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-Lemarie 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.

中文翻译：

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用快速傅立叶变换估计离散宇宙动量场的功率谱

基于快速傅立叶变换的估计器用于测量动量功率谱，包括动量的自功率谱、动量发散以及密度波动和动量发散的交叉谱。建议使用三阶 Bettle-Lemarie 缩放函数将离散对象分配给规则网格以进行快速傅立叶变换的算法来清除混叠效应。数值实验证明，该实现可以达到亚百分比精度，直到接近奈奎斯特频率。从理论上推导出去除体流对动量功率谱估计的影响并通过数值验证，减去体流在大尺度上几乎没有影响，但可能会导致非线性状态的有意义的差异，对于特殊速度准确或足够准确的样品，可能没有必要减去体积流量。测量和讨论了来自 N 体模拟的暗物质样本的动量功率谱。正如预期的那样，单环欧拉微扰理论的预测与模拟一致，仅比 z=0 的线性理论略好，但可以应用于更高的红移，并提高精度。模拟数据的测量和单环欧拉理论均表明动量场中含有强旋转部分，动量散度中存在较大的与密度场无关的随机成分。这三种动量功率谱各有特点。测量和讨论了来自 N 体模拟的暗物质样本的动量功率谱。正如预期的那样，单环欧拉微扰理论的预测与模拟一致，仅比 z=0 的线性理论略好，但可以应用于更高的红移，并提高精度。模拟数据的测量和单环欧拉理论均表明动量场中含有强旋转部分，动量散度中存在较大的与密度场无关的随机成分。这三种动量功率谱各有特点。测量和讨论了来自 N 体模拟的暗物质样本的动量功率谱。正如预期的那样，单环欧拉微扰理论的预测与模拟一致，仅比 z=0 的线性理论略好，但可以应用于更高的红移，并提高精度。模拟数据的测量和单环欧拉理论均表明动量场中含有强旋转部分，动量散度中存在较大的与密度场无关的随机成分。这三种动量功率谱各有特点。但可以应用于更高的红移，并提高精度。模拟数据的测量和单环欧拉理论均表明动量场中含有强旋转部分，动量散度中存在较大的与密度场无关的随机成分。这三种动量功率谱各有特点。但可以应用于更高的红移，并提高精度。模拟数据的测量和单环欧拉理论均表明动量场中含有强旋转部分，动量散度中存在较大的与密度场无关的随机成分。这三种动量功率谱各有特点。