Gravitational Instability of Cold Matter
Gravitational Instability of Cold Matter
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DOI：
10.1086/174501
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发表时间：
1993-07
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影响因子：
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通讯作者：
E. Bertschinger;B. Jain
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文献类型：
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作者：
E. Bertschinger;B. Jain
我们解决了无压，无旋的密度起伏的扰动Robertson-Walker时空的非线性演化使用一个新的拉格朗日方法的基础上的速度梯度和重力梯度张量。借用广义相对论的结果，我们得到了一组牛顿常微分方程的这些量后，一个给定的质量元素。利用这些拉格朗日流体方程，我们证明了以下结果：（1）对于给定的初始密度和增长率，具有零剪切的球顶帽扰动是坍缩最慢的构型。(2)初始密度最大值通常不是首先发生塌陷的位置。(3)如果剪切力不太小，初始欠致密区域可能会发生塌陷。如果外尔张量的磁性部分为零，则非线性演化完全由我们的方程局部描述;这个条件适用于球面、柱面和平面扰动，在其他情况下可能是一个很好的近似。假设外尔张量的磁性部分为零，我们精确计算了冷物质的非线性引力演化。我们发现，对于均匀各向同性的随机场，在Einstein-de Sitter宇宙中有56%的初始欠密区域坍缩.我们还表明，在这种假设下，崩溃的最后阶段一般是二维的，导致强烈的长丝状体，而不是泽尔多维奇煎饼。虽然这一结果可以解释N体模拟中的引力坍缩的普遍性，但它在一般情况下并不正确，这表明外尔张量的磁性部分在牛顿极限下不需要消失。
We solve the nonlinear evolution of pressureless, irrotational density fluctuations in a perturbed Robertson-Walker spacetime using a new Lagrangian method based on the velocity gradient and gravity gradient tensors. Borrowing results from general relativity, we obtain a set of Newtonian ordinary differential equations for these quantities following a given mass element. Using these Lagrangian fluid equations we prove the following results: (1) The spherical tophat perturbation, having zero shear, is the slowest configuration to collapse for a given initial density and growth rate. (2) Initial density maxima are not generally the sites where collapse first occurs. (3) Initially underdense regions may undergo collapse if the shear is not too small. If the magnetic part of the Weyl tensor vanishes, the nonlinear evolution is described purely locally by our equations; this condition holds for spherical, cylindrical, and planar perturbations and may be a good approximation in other circumstances. Assuming the vanishing of the magnetic part of the Weyl tensor, we compute the exact nonlinear gravitational evolution of cold matter. We find that 56\% of initially underdense regions collapse in an Einstein-de Sitter universe for a homogeneous and isotropic random field. We also show that, given this assumption, the final stage of collapse is generically two-dimensional, leading to strongly prolate filaments rather than Zel'dovich pancakes. While this result may explain the prevalence of filamentary collapses in N-body simulations, it is not true in general, suggesting that the magnetic part of the Weyl tensor need not vanish in the Newtonian limit.