The IA Guide: A Breakdown of Intrinsic Alignment Formalisms

TL;DR

This work compiles a compact, technical reference on intrinsic alignments (IA) of galaxies, delineating how IA signals are defined, measured, and modeled across 2D and 3D formalisms. It systematically surveys ellipticity definitions, shear concepts, IA correlations, and estimators, then outlines a spectrum of IA models from Linear and Nonlinear Alignment to TATT, EFT, and halo-based approaches, including observational status and self-calibration methods. The document also highlights IA’s impact on weak lensing analyses, redshift-space distortions, and potential cosmological applications, providing a framework for current and future analyses. Overall, it serves as a practical guide for researchers to navigate IA formalisms, not a full review, with curated references and clear notation conventions for cross-study consistency.

Abstract

We summarize common notations and concepts in the field of Intrinsic Alignments (IA). IA refers to physical correlations involving galaxy shapes, galaxy spins, and the underlying cosmic web. Its characterization is an important aspect of modern cosmology, particularly in weak lensing analyses. This resource is both a reference for those already familiar with IA and designed to introduce someone to the field by drawing from various studies and presenting a collection of IA formalisms, estimators, modeling approaches, alternative notations, and useful references.

Figures (10)

• Figure 1: Galaxy shapes and orientations traced over a portion of JWST's NIRCam image of Abell 2744.
• Figure 2: The quantities $a$, $b$ and $\theta$ that define the shape and orientation of an ellipse. The dotted line indicates an arbitrary reference axis.
• Figure 3: Visualization of the real and imaginary components of , as described in Section \ref{['sec:Ellipticity']}. These functionally contain the same information. $\epsilon_1$ is maximum when a shape is highly elongated and exactly aligned with the angle that the ellipticity is defined relative to, most commonly North. $\epsilon_2$ is maximum when the shape is aligned with $\pi/4$ away from the principal angle.
• Figure 4: The setup for obtaining the projected shape of a galaxy. In linear theory, the angular momentum vector $\mathbf{L}$ of the galaxy is aligned along the direction of tidal stretching. The projected axis ratio, $b/a$, is a function of $\mathbf{L}$ and the ratio of the disk's intrinsic thickness to its diameter (not shown here).
• Figure 5: Representation of the Northern Celestial Hemisphere. The observer is indicated by O and a given observed galaxy by galaxy. The purple basis indicates the rotated basis defined in Eq. (\ref{['eq:rotated_basis_1']}) and Eq. (\ref{['eq:rotated_basis_2']}), whereas $\phi_1$ is the angle from the North Pole.