The halo 3-point correlation function: a methodological analysis

Upcoming galaxy surveys will provide us with an unprecedented view of the Large -Scale Structure of the Universe and the realistic chance to extract valuable astrophysical and cosmological information from higher-order clustering statistics. This perspective poses new challenges, requiring both accurate and efficient estimators and a renewed assessment of possible systematic errors in the theoretical models and likelihood assumptions. This work investigates these issues in relation to the analysis of the 3-point correlation function (3PCF) in configuration space. We measure the 3PCF of 300 halo catalogs from the MINERVA simulations covering a total volume of 1000h-3Gpc3. Each 3PCF measurement includes all possible triangular configurations with sides between 20 and 130h-1 Mpc. In the first place, we test different estimates of the covariance matrix, a crucial aspect of the analysis. We compare the covariance computed numerically from the limited but accurate benchmark simulations set to the one obtained from 10000 approximate halo catalogs generated with the PINOCCHIO code. We demonstrate that the two numerically-estimated covariance matrices largely match, confirming the validity of approximate methods based on Lagrangian Perturbation Theory for generating mocks suitable for covariance estimation. We also compare the numerical covariance with a theoretical prediction in the Gaussian approximation. We find a good match between the two for separations above 40h-1 Mpc. We test the 3PCF tree-level model in Perturbation Theory. The model is adopted in a likelihood analysis aimed at the determination of bias parameters. We find that, for our sample of halos at redshift z = 1, the tree-level model performs well for separations r > 40h-1 Mpc. Results obtained with this scale cut are robust against different choices of covariance matrix. We compare to the analogous analysis of the halo bispectrum already presented in a previous publication, finding a remarkable agreement between the two statistics. We notice that such comparison relies, to the best of our knowledge for the first time, on a robust and consistent covariance estimate and on the inclusion of essentially all measurable configurations in Fourier as in configuration space. We then test different assumptions to build the model defining a robust combination of hypotheses that lead to unbiased parameter estimates. Our results confirm the importance of 3PCF, supplying a solid recipe for its inclusion in likelihood analyses. Moreover, it opens the path for further improvements, especially in modelling, to extract information from non-linear regimes.