The merger rate of galaxies in the Illustris Simulation: a comparison
  with observations and semi-empirical models
  We have constructed merger trees for galaxies in the Illustris Simulation by
directly tracking the baryonic content of subhalos. These merger trees are used
to calculate the galaxy-galaxy merger rate as a function of descendant stellar
mass, progenitor stellar mass ratio, and redshift. We demonstrate that the most
appropriate definition for the mass ratio of a galaxy-galaxy merger consists in
taking both progenitor masses at the time when the secondary progenitor reaches
its maximum stellar mass. Additionally, we avoid effects from `orphaned'
galaxies by allowing some objects to `skip' a snapshot when finding a
descendant, and by only considering mergers which show a well-defined `infall'
moment. Adopting these definitions, we obtain well-converged predictions for
the galaxy-galaxy merger rate with the following main features, which are
qualitatively similar to the halo-halo merger rate except for the last one: a
strong correlation with redshift that evolves as $\sim (1+z)^{2.4-2.8}$, a
power law with respect to mass ratio, and an increasing dependence on
descendant stellar mass, which steepens significantly for descendant stellar
masses greater than $\sim 2 \times 10^{11} \, {\rm M_{\odot}}$. These trends
are consistent with observational constraints for medium-sized galaxies
($M_{\ast} \gtrsim 10^{10} \, {\rm M_{\odot}}$), but in tension with some
recent observations of the close pair fraction for massive galaxies ($M_{\ast}
\gtrsim 10^{11} \, {\rm M_{\odot}}$), which report a nearly constant or
decreasing evolution with redshift. Finally, we provide a fitting function for
the galaxy-galaxy merger rate which is accurate over a wide range of stellar
masses, progenitor mass ratios, and redshifts.
