Using the Zeldovich dynamics to test expansion schemes
Using the Zeldovich dynamics to test expansion schemes
复制标题
使用 Zeldovich 动力学测试扩展方案
DOI：
10.1051/0004-6361:20078065
复制
发表时间：
2007
影响因子：
6.5
通讯作者：
P. Valageas
中科院分区：
文献类型：
--
作者：
P. Valageas
目标。我们将可用于研究引力聚集的各种展开方案应用于Zeldovich动力学的简单情况。方法：研究方法。利用著名的Zeldovich动力学精确解，我们可以将各种微扰方法的预测结果与精确的非线性结果进行比较。我们还可以研究它们的收敛性质和它们在高阶时的行为。结果。我们发现，在高度非线性的区域，大多数系统展开都不能恢复响应函数的衰变。“线性方法”导致高阶非线性区域的增长越来越快，除了在任何阶上给出有界响应的Pade近似。“非线性方法”设法在单环阶数获得一些阻尼值，但在更高的阶数却失败。虽然它恢复了精确的高斯衰减，但恢复高k极限并不是很合理，因为非线性功率的产生不是来自有限范围的波数(因此不存在简单的尺度分离)。没有一种方法能够在高度非线性的尺度上恢复物质功率谱的驰豫。可以以某种特别的方式强制实施高斯截断，以再现两个不同时间的精确两点函数的行为。然而，这一截止点与物质的聚集没有直接关系，在精确的等时统计数据中消失了，例如物质功率谱。在定量的水平上，在弱非线性尺度上，通常的微扰理论，以及在响应函数中增加这样一个高斯截断的非线性格式，是两种最有效的方法。我们可以预期这些结果也适用于引力动力学(这已经明确地在单圈顺序上进行了检验)，因为这两种动力学的运动方程的结构是相同的。
Aims. We apply various expansion schemes that may be used to study gravitational clustering to the simple case of the Zeldovich dynamics. Methods. Using the well-known exact solution of the Zeldovich dynamics we can compare the predictions of these various perturbative methods with the exact nonlinear result. We can also study their convergence properties and their behavior at high orders. Results. We find that most systematic expansions fail to recover the decay of the response function in the highly nonlinear regime. “Linear methods” lead to increasingly fast growth in the nonlinear regime for higher orders, except for Pade approximants that give a bounded response at any order. “Nonlinear methods” manage to obtain some damping at one-loop order but they fail at higher orders. Although it recovers the exact Gaussian damping, a resummation in the high-k limit is not justified very well as the generation of nonlinear power does not originate from a finite range of wavenumbers (hence there is no simple separation of scales). No method is able to recover the relaxation of the matter power spectrum on highly nonlinear scales. It is possible to impose a Gaussian cutoff in a somewhat ad-hoc fashion to reproduce the behavior of the exact two-point functions for two different times. However, this cutoff is not directly related to the clustering of matter and disappears in exact equal-time statistics such as the matter power spectrum. On a quantitative level, on weakly nonlinear scales, the usual perturbation theory, and the nonlinear scheme to which one adds an ansatz for the response function with such a Gaussian cutoff ,a re the two most efficient methods. We can expect these results to hold for the gravitational dynamics as well (this has been explicitly checked at one-loop order), since the structure of the equations of motion is identical for both dynamics.