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 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 similar to 10(13) h(-1) M-circle dot and greater than or similar to 5 x 10(13) h(-1) M-circle dot, respectively.