Quantifying the Cosmic Web I: The large-scale halo ellipticity-ellipticity and ellipticity-direction correlations

TL;DR

This paper measures and analyzes the large-scale ellipticity-ellipticity and ellipticity-direction correlations of dark matter halos in the Cosmic Web using Millennium Simulation data, revealing their dependence on redshift and halo mass.

Contribution

It provides the first detailed numerical analysis of EE and ED correlations across multiple redshifts and halo masses, with empirical fitting functions for these correlations.

Findings

EE correlations are strongest along the major axis and significant up to 10 Mpc/h.

ED correlations are stronger than EE and extend up to 50 Mpc/h.

Correlations decrease with decreasing redshift and increase with halo mass.

Abstract

The formation of dark matter halos tends to occur anisotropically along the filaments of the Cosmic Web, which induces both ellipticity-ellipticity (EE) correlations between the shapes of halos, as well as ellipticity-direction (ED) cross-correlations between halo shapes and the directions to neighboring halos. We analyze the halo catalogue and the semi-analytic galaxy catalogue of the recent Millennium Run Simulation to measure the EE and ED correlations numerically at four different redshifts (z=0, 0.5, 1 and 2). For the EE correlations, we find that (i) the major-axis correlation is strongest while the intermediate-axis correlation is weakest; (ii) the signal is significant at distances out to 10 Mpc/h; (iii) the signal decreases as z decreases; (iv) and its behavior depends strongly on the halo mass scale, with larger masses showing stronger correlations at large distances. For the ED correlations, we find that (i) the correlations are much stronger than the EE correlations, and are significant even out to distances of 50 Mpc/h; (ii) the signal also decreases as z decreases; (iii) and it increases with halo mass at all distances. We also provide empirical fitting functions for the EE and ED correlations. The EE correlations are found to scale linearly with the linear density correlation function, xi(r). While the ED cross-correlation is found to scale as xi^{1/2}(r) at large distances beyond 10 Mpc/h. The best-fit values of the fitting parameters for the EE and the ED correlations are all determined through chi^{2}-statistics. Our results may be useful for quantifying the filamentary distribution of dark matter halos over a wide range of scales.