标题： 优化泽尔多维奇近似 显示英文标题

标题： Optimizing the Zel'dovich Approximation

摘要： 我们最近了解到，泽尔多维奇近似可以成功应用于比以前提出的更广泛的引力不稳定场景；我们在此研究如何扩展这一范围。 在之前的工作中，我们研究了几种解析近似在微弱非线性阶段对引力团聚的准确性。 我们发现“截断泽尔多维奇近似”（TZA）在从线性到微弱非线性（$\sigma \sim 3$）阶段的广泛范围内优于其他近似方法（除了在一种情况下，普通泽尔多维奇近似更好）。 TZA 将傅里叶振幅设为零，对于大于$k_{n\ell}$的波数{\it 所有}，其中$k_{n\ell}$标记了向非线性阶段的过渡。 在这里，我们研究了广义 TZA 与一组$n$体模拟之间的互相关，窗口函数有三种形状：尖锐的$k$截断（如 CMS 中的情况），坐标空间中的方窗，或高斯型。 我们还研究了在每种窗口类型内不同初始尺度上的互相关。 我们发现$k$截断比 CMS 中尝试的其他方法都要好，它是这三个窗函数形状中的最优选择{这最差}。我们发现，高斯窗函数$e^{-k^2/2k_G^2}$应用于初始傅里叶振幅时是最好的选择。它在我们研究的所有情况下都大大改善了互相关性。高斯窗函数的最佳选择$k_G$（谱相关的）是 1-1.5 倍$k_{n\ell}$，其中$k_{n\ell}$由公式（3）定义。尽管在应用泽尔多维奇近似后，所有三个窗函数产生的功率谱和密度分布函数相似，但与$n$体模拟的相位一致性对于高斯窗函数更好。我们将高斯窗函数的成功归因于其在相位演化方面的优越处理。 显示英文摘要

摘要： We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that the ``truncated Zel'dovich approximation" (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear ($\sigma \sim 3$) regimes. TZA sets Fourier amplitudes equal to zero for {\it all} wavenumbers greater than $k_{n\ell}$, where $k_{n\ell}$ marks the transition to the nonlinear regime. Here, we study crosscorrelation of generalized TZA with a group of $n$--body simulations for three shapes of window function: sharp $k$--truncation (as in CMS), tophat in coordinate space, or a Gaussian. We also study the crosscorrelation as a function of initial scale within each window type. We find $k$--truncation, which was so much better than other things tried in CMS, is the {it worst} of these three window shapes. We find that a Gaussian window $e^{-k^2/2k_G^2}$ applied to the intial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation all cases we studied. The optimum choice of $k_G$ for the Gaussian window is (spectrum-- dependent) 1--1.5 times $k_{n\ell}$, with $k_{n\ell}$ defined by (3). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, phase agreement with the $n$--body simulation is better for the Gaussian window. We ascribe Gaussian window success to its superior treatment of phase evolution.