Tuesday, July 14, 2015

the Jeans instability the fluctuations in the density can grow if the effects of instabilities due to pressure("heat") are smaller than gravity caused by a fluctuation of density

Experimental and Theoretical Advances in Fluid Dynamics

https://books.google.com.hk/books?isbn=3642179584 - 翻譯這個網頁
Jaime Klapp, ‎Anne Cros, ‎Oscar Velasco Fuentes - 2011 - ‎Science
... he shows that the fluctuations in the density can grow if the effects of instabilities due to pressure are smaller than gravity caused by a fluctuation of density.
 

金斯不稳定性[编辑]

维基百科，自由的百科全书
跳转至： 导航、 搜索
在恒星形成过程中，当分子云的热压力不足以抵抗引力时，会在引力的作用下发生塌缩，这一现象称为金斯不稳定性。
星云必须达到流体静力平衡才能保持稳定，球状星云的平衡条件为：:\frac{dp}{dr}=-\frac{G\rho(r) M_{enc}(r)}{r^2}
https://en.wikipedia.org/wiki/Jeans_instability

在分子云的内部，存在引力和因分子热运动产生的热压力。如果热压力足够高，则微小的密度涨落能够被热压力所克服，如果热压力比起引力来是可以忽略的，那么微小的密度涨落能够被无限放大，最终导致整个分子云在引力的作用下塌缩。

金斯质量的近似值可以通过一个简单的物理参数的推导。
一个初始半径为R，质量为M的球形气体区域，声速为Cs。轻轻压缩这个区域。经过以下时间:t_{sound} = \frac{R}{c_s} \simeq (5 \times 10^5 \mbox{ yr}) \left(\frac{R}{0.1 \mbox{ pc}}\right) \left(\frac{c_s}{0.2 \mbox{ km s}^{-1}}\right)^{-1}声波可以传过这个区域，并反射回去，重新建立压力平衡的系统。
与此同时，重力会压缩系统，这个过程需要自由下落的时间，:t_{\rm ff} = \frac{1}{\sqrt{G \rho}} \simeq (2 \mbox{ Myr})\left(\frac{n}{10^3 \mbox{ cm}^{-3}}\right)^{-1/2}
其中G是万有引力常数，ρ是区域内的气体密度，n =ρ/μ为气体的粒子数密度，μ = 3.9×10-24 g是气体粒子的平均重量，按照氦分子数占20%的比例计算。引力坍缩的条件是: tff<tsound。
所得的金斯长度λJ约为：:\lambda_J = \frac{c_s}{\sqrt{G \rho}} \simeq (0.4 \mbox{ pc})\left(\frac{c_s}{0.2 \mbox{ km s}^{-1}}\right)\left(\frac{n}{10^3 \mbox{ cm}^{-3}}\right)^{-1/2}.
金斯质量MJ是包含在一个半径RJ球以内的质量（RJ是金斯长度的一半）：:M_J = \left(\frac{4\pi}{3}\right) \rho R_J^3 = \left(\frac{\pi}{6}\right) \frac{c_s^3}{G^{3/2} \rho^{1/2}} \simeq (2 \mbox{ M}_{\odot}) \left(\frac{c_s}{0.2 \mbox{ km s}^{-1}}\right)^3 \left(\frac{n}{10^3 \mbox{ cm}^{-3}}\right)^{-1/2}.
通过热分子运动公式的代入，:\lambda_J=\sqrt{\frac{15k_{B}T}{4\pi G \mu \rho}},
并可进一步化简为：:\lambda_J\approx\sqrt{\frac{k_B Tr^3}{GM \mu}}.
（金斯的推导原理请审慎判断引用）
https://en.wikipedia.org/wiki/Jeans_instability

塌缩的临界尺度为（原页面以下公式请审慎判断引用）
\lambda_\mathrm{J}=\sqrt{\frac{\pi k_BT}{G\rho m}}
称为金斯长度。如果密度扰动区域的长度大于金斯长度时，会发生引力塌缩。对于给定尺度L的分子云，定义金斯密度
\rho_\mathrm{J}=\frac{\pi k_BT}{GML^2}
定义金斯质量
M_\mathrm{J}\approx L^3\rho_J
当分子云的密度大于金斯密度或质量大于金斯质量时，会发生引力塌缩。塌缩的过程中介质的黏性可以忽略，因此塌缩时标是自由落体时标
\tau_\mathrm{ff}\approx\sqrt{\frac{r^3}{GM}}


事实上，由于下述原因，其他天体物理学家后来指出，金斯的原始分析是有缺陷的。金斯的分析假定星云崩塌区域的周围是无限、静态的介质。
有关质疑问是因为所有尺度大于金斯长度的区域也是不稳定的引力坍塌区，塌陷区周围所有静态介质因此也会产生引力坍塌。因此，相对于背景区域的密度，坍塌区域引力不稳定性的增长率比金斯原始分析所预测的要慢。该漏洞被称为“金斯骗局”。
金斯推导出的不稳定性条件实用性有限。
https://en.wikipedia.org/wiki/Jeans_instability

金斯的推导过程中，声速Cs这个“常数”的引入也是一个疑问，引用时也必须持审慎的态度。

Linear instability 1: isentropic fluctuations and Jeans ... - NED

ned.ipac.caltech.edu/.../Bert2_2.html

California Institute of Technology
Loading...
Including the Hubble damping term slows the growth of the Jeans instability ... For cs2 = 0 and an Einstein-de Sitter (flat, matter-dominated) background with a( tau ) ... plane wave remains constant; in the expanding case it damps in general.

  • Jeans instability - Wikipedia, the free encyclopedia

    https://en.wikipedia.org/wiki/Jeans_instability

    Wikipedia
    Loading...
    In physics, the Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when ... is the gravitational constant and r ...

  • [PDF]Lecture3

    www.iac.es/congreso/isapp2012/media/Longair-lectures/Longair3.pdf

    This is the famous Jeans' Instability and the time scale τ is the typical collapse .... perturbation in the case of the critical Einstein–de Sitter universe is algebraic. 10 ... that is, there is a decaying mode and one of constant amplitude ∆ = constant.

  • [PDF]The “Jeans swindle” A true story—mathematically speaking

    vigo.ime.unicamp.br/Eletro/swindle.pdf

    by MKH Kiessling - ‎2003 - ‎Cited by 39 - ‎Related articles
    dispersion relation, via a static universe with cosmological constant. The derivation ..... cosmological constant can suppress the Jeans instability. For the density ...

  • Growth of perturbations in an expanding universe with Bose ...

    arxiv.org › astro-ph

    arXiv
    Loading...
    by PH Chavanis - ‎2011 - ‎Cited by 43 - ‎Related articles
    Mar 14, 2011 - ... expanding Newtonian universe with Bose-Einstein condensate dark ... enhance the Jeans instability and fasten the formation of structures.

  • [PDF]The "Jeans Swindle": the end of a myth - arXiv

    arxiv.org/pdf/1108.5519

    arXiv
    Loading...
    by AI Ershkovich - ‎2011 - ‎Cited by 2 - ‎Related articles
    mathematically rigorous derivation of the Jeans instability criterion: the unperturbed gas is in a static equilibrium if the cosmological constant Λ is introduced.

  • Experimental and Theoretical Advances in Fluid Dynamics

    https://books.google.com/books?isbn=3642179584
    Jaime Klapp, ‎Anne Cros, ‎Oscar Velasco Fuentes - 2011 - ‎Science
    One way to explain this behavior is to introduce a constant in the Einstein field ... Then, we linearize this set of equations to study the Jeans' instability of this ...

  • [PDF]Jeans Instability and Gravitational Collapse

    www.physics.drexel.edu/students/courses/physics.../jeans_instability.pdf

    rigorous and non-rigorous derivations of the Jeans criterion (named after Sir James Jeans ... We will confine ourselves here to isentropic flows, with S = constant.

  • The “Jeans swindle”: A true story—mathematically speaking ...

    www.researchgate.net/.../222185973_The_Jeans_swindle_A_t...
    ResearchGate
    Loading...
    Dec 28, 2014 - Official Full-Text Publication: The “Jeans swindle”: A true ... of Jeans' dispersion relation, via a static universe with cosmological constant.

  • Jeans instability Cold Matt. - JP conf - ResearchGate

    www.researchgate.net/.../272998233_Jeans_instability_Cold_...
    ResearchGate
    Loading...
    Mar 2, 2015 - Publication » Jeans instability Cold Matt. - JP conf. ... Dataset: Jeans instability Cold Matt. - JP conf. 119.53 KB. See full-text. Page 1.

    • Posted by at

    No comments:

    Post a Comment

    Subscribe to: Post Comments (Atom)