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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Rotational Brownian motion (astronomy) ： ウィキペディア英語版 Rotational Brownian motion (astronomy) In astronomy, rotational Brownian motion refers to the random walk in orientation of a binary star's orbital plane, induced by gravitational perturbations from passing stars. ==Theory== Consider a binary that consists of two massive objects (stars, black holes etc.) and that is embedded in a stellar system containing a large number of stars. Let $M\_1$ and $M\_2$ be the masses of the two components of the binary whose total mass is $M\_=M\_1+M\_2$. A field star that approaches the binary with impact parameter $p$ and velocity $V$ passes a distance $r\_p$ from the binary, where $$ p^2=r_p^2\left(1+2GM_/V^2r_p\right) \approx 2GM_r_p/V^2; the latter expression is valid in the limit that gravitational focusing dominates the encounter rate. The rate of encounters with stars that interact strongly with the binary, i.e. that satisfy , is approximately $n\backslash pi\; p^2\; \backslash sigma\; =2\backslash pi\; GM\_\; n\; a/\backslash sigma$ where $n$ and $\backslash sigma$ are the number density and velocity dispersion of the field stars and $a$ is the semi-major axis of the binary. As it passes near the binary, the field star experiences a change in velocity of order $$ \Delta V \approx V_ = \sqrt , where $V\_$ is the relative velocity of the two stars in the binary. The change in the field star's specific angular momentum with respect to the binary, $l$, is then Δ''l'' ≈ ''a'' ''V''bin. Conservation of angular momentum implies that the binary's angular momentum changes by Δ''l''bin ≈ -(m/μ12)Δ''l'' where ''m'' is the mass of a field star and μ12 is the binary reduced mass. Changes in the magnitude of ''l''bin correspond to changes in the binary's orbital eccentricity via the relation ''e'' = 1 - ''l''b2/''GM''12μ12''a''. Changes in the direction of ''l''bin correspond to changes in the orientation of the binary, leading to rotational diffusion. The rotational diffusion coefficient is $$ \langle\Delta\xi^2\rangle = \langle\Delta l_^2\rangle / l_^2 \approx \left(a \approx where ρ = ''mn'' is the mass density of field stars. Let ''F''(θ,''t'') be the probability that the rotation axis of the binary is oriented at angle θ at time ''t''. The evolution equation for ''F'' is 〔 〕 $$ = \left(\sin\theta \right). If <Δξ2>, ''a'', ρ and σ are constant in time, this becomes $$ = \left(\right ) where μ = cos θ and τ is the time in units of the relaxation time ''t''rel, where $$ t_ \approx . The solution to this equation states that the expectation value of μ decays with time as $$ \overline\mu = \overline_0 e^. Hence, ''t''rel is the time constant for the binary's orientation to be randomized by torques from field stars. 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「Rotational Brownian motion (astronomy)」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.