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

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 ($χ^2/\mathrm{dof} = 1.27$) 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.

💡 Research Summary

The paper presents a novel thermodynamic approach to modeling the galaxy three‑point correlation function (3PCF), aiming to resolve the long‑standing discrepancy between the perturbation‑theory prediction for dark matter (Q_dm ≈ 1.6) and the observed galaxy value (Q_gal ≈ 0.5). The authors start from the BBGKY hierarchy, which describes the evolution of N‑point distribution functions in a gravitating system, and close the third‑order equation using a physically motivated hierarchical ansatz. This ansatz, ζ(r₁₂,r₂₃,r₃₁)=Q