The spatial and velocity bias of linear density peaks and proto-haloes in the Lambda cold dark matter cosmology

TL;DR

This study uses high-resolution simulations to analyze the bias in the distribution and velocities of proto-haloes in the LCDM universe, testing theoretical models against numerical data.

Contribution

It validates the scale-dependence of bias predictions for velocity divergence and highlights discrepancies in density bias parameters, revealing limitations of current models.

Findings

Velocity bias coefficients match theoretical predictions.

Density bias parameters do not match predictions, especially for lower mass haloes.

Detects stochasticity in density bias on large scales.

Abstract

We use high resolution N-body simulations to investigate the Lagrangian bias of cold dark matter haloes within the LCDM cosmology. Our analysis focuses on "proto-haloes", which we identify in the simulation initial conditions with the subsets of particles belonging to individual redshift-zero haloes. We then calculate the number-density and velocity-divergence fields of proto-haloes and estimate their auto spectral densities. We also measure the corresponding cross spectral densities with the linear matter distribution. We use our results to test a Lagrangian-bias model presented by Desjacques and Sheth which is based on the assumption that haloes form out of local density maxima of a specific height. Our comparison validates the predicted functional form for the scale-dependence of the bias for both the density and velocity fields. We also show that the bias coefficients are accurately predicted for the velocity divergence. On the contrary, the theoretical values for the density bias parameters do not accurately match the numerical results as a function of halo mass. This is likely due to the simplistic assumptions that relate virialized haloes to density peaks of a given height in the model. We also detect appreciable stochasticity for the Lagrangian density bias, even on very large scales. These are not included in the model at leading order but correspond to higher order corrections.