各向异性晕三阶相关函数的建模与测量：一项协调研究
Modeling and measuring the anisotropic halo 3-point correlation function: a coordinated study
AI总结：
本文提出了一种新的高效方法，用于建模和估计各向异性三阶相关函数（3PCF）的各阶矩及其估计量，通过比较模型预测与直接测量，验证了该方法在探测聚类各向异性方面的有效性，并展示了结合二阶相关函数（2PCF）和三阶相关函数对参数估计的改进。
摘要：
正在进行和未来的光谱星系调查将覆盖前所未有的体积，其中物体数量足够大，可以有效地通过高阶统计量探测聚类各向异性。在本文中，我们提出了一种新颖且高效的实现，用于建模各向异性三阶相关函数（3PCF）的各阶矩及其估计量。为了评估我们模型的性能，我们将其预测结果与通过我们估计量直接获得的3PCF测量结果进行了比较，这些测量结果来自298个暗物质晕目录，这些目录源自$z=1$时刻的$N$-body模拟。在统计分析中，我们使用了一个独立的3000个伪晕目录集合来估计协方差矩阵，这些目录在同一红移处。然后，我们通过结合二阶相关函数（2PCF）与三阶相关函数进行分析，包括和不包括其各向异性部分。在仅使用三阶相关函数的分析中，添加三阶相关函数的各向异性部分有效地打破了增长率$f$与线性偏差$b_1$之间的退化，显著降低了它们的不确定性。它也显著提高了Alcock-Paczynski参数$\varepsilon$的精度，但并未减少我们发现的约1%的各向异性膨胀参数$α$的估计偏差。联合2PCF+3PCF分析减少了，但并未完全消除AP和各向异性膨胀参数的偏差，并打破了$f$-$b_1$-$σ_8$的退化，从而总体上得到更紧的约束。各向异性三阶相关函数对联合分析贡献有限，因为树级三阶相关函数模型无法捕捉主要编码在小尺度和压缩三角形配置中的各向异性信息。需要更高级的模型才能充分利用这一信息。
英文摘要：
Ongoing and future spectroscopic galaxy surveys will cover unprecedented volumes with a number of objects large enough to effectively probe clustering anisotropies through higher-order statistics. In this work, we present a novel and efficient implementation of both a model for the multipole moments of the anisotropic 3-point correlation function (3PCF) and of their estimator. To evaluate the performance of our model, we compared its predictions against direct 3PCF measurements obtained with our estimator from a set of 298 dark matter halo catalogs drawn from the $z=1$ snapshots of $N$-body simulations. For the statistical analysis, we employed a covariance matrix estimated from an independent suite of 3000 mock halo catalogs at the same redshift. We then repeated the analysis by combining the 2-point correlation function (2PCF) to the 3PCF, with and without including its anisotropic part. In the 3PCF-only analysis, the addition of the anisotropic component of the 3PCF effectively breaks the degeneracy between the growth rate $f$ and the linear bias $b_1$, significantly reducing their uncertainties. It also significantly improves the precision of the Alcock-Paczynski parameter $\varepsilon$ but does not reduce the $\sim 1$% offset we find in the estimate of the isotropic dilation parameter $α$. The joint 2PCF+3PCF analysis reduces, though does not fully remove, biases in the AP and isotropic dilation parameters and breaks the $f$-$b_1$-$σ_8$ degeneracy, leading to tighter constraints overall. The anisotropic 3PCF adds little to the joint analysis because the tree-level 3PCF model fails to capture the anisotropic information primarily encoded on small scales and in squeezed triangle configurations. A more advanced model will be required to exploit this information fully.
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