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Virial Mass
In astrophysics, the virial mass is the mass of a gravitationally bound astrophysical system, assuming the virial theorem applies. In the context of galaxy formation and dark matter halos, the virial mass is defined as the mass enclosed within the virial radius r_ of a gravitationally bound system, a radius within which the system obeys the virial theorem. The virial radius is determined using a "top-hat" model. A spherical "top hat" density perturbation destined to become a galaxy begins to expand, but the expansion is halted and reversed due to the mass collapsing under gravity until the sphere reaches equilibrium – it is said to be ''virialized''. Within this radius, the sphere obeys the virial theorem which says that the average kinetic energy is equal to minus one half times the average potential energy, \langle T \rangle = -\frac \langle U \rangle, and this radius defines the virial radius. Virial radius The virial radius of a gravitationally bound astrophysical system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the heavenly bodies, rather than their positions or motions in space–''what'' they are, rather than ''where'' they are." Among the subjects studied are the Sun, other stars, galaxies, extrasolar planets, the interstellar medium and the cosmic microwave background. Emissions from these objects are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, ''astrophysicists'' apply concepts and methods from many disciplines of physics, including classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity. In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor). The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately The modern notation of Newton's law involving was introduced in the 1890s by C. V. Boys. The first impl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stellar Astronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond Earth's atmosphere. Cosmology is a branch of astronomy that studies the universe as a whole. Astronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Babylonians, Greeks, Indians, Egyptians, Chinese, Maya, and many ancient indigenous peoples of the Americas. In the past, astronomy included disciplines as diverse as astrometry, celestial navigation, observational astronomy, and the making of calendars. Nowadays, professional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virial Theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. Mathematically, the theorem states \left\langle T \right\rangle = -\frac12\,\sum_^N \bigl\langle \mathbf_k \cdot \mathbf_k \bigr\rangle where is the total kinetic energy of the particles, represents the force on the th particle, which is located at position , and angle brackets represent the average over time of the enclosed quantity. The word virial for the right-hand side of the equation derives from ''vis'', the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870. The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dark Matter Halo
According to modern models of physical cosmology, a dark matter halo is a basic unit of cosmological structure. It is a hypothetical region that has decoupled from cosmic expansion and contains gravitationally bound matter. A single dark matter halo may contain multiple virialized clumps of dark matter bound together by gravity, known as subhalos. Modern cosmological models, such as ΛCDM, propose that dark matter halos and subhalos may contain galaxies. The dark matter halo of a galaxy envelops the galactic disc and extends well beyond the edge of the visible galaxy. Thought to consist of dark matter, halos have not been observed directly. Their existence is inferred through observations of their effects on the motions of stars and gas in galaxies and gravitational lensing. Dark matter halos play a key role in current models of galaxy formation and evolution. Theories that attempt to explain the nature of dark matter halos with varying degrees of success include cold dark m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeans Equations
The Jeans equations are a set of partial differential equations that describe the motion of a collection of stars in a gravitational field. The Jeans equations relate the second-order velocity moments to the density and potential of a stellar system for systems without collision. They are analogous to the Euler equations for fluid flow and may be derived from the collisionless Boltzmann equation. The Jeans equations can come in a variety of different forms, depending on the structure of what is being modelled. Most utilization of these equations has been found in simulations with large number of gravitationally bound objects. History The Jeans equations were originally derived by James Clerk Maxwell. However, they were first applied to astronomy by James Jeans in 1915 while working on stellar hydrodynamics. Since then, multiple solutions to the equations have been calculated analytically and numerically. Some notable solutions include a spherically symmetric solution, derived ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einasto Profile
The Einasto profile (or Einasto model) is a mathematical function that describes how the density \rho of a spherical stellar system varies with distance r from its center. Jaan Einasto introduced his model at a 1963 conference in Alma-Ata, Kazakhstan. The Einasto profile possesses a power law logarithmic slope of the form: : \gamma(r) \equiv -\frac \propto r^ which can be rearranged to give : \rho(r) \propto \exp . The parameter \alpha controls the degree of curvature of the profile. This can be seen by computing the slope on a log-log plot: : d\ (\log\rho)/d\ (\log r) \propto -r^ . The larger \alpha, the more rapidly the slope varies with radius (see figure). Einasto's law can be described as a generalization of a power law, \rho\propto r^, which has a constant slope on a log-log plot. Einasto's model has the same mathematical form as Sersic's law, which is used to describe the surface brightness (i.e. projected density) profile of galaxies. Einasto's model has been used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cold Dark Matter
In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a small fraction being the ordinary baryonic matter that composes stars, planets, and living organisms. ''Cold'' refers to the fact that the dark matter moves slowly compared to the speed of light, while ''dark'' indicates that it interacts very weakly with ordinary matter and electromagnetic radiation. Proposed candidates for CDM include weakly interacting massive particles, primordial black holes, and axions. History The theory of cold dark matter was originally published in 1982 by James Peebles; while the warm dark matter picture was proposed independently at the same time by J. Richard Bond, Alex Szalay, and Michael Turner; and George Blumenthal, H. Pagels, and Joel Primack. A review article in 1984 by Blumenthal, Sandra Moore Fab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navarro–Frenk–White Profile
The Navarro–Frenk–White (NFW) profile is a spatial mass distribution of dark matter fitted to dark matter halos identified in N-body simulations by Julio Navarro, Carlos Frenk and Simon White. The NFW profile is one of the most commonly used model profiles for dark matter halos. Density distribution In the NFW profile, the density of dark matter as a function of radius is given by: : \rho (r)=\frac where ''ρ''0 and the "scale radius", ''Rs'', are parameters which vary from halo to halo. The integrated mass within some radius ''R''max is : M=\int_0^ 4\pi r^2 \rho (r) \, dr=4\pi \rho_0 R_s^3 \left \ln\left(\frac\right)-\frac\right The total mass is divergent, but it is often useful to take the edge of the halo to be the virial radius, ''R''vir, which is related to the "concentration parameter", ''c'', and scale radius via : R_\mathrm=cR_s (Alternatively, one can define a radius at which the average density within this radius is \Delta times the critical or mean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ΛCDM
The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parameterization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda (Greek Λ) associated with dark energy; second, the postulated cold dark matter (abbreviated CDM); and third, ordinary matter. It is frequently referred to as the ''standard model'' of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos: * the existence and structure of the cosmic microwave background * the large-scale structure in the distribution of galaxies * the observed abundances of hydrogen (including deuterium), helium, and lithium * the accelerating expansion of the universe observed in the light from distant galaxies and supernovae The model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concorda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virial Theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. Mathematically, the theorem states \left\langle T \right\rangle = -\frac12\,\sum_^N \bigl\langle \mathbf_k \cdot \mathbf_k \bigr\rangle where is the total kinetic energy of the particles, represents the force on the th particle, which is located at position , and angle brackets represent the average over time of the enclosed quantity. The word virial for the right-hand side of the equation derives from ''vis'', the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870. The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein–de Sitter Universe
The Einstein–de Sitter universe is a model of the universe proposed by Albert Einstein and Willem de Sitter in 1932. On first learning of Edwin Hubble's discovery of a linear relation between the redshift of the galaxies and their distance, Einstein set the cosmological constant to zero in the Friedmann equations, resulting in a model of the expanding universe known as the Friedmann–Einstein universe. In 1932, Einstein and De Sitter proposed an even simpler cosmic model by assuming a vanishing spatial curvature as well as a vanishing cosmological constant. In modern parlance, the Einstein–de Sitter universe can be described as a cosmological model for a flat matter-only Friedmann–Lemaître–Robertson–Walker metric (FLRW) universe. Lars Bergström & Ariel Goobar: "''Cosmology and Particle Astrophysics''", 2nd ed. Springer (2004), p. 70+77. . In the model, Einstein and de Sitter derived a simple relation between the average density of matter in the universe and its expan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
