Abstract
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.
Highlights
The modelling of intrinsic galaxy alignments has lagged behind similar efforts for other large-scale structure probes
6 Conclusions In Paper I [43], we had presented an effective field theory (EFT) expansion of galaxy intrinsic shapes, sizes and number density tracers that allows one to perform a complete prediction of three-dimensional Fourier-space statistics, i.e. power spectra up to the one-loop order and tree-level bispectra
We developed the projection formalism that relates these 3D correlators, which describe the physical dynamics of the observables, with the projected quantities that live on the 2D plane of the sky
Summary
The three-dimensional shapes of galaxies in their rest frame are spin-2 quantities that can be described in terms of a well-defined expansion in local gravitational observables. We presented a new EFT expansion for the former in Paper I [43], while the latter is described by the usual EFT of scalar biased tracers [44, 45] in complete analogy to the case of galaxy number counts This formalism allowed us to provide expressions for the two-point correlations between the intrinsic galaxy shape field and other scalar fields up to next-to-leading order, for which we drew analogies with the EFT application to scalar quantities, such as the number density of biased tracers [44, 45]. The computation of correlations between biased tensorial and scalar fields can be simplified by considerations of isotropy To this end, in Paper I [43] we proposed to decompose any given tensorial field in spherical tensors [46] of multipole order = 2, whose transformation properties under rotation are known.
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