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.
Categories: astro-ph