论文标题
改善星系的各向异性3点相关函数的视线：质心和单位矢量平均方法缩放为$ \ mathcal {o}（n^2）$
Improving the Line of Sight for the Anisotropic 3-Point Correlation Function of Galaxies: Centroid and Unit-Vector-Average Methods Scaling as $\mathcal{O}(N^2)$
论文作者
论文摘要
测量星系三胞胎之间的相关性的3点相关函数（3PCF）编码有关特殊速度的信息，这些信息扭曲了沿视线远离其真实位置的星系位置的观察到的星系位置。要访问此信息，我们必须不仅跟踪3PCF对每个三角形的形状的依赖性，而且还必须在其视线方面的方向。因此，视线的不同选择将影响测得的3pcf。到目前为止，视线已被视为单个三胞胎成员（STM）的方向，但是使用哪个三重态成员会影响3PCF的统计误差的约20％。对于DESI（2019-24），更精确的5倍，这将转化为统计误差的100％，将总误差栏增加40％。我们在这里提出了一种新方法，该方法是三胞胎成员之间完全对称的新方法，并使用三个星系位置向量的平均值（我们向三角形质心）或单位（方向）向量的平均值使用。天真地，这些方法似乎需要三重态计数，将其缩放为$ n^3 $，而调查中的对象数量是$ n $。通过利用固体谐波定理，我们在这里展示如何将这些方法评估为$ n^2 $。我们希望它们可以用于对即将进行的红移调查（例如Desi）的各向异性3PCF进行健壮，无系统性的测量。因此，这样做会打开一个额外的通道，以限制结构的生长速度，从而了解物质密度并测试重力理论。
The 3-Point Correlation Function (3PCF), which measures correlations between triplets of galaxies encodes information about peculiar velocities, which distort the observed positions of galaxies along the line of sight away from their true positions. To access this information, we must track the 3PCF's dependence not only on each triangle's shape, but also on its orientation with respect to the line of sight. Consequently, different choices for the line of sight will affect the measured 3PCF. Up to now, the line of sight has been taken as the direction to a single triplet member (STM), but which triplet member is used impacts the 3PCF by ~20% of the statistical error for a BOSS-like survey. For DESI (2019-24), which is 5X more precise, this would translate to 100% of the statistical error, increasing the total error bar by 40%. We here propose a new method that is fully symmetric between the triplet members, and uses either the average of the three galaxy position vectors (which we show points to the triangle centroid), or the average of their unit (direction) vectors. Naively, these approaches would seem to require triplet counting, scaling as $N^3$, with $N$ the number of objects in the survey. By harnessing the solid harmonic shift theorem, we here show how these methods can be evaluated scaling as $N^2$. We expect that they can be used to make a robust, systematics-free measurement of the anisotropic 3PCF of upcoming redshift surveys such as DESI. So doing will in turn open an additional channel to constrain the growth rate of structure and thereby learn the matter density as well as test the theory of gravity.
