Redshift Evolution of the Merger Fraction of Galaxies in Cold Dark Matter Cosmologies

We use semianalytical modeling of galaxy formation to study the redshift evolution of the galaxy merger fractions and merger rates in Λ cold dark matter (ΛCDM) and quintessence (QCDM) cosmologies, their dependence on physical parameters such as the environment, the merger timescale, the way major mergers are defined, and the minimum mass of objects taken into account. We find that for a given final halo mass the redshift dependence of the merger fraction F_mg and the resulting merger rate can be fitted well by a power law for redshifts z ≲ 1. The normalization F_mg(0) and the slope m depend on the final halo mass. For a given merger timescale t_merg and an assumed maximum mass ratio R_major for major mergers, F_mg(0) and m depend exponentially on each other. The slope m depends logarithmically on the ratio of the final halo mass and the minimum halo mass taken into account. In addition, the local normalization F_mg(0) increases for larger R_major while m decreases. We compare the predicted merger fraction with recent observations and find that the model cannot reproduce both the merger index and the normalization at the same time. In general the model underestimates F_mg(0) and m by a factor of 2.