Intrinsic galaxy alignments yield an important contribution to the observed statistics of galaxy shapes. The general bias expansion for galaxy sizes and shapes in three dimensions has been recently described by Vlah, Chisari & Schmidt using the general perturbative effective field theory (EFT) framework, in analogy to the clustering of galaxies. In this work, we present a formalism that uses the properties of spherical tensors to project galaxy shapes onto the observed sky in the flat-sky approximation, and compute the two-point functions at next-to-leading order as well as the leading-order three-point functions of galaxy shapes and number counts. The resulting expressions are given in forms that are convenient for efficient numerical implementation. For a source redshift distribution typical of Stage IV surveys, we find that nonlinear intrinsic alignment contributions to galaxy shape correlations become relevant at angular wavenumbers l ≳ 100.

内在星系排列对观测到的星系形状统计有重要贡献。最近，Vlah、Chisari 和 Schmidt 使用一般微扰有效场论 (EFT) 框架描述了星系大小和形状在三个维度上的一般偏差扩展，类似于星系的聚类。在这项工作中，我们提出了一种形式主义，它使用球面张量的性质将星系形状投影到平坦天空近似中的观测天空，并以次前导顺序计算两点函数以及前导-对星系形状和数量计数的三点函数进行排序。结果表达式以便于有效数值实现的形式给出。对于第四阶段调查典型的源红移分布，