Connecting the Dots: Tracking Galaxy Evolution Using Constant Cumulative Number Density at 3<z<7

Abstract: 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.