An Enhanced Thermodynamic Framework for Third-Order Galaxy Correlation Functions: A Physically Motivated Closure and Observational Test

TL;DR

This paper introduces a thermodynamic framework for the galaxy three-point correlation function, providing an analytic solution and observational validation that addresses discrepancies between theory and measurements.

Contribution

It develops a physically motivated closure for the 3PCF hierarchy, incorporating virial effects and velocity dispersion, validated with SDSS/BOSS data.

Findings

Excellent fit to SDSS/BOSS measurements ($^2/of=1.27)

Addresses discrepancy between dark matter and galaxy 3PCF predictions

Links thermodynamic temperature to velocity dispersion (Fingers-of-God)

Abstract

The three-point correlation function (3PCF) is a crucial probe of non-Gaussianity and nonlinear structure formation. We develop a thermodynamic framework for the galaxy 3PCF by closing the BBGKY hierarchy with a physically motivated hierarchical ansatz, yielding a separable, analytic solution for the equilateral 3PCF. Our framework addresses the apparent discrepancy between the perturbation theory prediction for dark matter ($Q_{dm} \approx 1.6$) and observed galaxy measurements ($Q_{gal} \approx 0.5$) by incorporating thermodynamic virial effects and velocity dispersion. We validate this model with SDSS/BOSS CMASS measurements, obtaining an excellent fit ($\chi^2/\mathrm{dof} = 1.27$) across $1$-$50,h^{-1}\mathrm{Mpc}$. The analysis utilizes the Szapudi-Szalay estimator with robust covariance estimation from the SLICS simulation suite. By linking the thermodynamic temperature $T$ to the small-scale velocity dispersion (Fingers-of-God), we establish the thermodynamic approach as a predictive, complementary description of higher-order galaxy clustering on quasi-linear scales.