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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 Firehose instability ： ウィキペディア英語版 Firehose instability The firehose instability (or hose-pipe instability) is a dynamical instability of thin or elongated galaxies. The instability causes the galaxy to buckle or bend in a direction perpendicular to its long axis. After the instability has run its course, the galaxy is less elongated (i.e. rounder) than before. Any sufficiently thin stellar system, in which some component of the internal velocity is in the form of random or counter-streaming motions (as opposed to rotation), is subject to the instability. The firehose instability is probably responsible for the fact that elliptical galaxies and dark matter haloes never have axis ratios more extreme than about 3:1, since this is roughly the axis ratio at which the instability sets in. It may also play a role in the formation of barred spiral galaxies, by causing the bar to thicken in the direction perpendicular to the galaxy disk.〔 〕 The firehose instability derives its name from a similar instability in magnetized plasmas. However, from a dynamical point of view, a better analogy is with the Kelvin–Helmholtz instability, or with beads sliding along an oscillating string.〔In spite of its name, the firehose instability is not related dynamically to the oscillatory motion of a hose spewing water from its nozzle.〕 ==Stability analysis: sheets and wires== The firehose instability can be analyzed exactly in the case of an infinitely thin, self-gravitating sheet of stars.〔 If the sheet experiences a small displacement $h(x,t)$ in the $z$ direction, the vertical acceleration for stars of $x$ velocity $u$ as they move around the bend is :$$ a_z = \left( + u\right)^2h = + 2u + u^2 ,\, provided the bend is small enough that the horizontal velocity is unaffected. Averaged over all stars at $x$, this acceleration must equal the gravitational restoring force per unit mass $F\_x$. In a frame chosen such that the mean streaming motions are zero, this relation becomes :$$ + \sigma_u^2 - F_z(x,t) =0,\, where $\backslash sigma\_u$ is the horizontal velocity dispersion in that frame. For a perturbation of the form :$$ h(x,t)=H\exp\left(t\right)\right ) the gravitational restoring force is :$$ F_z(x,t) = -G\Sigma\int_^\infty dy' \int_^ {\left(h(x,t) - h(x',t)\right )\over \left()^{3/2}}dx' = -2\pi G\Sigma k h(x,t) where $\backslash Sigma$ is the surface mass density. The dispersion relation for a thin self-gravitating sheet is then〔 :$$ \omega^2 = 2\pi G\Sigma k - \sigma_u^2 k^2. The first term, which arises from the perturbed gravity, is stabilizing, while the second term, due to the centrifugal force that the stars exert on the sheet, is destabilizing. For sufficiently long wavelengths: :$$ \lambda =2\pi/k > \lambda_J = \sigma_u^2/G\Sigma the gravitational restoring force dominates, and the sheet is stable; while at short wavelengths the sheet is unstable. The firehose instability is precisely complementary, in this sense, to the Jeans instability in the plane, which is ''stabilized'' at short wavelengths, . A similar analysis can be carried out for a galaxy that is idealized as a one-dimensional wire, with density that varies along the axis. This is a simple model of a (prolate) elliptical galaxy. Some unstable eigenmodes are shown in Figure 2 at 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「Firehose instability」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.