Using Cumulative Number Densities to Compare Galaxies across Cosmic Time
  Comparing galaxies across redshifts at fixed cumulative number density is a
popular way to estimate the evolution of specific galaxy populations. This
method ignores scatter in mass accretion histories and galaxy-galaxy mergers,
which can lead to errors when comparing galaxies over large redshift ranges
(Delta z > 1). We use abundance matching in the LCDM paradigm to estimate the
median change in number density with redshift and provide a simple fit (+0.16
dex per unit Delta z) for progenitors of z = 0 galaxies. We find that galaxy
descendants do not evolve in the same way as galaxy progenitors, largely due to
scatter in mass accretion histories. We also provide estimates for the 1-sigma
range of number densities corresponding to galaxy progenitors and descendants.
Finally, we discuss some limits on number density comparisons, which arise due
to difficulties measuring physical quantities (e.g., stellar mass) consistently
across redshifts. A public tool to calculate number density evolution for
galaxies, as well as approximate halo masses, is available online.
