[Paper Review] Evolution of halo-halo clustering and bias in a LCDM model

Andrey V. Kravtsov, Anatoly Klypin+2 more|arXiv (Cornell University)|Sep 29, 1998

Galaxies: Formation, Evolution, Phenomena3 citations

TL;DR

This study uses high-resolution N-body simulations in a ΛCDM framework to investigate halo-halo clustering and scale-dependent bias, resolving the overmerging problem in dense regions. It finds that galaxy-size halos follow a power-law correlation function with slope ~1.6–1.8, and scale-dependent bias emerges at scales <7/h Mpc, with excellent agreement between simulated halo clustering and observed galaxy data at z=0 and high redshifts.

ABSTRACT

We study the evolution of the halo-halo correlation function and bias in a LCDM model using very high-resolution N-body simulations. The high force and mass resolution allows dark matter (DM) halos to survive in the tidal fields in high-density regions and thus prevents the ambiguities related with the ``overmerging problem.'' Numbers of galaxy-size halos in cluster-like objects in our simulation are similar to the numbers of galaxies observed in real clusters. This allows us to estimate for the first time the evolution of the correlation function and bias at small (down to ~100/h kpc) scales. We compare particle distribution, dark matter correlation function, density profiles, and halo mass function produced with our N-body code and corresponding results of the AP3M simulations. We find that at all epochs the 2-point correlation function of galaxy-size halos xihh is well approximated by a power-law with slope ~1.6-1.8. The difference between the shape of xihh and the shape of the correlation function of matter results in the scale-dependent bias at scales &lt;7/h Mpc, which we find to be a generic prediction of the hierarchical models, independent of the epoch and of the model details. We find that our results agree well with existing clustering data at different redshifts, indicating the general success of the picture of structure formation in which galaxies form inside the host DM halos. Particularly, we find an excellent agreement in both slope and the amplitude between xihh(z=0) in our simulation and the galaxy correlation function measured using the APM galaxy survey. At high redshifts, the observed clustering of the Lyman-break galaxies is also reasonably well reproduced by the models.

Motivation & Objective

• To study the evolution of halo-halo clustering and bias in a ΛCDM model with high-resolution simulations.
• To overcome the overmerging problem in dark matter simulations by using high force and mass resolution.
• To compare simulated halo clustering with observational data on galaxy clustering at different redshifts.
• To assess the consistency of the hierarchical structure formation model where galaxies form within dark matter halos.
• To quantify the scale dependence of bias at small scales (~100/h kpc) and its evolution over time.

Proposed method

• Conducting very high-resolution N-body simulations of a ΛCDM cosmological model to resolve dark matter halos in high-density regions.
• Using a high-force and high-mass resolution code to prevent artificial merging of subhalos in tidal environments.
• Measuring the two-point halo-halo correlation function (xihh) at multiple redshifts to track clustering evolution.
• Comparing the simulated halo correlation function with matter correlation function to quantify scale-dependent bias.
• Validating results against AP3M simulations and observational data from the APM survey and Lyman-break galaxies.
• Analyzing density profiles, mass functions, and particle distributions to ensure simulation reliability and consistency.

Experimental results

Research questions

• RQ1 How does the halo-halo correlation function evolve over time in a ΛCDM model?
• RQ2 What is the nature and scale dependence of bias between halos and underlying matter in hierarchical structure formation?
• RQ3 To what extent do simulated galaxy-size halos reproduce observed galaxy clustering amplitudes and slopes at z=0?
• RQ4 Can high-resolution simulations resolve the overmerging problem and produce realistic cluster-like halo populations?
• RQ5 How well do simulated halo clustering results match high-redshift observations of Lyman-break galaxies?

Key findings

• The two-point halo-halo correlation function (xihh) follows a power-law with a slope of approximately 1.6–1.8 at all redshifts studied.
• Scale-dependent bias emerges at scales below 7/h Mpc, a generic feature of hierarchical models independent of epoch and model details.
• The simulated halo correlation function at z=0 matches the APM galaxy survey in both amplitude and slope, indicating strong consistency with observations.
• The number of galaxy-sized halos in cluster-like structures in the simulation matches observed galaxy counts in real clusters.
• High-redshift clustering of Lyman-break galaxies is reasonably well reproduced by the model, supporting the halo-based galaxy formation picture.
• The simulation results show good agreement with AP3M simulations in particle distribution, matter correlation function, density profiles, and mass function.