A Comparison of Galaxy Merger History Observations and Predictions from
  Semi-Analytic Models
  We present a detailed analysis of predicted galaxy-galaxy merger fractions
and rates in the Millennium simulation and compare these with the most up to
date observations of the same quantities up to z~3. We carry out our analysis
by considering the predicted merger history in the Millennium simulation within
a given time interval, as a function of stellar mass. This method, as opposed
to pair fraction counts, considers mergers that have already taken place, and
allows a more direct comparison with the observed rates and fractions measured
with the concentration-asymmetry-clumpiness (CAS) method. We examine the
evolution of the predicted merger fraction and rate in the Millennium
simulation for galaxies with stellar masses M_* ~ 10^9 - 10^12 M_sun. We find
that the predicted merger rates and fractions match the observations well for
galaxies with M_* > 10^11 M_sun at z<2, while significant discrepancies occur
at lower stellar masses, and at z>2 for M_* > 10^11 M_sun systems. At z>2 the
simulations underpredict the observed merger fractions by a factor of 4-10. The
shape of the predicted merger fraction and rate evolutions are similar to the
observations up to z~2, and peak at 1<z<2 in almost all mass bins. The
exception is the merger rate of galaxies with M_* > 10^11 M_sun. We discuss
possible reasons for these discrepancies, and compare different realisations of
the Millennium simulation to understand the effect of varying the physical
implementation of feedback. We conclude that the comparison is potentially
affected by a number of issues, including uncertainties in interpreting the
observations and simulations in terms of the assumed merger mass ratios and
merger time-scales. (abridged)
