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 ({\Δ}z {\>} 1). We use abundance matching in the {\Λ}CDM paradigm to estimate the median change in cumulative number density with redshift and provide a simple fit (+0.16 dex per unit {\Δ}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{$σ$} range of cumulative number densities corresponding to galaxy progenitors and descendants. Finally, we discuss some limits on cumulative number density comparisons, which arise due to difficulties measuring physical quantities (e.g., stellar mass) consistently across redshifts. A public tool to calculate cumulative number density evolution for galaxies, as well as approximate halo masses, is available online.