Statistics of galaxy mergers: bridging the gap between theory and observation

We present a study of galaxy mergers up to z = 10 using the Planck Millennium cosmological dark matter simulation and the GALFORM semi-analytical model of galaxy formation. Utilizing the full 800 Mpc³ volume of the simulation, we studied the statistics of galaxy mergers in terms of merger rates and close pair fractions. We predict that merger rates begin to drop rapidly for high-mass galaxies (M_* > 10^11.3-10^10.5 M_⊙ for z = 0-4), as a result of the exponential decline in the galaxy stellar mass function. The predicted merger rates for massive galaxies (M_* > 10¹⁰ M_⊙) increase and then turn over with increasing redshift, by z = 3.5, in disagreement with hydrodynamical simulations and semi-empirical models. In agreement with most other models and observations, we find that close pair fractions flatten or turn over at some redshift (dependent on the mass selection). We conduct an extensive comparison of close pair fractions, and highlight inconsistencies among models, but also between different observations. We provide a fitting formula for the major merger time-scale for close galaxy pairs, in which the slope of the stellar mass dependence is redshift dependent. This is in disagreement with previous theoretical results that implied a constant slope. Instead, we find a weak redshift dependence only for massive galaxies (M_* > 10¹⁰ M_⊙): in this case the merger time-scale varies approximately as $M_*^{-0.55}$. We find that close pair fractions and merger time-scales depend on the maximum projected separation as $r_\mathrm{max}^{1.32}$, in agreement with observations of small-scale clustering of galaxies.