curve formula_99 is an arc of a circle, and with the integral limited to the two-dimensional plane. That is, the height of the curve is proportional to the area of the circle subtended by the circular arc, which follows by Stokes' theorem. It is more generally possible to define the Heisenberg"
"= (RR) = (RR) = (RRRR) = 1. Coxeter–Dynkin diagram In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes). It describes a kaleidoscopic construction: each graph ""node"" represents a mirror (domain facet) and the label attached to a branch encodes the dihedral angle order between two mirrors (on a domain ridge). An unlabeled branch implicitly represents order-3. Each diagram represents a Coxeter group, and Coxeter groups are classified by their associated diagrams. Dynkin diagrams are closely related objects,"
"Hurwitz surface In Riemann surface theory and hyperbolic geometry, a Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(""g"" − 1) automorphisms, where ""g"" is the genus of the surface. This number is maximal by virtue of Hurwitz's theorem on automorphisms . They are also referred to as Hurwitz curves, interpreting them as complex algebraic curves (complex dimension 1 = real dimension 2). The Fuchsian group of a Hurwitz surface is a finite index torsionfree normal subgroup of the (ordinary) (2,3,7) triangle group. The finite quotient group is precisely the automorphism group. Automorphisms of complex"
"values yields the Ehrenfest theorem featured in the correspondence principle. By the Stone–von Neumann theorem, the Heisenberg picture and the Schrödinger picture are unitarily equivalent. In some sense, the Heisenberg picture is more natural and convenient than the equivalent Schrödinger picture, especially for relativistic theories. Lorentz invariance is manifest in the Heisenberg picture. This approach also has a more direct similarity to classical physics: by replacing the commutator above by the Poisson bracket, the Heisenberg equation becomes an equation in Hamiltonian mechanics. The expectation value of an observable ""A"", which is a Hermitian linear operator for a given state formula_23,"
"the quantum system. The Heisenberg–Robertson or Schrödinger uncertainty relations do not fully capture the incompatibility of observables in a given quantum state. The stronger uncertainty relations give non-trivial bounds on the sum of the variances for two incompatible observables. For two non-commuting observables formula_1 and formula_2 the first stronger uncertainty relation is given by where formula_6, formula_7, formula_8 is a vector that is orthogonal to the state of the system, i.e., formula_9 and one should chose the sign of formula_10 so that this is a positive number. The other non-trivial stronger uncertainty relation is given by where formula_12 is a"
"Lorentz–Heaviside units Lorentz–Heaviside units (or Heaviside–Lorentz units) constitute a system of units (particularly electromagnetic units) within CGS, named for Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that the electric constant and magnetic constant do not appear, having been incorporated implicitly into the unit system and electromagnetic equations. Lorentz–Heaviside units may be regarded as normalizing and , while at the same time revising Maxwell's equations to use the speed of light instead. Lorentz–Heaviside units, like SI units but unlike Gaussian units, are ""rationalized"", meaning that there are no factors of appearing explicitly in Maxwell's equations."
"is . Set to get the HLU form: . The Gaussian form does not have the in the denominator. By setting with HLU, Maxwell's equations and the Lorentz equation become the same as the SI example with . Because these equations can be easily related to SI work, HLU-style (i.e. rationalized) systems are becoming more fashionable. Lorentz–Heaviside units Lorentz–Heaviside units (or Heaviside–Lorentz units) constitute a system of units (particularly electromagnetic units) within CGS, named for Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that the electric constant and magnetic constant do not appear, having been"