基于汉克尔变换的双谱窗口卷积
Bispectrum-window convolution via Hankel transform
AI总结：
本文提出利用二维FFTlog算法将功率谱卷积方法扩展到双谱，通过混合矩阵实现红移空间双谱多极矩与巡天窗口函数的精确卷积，并在球形窗口模型和数值模拟中验证了其百分之一水平的精度及无偏参数约束能力。
摘要：
我们提出了一种方法，用于对红移空间中双谱多极矩的模型预测与巡天窗口函数进行精确卷积。我们将一种广泛应用于功率谱卷积的方法扩展到双谱，并利用了二维FFTlog算法。作为对其精度的初步检验，我们考虑了实空间中球形窗口函数的玩具模型。该设置提供了窗口三点函数的解析评估，因此能够分离并量化该方法可能存在的系统误差。我们发现，以混合矩阵形式实现的卷积与来自大量模拟暗晕目录的测量结果相比，差异在百分之一水平。在对总模拟体积为$100\, h^{-3} \, {\ m Gpc}^3$的一组数值模拟进行似然分析时，该方法还能恢复对暗晕偏置参数的无偏约束。对于这些测试所要求的精度水平，与混合矩阵的乘法可在一秒或更短时间内完成。
英文摘要：
We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the bispectrum, taking advantage of a 2D-FFTlog algorithm. As a preliminary test of its accuracy, we consider the toy model of a spherical window function in real space. This setup provides an analytical evaluation of the 3-point function of the window, and therefore it allows to isolate and quantify possible systematic errors of the method. We find that our implementation of the convolution in terms of a mixing matrix shows differences at the percent level in comparison to the measurements from a very large set of mock halo catalogs. It is also able to recover unbiased constraints on halo bias parameters in a likelihood analysis of a set of numerical simulations with a total volume of $100\, h^{-3} \, {\rm Gpc}^3$. For the level of accuracy required by these tests, the multiplication with the mixing matrix is performed in the time of one second or less.
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