用快速傅里叶变换估计离散宇宙动量场的功率谱
Estimating power spectrum of discrete cosmic momentum field with fast Fourier transform
摘要：
基于快速傅里叶变换，给出了动量功率谱的估计方法，包括动量的自功率谱、动量散度、密度涨落和动量散度的互谱。提出了利用三阶Bettle-Lemarié尺度函数将离散目标分配到规则网格进行快速傅里叶变换的算法，以消除混叠效应。数值实验表明，该算法在接近奈奎斯特频率时，可以达到亚百分之一的精度。从理论上推导了去除整体流对动量功率谱估计的影响，并进行了数值验证。在大尺度下，去除整体流对动量功率谱估计的影响很小，但在非线性区域可能会引起有意义的差异，对于特征速度精确或足够精确的样本，可能没有必要去除整体流。测量并讨论了N体模拟中暗物质的动量功率谱。正如预期的那样，单圈欧拉微扰理论的预测与模拟的一致性仅略好于z=0时的线性理论，但可以以更高的精度应用于更高的红移。模拟数据的测量和单圈欧拉理论都揭示了动量场包含很强的旋转部分，动量散度中存在很大的随机分量，与密度场无关。三种动量功率谱各有特点。
英文摘要：
Fast Fourier transform based estimators are formulated for measuring momentum power spectra, including the auto power spectra of the momentum, the momentum divergence, and the cross spectrum of density fluctuation and momentum divergence. Algorithms using the third order Bettle-Lemarié scaling function to assign discrete objects to regular grids for fast Fourier transform are proposed to clean alias effects. Numerical experiments prove that the implementation can achieve sub-percent precision till close to the Nyquist frequency. Impact of removing bulk flow on estimation of momentum power spectra are derived theoretically and verified numerically, subtracting bulk flow has little effects at large scales but might induce meaningful differences in nonlinear regime, and probably it is not necessary to subtract bulk flow for samples which peculiar velocities are exact or sufficiently accurate. Momentum power spectra of dark matter samples from N-body simulation are measured and discussed. As expected, prediction of the one loop Eulerian perturbation theory agrees with simulation only slightly better than the linear theory at z=0, but can be applied to higher redshift with improved accuracy. Measurements of simulation data and the one loop Eulerian theory both reveal that the momentum field contains strong rotational part, and there is a large stochastic component in the divergence of momentum which is not correlated with the density field. The three kinds of momentum power spectra have their own characteristics.
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