Convergence of Galaxy Properties with Merger Tree Temporal Resolution
  Dark matter halo merger trees are now routinely extracted from cosmological
simulations of structure formation. These trees are frequently used as inputs
to semi-analytic models of galaxy formation to provide the backbone within
which galaxy formation takes place. By necessity, these merger trees are
constructed from a finite set of discrete "snapshots" of the N-body simulation
and so have a limited temporal resolution. To date, there has been little
consideration of how this temporal resolution affects the properties of
galaxies formed within these trees. In particular, the question of how many
snapshots are needed to achieve convergence in galaxy properties has not be
answered. Therefore, we study the convergence in the stellar and total baryonic
masses of galaxies, distribution of merger times, stellar mass functions and
star formation rates in the Galacticus model of galaxy formation as a function
of the number of "snapshot" times used to represent dark matter halo merger
trees. When utilizing snapshots between z=20 and z=0, we find that at least 128
snapshots are required to achieve convergence to within 5% for galaxy masses.
This convergence is obtained for mean quantities averaged over large samples of
galaxies - significant variance for individual galaxies remains even when using
very large numbers of snapshots. We find only weak dependence of the rate of
convergence on the distribution of snapshots in time - snapshots spaced
uniformly in the expansion factor, uniformly in the logarithm of expansion
factor or uniformly in the logarithm of critical overdensity for collapse work
equally well in almost all cases. We provide input parameters to Galacticus
which allow this type of convergence study to be tuned to other simulations and
to be carried out for other galaxy properties.
