翻訳と辞書 Words near each other ・ Oskar Edøy ・ Oskar Ekberg ・ Oskar Engelhard von Löwis of Menar ・ Oskar Enkvist ・ Osip Mandelstam ・ Osip Mikhailovich Lerner ・ Osip Minor ・ Osip Notovich ・ Osip Petrov ・ Osip Piatnitsky ・ Osip Senkovsky ・ Osip Startsev ・ Osip Yermansky ・ Osipaonica ・ Osipenko ・ Osipkov–Merritt model ・ Osipov ・ Osipov State Russian Folk Orchestra ・ Osipy-Kolonia ・ Osipy-Lepertowizna ・ Osipy-Wydziory Drugie ・ Osipy-Wydziory Pierwsze ・ Osipy-Zakrzewizna ・ OSiR Skałka ・ OSiR Stadium in Olsztyn ・ OSiR Stadium in Słubice ・ Osira ・ Osire ・ Osireion ・ Osiriaca ptousalis Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Osipkov–Merritt model ： ウィキペディア英語版 Osipkov–Merritt model Osipkov–Merritt models (named for Leonid Osipkov and David Merritt) are mathematical representations of spherical stellar systems (galaxies, star clusters, globular clusters etc.). The Osipkov-Merritt formula generates a one-parameter family of phase-space distribution functions that reproduce a specified density profile (representing stars) in a specified gravitational potential (in which the stars move). The density and potential need not be self-consistently related. A free parameter adjusts the degree of velocity anisotropy, from isotropic to completely radial motions. The method is a generalization of Eddington's formula〔Eddington, A. (1916), ( The distribution of stars in globular clusters, ) ''Mon. Not. R. Astron. Soc.'', 76, 572〕 for constructing isotropic spherical models. The method was derived independently by its two eponymous discoverers.〔Osipkov, L. P. (1979), ( Spherical systems of gravitating bodies with an ellipsoidal velocity distribution, ) ''Pis'ma v Astron. Zhur.'', 5, 77〕〔Merritt, D. (1985), ( Spherical stellar systems with spheroidal velocity distributions, ) ''Astron. J.'', 90, 1027〕 The latter derivation includes two additional families of models (Type IIa, b) with tangentially anisotropic motions. ==Derivation== According to Jeans's theorem, the phase-space density of stars ''f'' must be expressible in terms of the isolating integrals of motion, which in a spherical stellar system are the energy ''E'' and the angular momentum ''J''. The Osipkov-Merritt ''ansatz'' is :$f\; =\; f(Q)\; =\; f(E+J^2/2r\_a^2)$ where ''ra'', the "anisotropy radius", is a free parameter. This ''ansatz'' implies that ''f'' is constant on spheroids in velocity space since :$$ 2Q = v_r^2 + (1+r^2/r_a^2)v_t^2 + 2\Phi(r) where ''v''r, ''v''t are velocity components parallel and perpendicular to the radius vector ''r'' and Φ(''r'') is the gravitational potential. The density ''ρ'' is the integral over velocities of ''f'': :$$ \rho(r) = 2\pi\int\int f(E,J) v_t dv_t dv_r which can be written :$$ \rho(r) = \int_\Phi^0 dQ f(Q) \int_0^ dJ^2\left()^ or :$$ \rho(r) = \int_\Phi^0 dQ \sqrtf(Q). This equation has the form of an Abel integral equation and can be inverted to give ''f'' in terms of ''ρ'': :$$ f(Q) = \int_Q^0 ,\ \ \ \ \ \rho^'(\Phi) = \left()\rho\left(). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Osipkov–Merritt model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.