The Halo Mass‐Bias Redshift Evolution in the ΛCDM Cosmology

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 ΛCDM 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 ~10 13 h −1 M ☉ and ≳5 × 10 13 h −1 M ☉ , respectively.