The Halo Mass-Bias Redshift Evolution in the $\Lambda$CDM Cosmology

TL;DR

This paper develops an analytic model for the evolution of linear bias of dark matter halos in the DM cosmology, calibrated with simulations and compared with observational data, revealing differences in bias evolution for various QSO selections.

Contribution

It introduces a second order differential equation-based model for bias evolution that accounts for interactions and merging, calibrated with simulations and validated against observations.

Findings

Bias evolution differs between optical and X-ray selected QSOs.

Typical dark matter halo masses for QSOs are around 10^{13} to 5 imes 10^{13} h^{-1} M_{\u2299}.

The model shows good agreement with observational data.

Abstract

We derive an analytic model for the redshift evolution of linear-bias, allowing for interactions and merging of the mass-tracers, by solving a second order differential equation based on linear perturbation theory and the Friedmann-Lemaitre solutions of the cosmological field equations. We then study the halo-mass dependence of the bias evolution, using the dark matter halo distribution in a $\Lambda$CDM simulation in order to calibrate the free parameters of the model. Finally, we compare our theoretical predictions with available observational data and find a good agreement. In particular, we find that the bias of optical QSO's evolve differently than those selected in X-rays and that their corresponding typical dark matter halo mass is $\sim 10^{13} h^{-1} M_{\odot}$ and $\magcir 5 \times 10^{13} h^{-1} M_{\odot}$, respectively.