Connecting the Dots: Tracking Galaxy Evolution Using Constant Cumulative
  Number Density at 3<z<7
  Using the cosmological smoothed particle hydrodynamical code GADGET-3 we make
a realistic assessment of the technique of using constant cumulative number
density as a tracer of galaxy evolution at high redshift. We find that over a
redshift range of $3\leq z \leq7$ one can on average track the growth of the
stellar mass of a population of galaxies selected from the same cumulative
number density bin to within $\sim 0.20$ dex. Over the stellar mass range we
probe ($10^{10.39}\leq M_s/M_\odot \leq 10^{10.75}$ at $z =$ 3 and
$10^{8.48}\leq M_s/M_\odot \leq 10^{9.55}$ at $z =$ 7) one can reduce this bias
by selecting galaxies based on an evolving cumulative number density. We find
the cumulative number density evolution exhibits a trend towards higher values
which can be quantified by simple linear formulations going as $-0.10\Delta z$
for descendants and $0.12\Delta z$ for progenitors. Utilizing such an evolving
cumulative number density increases the accuracy of descendant/progenitor
tracking by a factor of $\sim2$. This result is in excellent agreement, within
$0.10$ dex, with abundance matching results over the same redshift range.
However, we find that our more realistic cosmological hydrodynamic simulations
produce a much larger scatter in descendant/progenitor stellar masses than
previous studies, particularly when tracking progenitors. This large scatter
makes the application of either the constant cumulative number density or
evolving cumulative number density technique limited to average stellar masses
of populations only, as the diverse mass assembly histories caused by
stochastic physical processes such as gas accretion, mergers, and star
formation of individual galaxies will lead to a larger scatter in other
physical properties such as metallicity and star-formation rate.
