Three-point intrinsic alignments of galaxies and haloes in the FLAMINGO simulations

TL;DR

This study measures and models the third-order intrinsic alignment signal in galaxies and haloes within the FLAMINGO hydrodynamical simulations, using the $3$PCF and third-order aperture-mass statistics. It demonstrates that a tree-level effective field theory (EFT) of intrinsic alignments, with four bias operators, accurately describes large-scale IA on scales $R_i\gtrsim 25$–$30$ Mpc, and that a reduced EFT assuming linear Lagrangian bias (co-evolution relations) provides an especially good fit with minimal bias and fewer free parameters. The results show that higher-order IA parameters roughly follow linear-Lagrangian relations across mass and redshift, and that galaxies broadly track the alignment properties of their host haloes, with velocity-shear and tidal-torquing contributions playing significant roles. These findings offer a physically motivated, self-consistent framework for incorporating higher-order IA information into weak-lensing analyses, with implications for photometric surveys where constraining IA parameters is challenging and model simplifications can reduce biases. Caution is advised when extrapolating to smaller scales or lower-mass galaxies, and future work should extend these results to broader samples and include potential binning and integration-cut effects in observational contexts.

Abstract

Third-order statistics provide information beyond two-point measures, but extracting this information requires accurate and consistent modelling. We measure and detect the three-point correlation function and third-order aperture-mass statistics of intrinsic alignments (IA) for galaxies and for haloes with $M_{\rm halo} > 10^{13}\,{\rm M}_\odot$ in the $(2.8\,\mathrm{Gpc})^3$ simulation volume of the FLAMINGO hydrodynamical simulation suite. We model the third-order aperture-mass statistics and show that on large scales both the galaxy and halo samples are well described by the tree-level effective field theory (EFT) of IA across the three dark matter density-shape combinations and a wide range of triangle configurations, with the alignment amplitude consistent with that inferred from two-point statistics. We compare the full EFT to several other models: a version neglecting the velocity-shear term, the non-linear alignment model (NLA), and to a reduced EFT assuming co-evolution relations that follow from the assumption that alignment is linear in Lagrangian space. The first two models yield biased constraints on the alignment amplitude, but the reduced EFT performs remarkably well, achieving a low reduced chi-squared and minimal bias. We examine the redshift and mass dependence of the higher-order bias parameters, finding that the linear Lagrangian bias assumption is approximately satisfied across the explored halo mass and redshift ranges for both galaxies and haloes, suggesting that the galaxies broadly follow the alignment properties of their host haloes. These co-evolution relations can be valuable for photometric shear surveys, where limited constraining power on IA parameters favours models with fewer free parameters.

Figures (16)

• Figure 1: The upper panel shows the ellipticity distribution of either galaxies or haloes given a certain mass cut at $z=0$. The ellipticities are obtained via the simple, non-iterative, inertia tensor using only particles within the half mass radius of the object. The lower panel shows the corresponding mass ranges. A minimum of 300 stellar particles and a dark matter halo mass cut of $M_{\rm h} \geq 10^{13}\,{\rm M}_\odot$ are applied. The dotted histogram indicates dark matter haloes below this mass threshold that still satisfy the stellar particle cut; this subsample is not used in the analysis.
• Figure 2: We define the triangles using the side-angle-side congruence criterion (SAS). In the $\times$ projection, shapes located at vertex $r_1$ are projected along the red dashed line, shapes at $r_2$ along $d_1$ and shapes at $r_3$ along $d_2$. The red dashed line is oriented at an angle $\frac{1}{2}(\varphi_1 + \varphi_2)$ relative to the $x$-axis, where $\varphi_1$ and $\varphi_2$ denote the polar angles (measured from the $x$-axis) of $d_1$ and $d_2$ respectively.
• Figure 3: Alignment around galaxy pairs (red dots) separated by a distance $d_3$. The colour map represents the amplitude of the total alignment signal on a logarithmic scale. The black lines indicate the orientation of the galaxies. The grey circle has a radius of $d_3/2$ and is centered at $(d_3/2,\, 0)$; according to Thales' theorem, any triangle formed with points inside this circle has an opening angle larger than $90^\circ$, while triangles formed with points outside the circle have an opening angle smaller than $90^\circ$.
• Figure 4: The $\phi$ dependence of the radial components (the real part of the 3PCF) of the connected 3PCF for position-position-shape correlations (ggI), position-shape-shape correlations (gII) and shape-shape-shape correlations (III). Here we show our main sample of galaxies and haloes with $M_{\rm h} > 10^{13}$ M$_\odot$ at $z=0$.
• Figure 5: Posteriors of the EFT parameters fitted to $\langle NNM_{\rm ap}\rangle$ of both galaxies and haloes. The grey lines show the alignment amplitude obtained from two-point statistics at scales $\geq$ 40 Mpc. The one (two) sigma around the two-point estimate is shown as a shaded region. We show the posteriors for our main samples of $M_{\rm h} > 10^{13}$ M$_\odot$ at $z=0$ omitting triangles with radii $R_i$ smaller than 30 Mpc for the three-point statistics.