arXiv 2102.086292021-02astro-ph.COastro-ph.IM

精确的P $^{3}$ M算法用于引力透镜的模拟研究

An Accurate P$^{3}$M Algorithm for Gravitational Lensing Studies in Simulations

Kun Xu, Yipeng Jing

备注：: 11 pages, 6 figures, accepted for publication on ApJ
发表信息：: The Astrophysical Journal, Volume 915, 2021, Number 2
DOI：: 10.3847/1538-4357/ac0249

摘要：

本文提出了一种二维粒子-网格（P $^3$ M）算法，该算法具有优化的格林函数和自适应的软化长度，用于N体模拟中引力透镜的研究。给出了优化格林函数$\hat{G}(\rm{k})$的解析形式。软化计划（$S$）的PM和PP的计算进行了研究，以准确的力计算和抑制颗粒离散效应。我们的方法是两个数量级更准确的比简单的PM算法与{ \it穷人的}格林函数（$\propto1/k^2$）在几个网格单元或更小的规模。力的各向异性也比传统的PM计算小得多。我们的算法可以在所有尺度上实现优于0.1%的力精度，这使得它成为{ \textit{micro} }透镜研究的理想（准确和快速）算法。当我们应用该算法计算N体模拟中的{ \textit{weak} }和{ \textit{strong} }透镜量时，粒子离散性引起的泊松噪声是主要的误差。泊松噪声可以通过平滑粒子分布来抑制，这可以通过简单地在PP计算中选择自适应软化长度来实现。我们提出了一个标准，设置自适应软化长度。我们的算法也适用于宇宙学模拟。我们提供了一个\textsc{python}实现\texttt{P3Mlens}，这个算法。

英文摘要：

We present a two-dimensional (2D) Particle-Particle-Particle-Mesh (P$^3$M) algorithm with an optimized Green function and adaptive softening length for gravitational lensing studies in N-Body simulations. The analytical form of the optimized Green function $\hat{G}(\rm{k})$ is given. The softening schemes ($S$) are studied for both the PM and the PP calculations in order for accurate force calculation and suppression of the particle discreteness effect. Our method is two orders of magnitude more accurate than the simple PM algorithm with the {\it poor man's} Green function ($\propto1/k^2$) at a scale of a few mesh cells or smaller. The force anisotropy is also much smaller than the conventional PM calculation. We can achieve a force accuracy better than 0.1 percent at all scales with our algorithm, which makes it an ideal (accurate and fast) algorithm for {\textit{micro}} lensing studies . When we apply the algorithm to computing {\textit{weak}} and {\textit{strong}} lensing quantities in N-Body simulations, the errors are dominated by the Poisson noise caused by particle discreteness. The Poisson noise can be suppressed by smoothing out the particle distribution, which can be achieved by simply choosing an adaptive softening length in the PP calculation. We have presented a criterion to set the adaptive softening length. Our algorithm is also applicable to cosmological simulations. We provide a \textsc{python} implementation \texttt{P3Mlens} for this algorithm.

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