[Paper Review] Three-point correlation function in the quasilinear regime

Jing Yi, G. Boêrner|arXiv (Cornell University)|Jun 20, 1996

Galaxies: Formation, Evolution, Phenomena2 references7 citations

TL;DR

This paper applies second-order Eulerian perturbation theory (SEPT) to compute the three-point correlation function (3PCF) in the quasilinear regime for SCDM, LCDM, and MDM cosmological models, finding distinct 3PCF shapes across models. N-body simulations show SEPT predictions are inaccurate even at small scales (r < 10 Mpc), though all models exhibit strong triangle-shape dependence in the 3PCF, which is observable in galaxy clustering if galaxies trace mass.

ABSTRACT

Using the second-order Eulerian perturbation theory (SEPT), we study the three-point correlation function $ζ$ in the quasilinear regime for the SCDM, LCDM and MDM models, with the interesting result that these three models have distinctive three-point correlation functions. We test this SEPT prediction using a large set of high-resolution N-body simulations. The N-body results show that the SEPT prediction for $ζ$ is not accurate even in the quasilinear regime ($r\la 10 \mpc$), in contrast to previous N-body tests on the skewness. However, similar to the perturbation theory, our N-body results still predict a strong dependence of the three-point correlation on the triangle shape which is observable in the distribution of galaxies if the galaxies trace the distribution of the underlying mass

Motivation & Objective

• To investigate the three-point correlation function (3PCF) in the quasilinear regime using second-order Eulerian perturbation theory (SEPT).
• To compare SEPT predictions for the 3PCF across three cosmological models: SCDM, LCDM, and MDM.
• To test the accuracy of SEPT against high-resolution N-body simulations in the quasilinear regime (r < 10 Mpc).
• To assess the observability of 3PCF shape dependence on triangle geometry in galaxy distributions.

Proposed method

• Second-order Eulerian perturbation theory (SEPT) is used to analytically compute the three-point correlation function in the quasilinear regime.
• The method computes the 3PCF as a function of triangle shape, incorporating non-Gaussian corrections from second-order density fields.
• Theoretical predictions are derived for three cosmological models: SCDM, LCDM, and MDM, with distinct power spectra.
• High-resolution N-body simulations are performed to generate empirical 3PCF measurements for direct comparison with SEPT predictions.
• The 3PCF is evaluated as a function of scale and triangle shape (e.g., equilateral, isosceles, squeezed) to assess geometric dependence.
• Theoretical and simulated 3PCF results are compared to test the validity of SEPT in the quasilinear regime.

Experimental results

Research questions

• RQ1 How does the three-point correlation function differ across SCDM, LCDM, and MDM models in the quasilinear regime?
• RQ2 To what extent does second-order Eulerian perturbation theory accurately predict the 3PCF in the quasilinear regime?
• RQ3 Does the 3PCF exhibit a strong dependence on triangle geometry (shape) in these models?
• RQ4 Can the predicted 3PCF shape dependence be observed in galaxy distributions if galaxies trace mass?
• RQ5 Why does SEPT fail to match N-body simulation results despite its success in predicting skewness?

Key findings

• The three-point correlation function predicted by SEPT shows distinct shapes for SCDM, LCDM, and MDM models, indicating model differentiation potential.
• SEPT predictions for the 3PCF show poor agreement with high-resolution N-body simulations even at scales r < 10 Mpc in the quasilinear regime.
• Despite SEPT's inaccuracy, the N-body simulations confirm a strong dependence of the 3PCF on triangle shape, which is robust across models.
• The triangle-shape dependence of the 3PCF is observable in galaxy clustering if galaxies trace the underlying mass distribution.
• The discrepancy between SEPT and simulations suggests limitations in perturbation theory for the 3PCF, even in the quasilinear regime.
• The results imply that higher-order corrections or non-perturbative effects may be necessary for accurate 3PCF modeling.