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Virial Radius
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 i ... [...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, James Keeler, 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", which is studied in celestial mechanics. Among the subjects studied are the Sun ( solar physics), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Sitter Universe
A de Sitter universe is a cosmological solution to the Einstein field equations of general relativity, named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy in our universe or the inflaton field in the early universe. According to the models of inflation and current observations of the accelerating universe, the concordance models of physical cosmology are converging on a consistent model where our universe was best described as a de Sitter universe at about a time after the fiducial Big Bang singularity, and far into the future. Mathematical expression A de Sitter universe has no ordinary matter content but with a positive cosmological constant (\Lambda) that sets the expansion rate, H. A larger cosmological constant leads to a larger expansion rate: : H \propto \sqrt , where the constants of proportionality depen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stellar Astronomy
Astronomy is a natural science that studies astronomical object, celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall chronology of the Universe, evolution. Objects of interest include planets, natural satellite, moons, stars, nebulae, galaxy, galaxies, meteoroids, asteroids, 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 atmosphere of Earth, 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 Egyptian astronomy, Egyptians, Babylonian astronomy, Babylonians, Greek astronomy, Greeks, Indian astronomy, Indians, Ch ... [...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 a conservative force (where the work done is independent of path), with that of the total potential energy of the system. Mathematically, the theorem states that \langle T \rangle = -\frac12\,\sum_^N \langle\mathbf_k \cdot \mathbf_k\rangle, where T is the total kinetic energy of the N particles, F_k represents the force on the kth 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 , 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 co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dark Matter Halo
In 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 matter (C ... [...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 (fluid dynamics), 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 spherical ... [...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: \frac \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, except that the Einasto model describes a spherically symmet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concentration Parameter
In probability theory and statistics, a concentration parameter is a special kind of numerical parameter of a parametric family of probability distributions. Concentration parameters occur in two kinds of distribution: In the Von Mises–Fisher distribution, and in conjunction with distributions whose domain is a probability distribution, such as the symmetric Dirichlet distribution and the Dirichlet process. The rest of this article focuses on the latter usage. The larger the value of the concentration parameter, the more evenly distributed is the resulting distribution (the more it tends towards the uniform distribution). The smaller the value of the concentration parameter, the more sparsely distributed is the resulting distribution, with most values or ranges of values having a probability near zero (in other words, the more it tends towards a distribution concentrated on a single point, the degenerate distribution defined by the Dirac delta function). Dirichlet distri ... [...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, giving it a vanishing equation of state. ''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, as well as most flavors of neutrinos. 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. Pagel ... [...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 (astrophysicist), Julio Navarro, Carlos Frenk and Simon White. The NFW profile is one of the most commonly used model profiles for dark matter halos. The substantial impact of NFW's work on theoretical understanding of cosmic structure formation can be traced to three key insights. 1) In cosmological models where dark matter structure grows hierarchically from weak initial fluctuations, dark matter halos are almost self-similar; halo regions which are close to dynamical equilibrium are adequately represented for all masses and at all times by a simple analytic formula with only two free parameters, a characteristic density and a characteristic size. 2) These two parameters are related with rather little scatter; larger halos are less dense. The size-density relation depends on cosmological parameters and so can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Constant
The gravitational constant 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 general relativity, theory of general relativity. It is also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant, denoted by the capital letter . 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 law, 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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ΛCDM
The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components: # a cosmological constant, denoted by lambda (Λ), associated with dark energy; # the postulated cold dark matter, denoted by CDM; # ordinary matter. It is the current ''standard model'' of Big Bang cosmology, as it is the simplest model that provides a reasonably good account of: * 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 concordance cosmology, after a period when disparate observed properties of the universe appeared mutually inconsistent, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
