# Using galaxy pairs to investigate the three-point correlation function in the squeezed limit

## TL;DR

This paper develops an efficient FFT-based method to analyze the squeezed limit of the three-point correlation function using galaxy pairs, revealing insights into galaxy-halo connections and the impact of large-scale structures.

## Contribution

It introduces a novel algorithm for computing the squeezed 3PCF with galaxy pairs, applied to simulations, and explores its potential to constrain complex HOD models.

## Key findings

- Peak in pair-galaxy bias at ~2 Mpc separation
- Strong anisotropy in signals tracking filamentary structures
- Squeezed 3PCF varies significantly, offering additional galaxy-halo information

## Abstract

We investigate the three-point correlation function (3PCF) in the squeezed limit by considering galaxy pairs as discrete objects and cross-correlating them with the galaxy field. We develop an efficient algorithm using Fast Fourier Transforms to compute such cross-correlations and their associated pair-galaxy bias bpg and the squeezed 3PCF coefficient Qeff. We implement our method using N-body cosmological simulations and a fiducial Halo Occupation Distribution (HOD) and present the results in both the real space and redshift space. In real space, we observe a peak in bpg and Qeff at pair separation of ~ 2 Mpc, attributed to the fact that galaxy pairs at 2 Mpc separation trace the most massive dark matter halos. We also see strong anisotropy in the bpg and Qeff signals that track the large-scale filamentary structure. In redshift space, both the 2 Mpc peak and the anisotropy are significantly smeared out along the line-of-sight due to Finger-of-God effect. In both the real space and redshift space, the squeezed 3PCF shows a factor of 2 variation, contradicting the hierarchical ansatz but offering rich information on the galaxy-halo connection. Thus, we explore the possibility of using the squeezed 3PCF to constrain the HOD. When we compare two simple HOD models that are closely matched in their projected two-point correlation function (2PCF), we do not yet see a strong variation in the 3PCF that is clearly disentangled from variations in the projected 2PCF. Nevertheless, we propose that more complicated HOD models, e.g. those incorporating assembly bias, can break degeneracies in the 2PCF and show a distinguishable squeezed 3PCF signal.