On matching galaxy number densities to reconstruct galaxy evolutionary tracks

The cumulative number density matching approach equates number densities between adjacent redshifts to derive empirical galaxy evolution tracks from the observed galaxy stellar mass function. However, it is well known that this approach overlooks scatter in mass assembly histories and merger effects, with previous studies relying on model-based corrections, either from hydrodynamical cosmological simulations or adjustments to the evolution of cumulative number density with redshift. Here, we revisit this approach, showing that dark matter halo assembly histories imply evolving number densities that are far from constant. These exhibit an average slope of $d \log n_\text{vir} /dz \sim 0.2$ dex for progenitors at $z=0$, leading to evolutionary tracks where galaxies are $\sim2-3$ times smaller in mass at $z\sim2$ and an order of magnitude smaller by $z\sim7$ compared to the number density matching approach. We show that evolving halo number densities provide realistic evolutionary tracks without relying on model-based corrections. Accounting for random errors in stellar mass measurements is also crucial for robust track derivation. We also discuss a generalization that incorporates a galaxy's star formation activity. When additionally considering the scatter around the $M_\ast-M_\text{vir}$ relation ($\sim0.15$ dex), our evolving halo cumulative number density approach shows that some observed stellar masses, $M_{\text{obs},\ast}$, can exceed the universal baryon fraction $f_\text{bar}\sim0.16$. For instance, at $z=5$, around $2\%$ of progenitor galaxies of haloes with $M_\text{vir} \sim 3\times 10^{12}\,M_\odot$ have $M_{\text{obs},\ast}>f_\text{bar} \; M_\text{vir}$, suggesting a potential ``early galaxy formation problem''. However, when deconvolving mass from random errors this tension is reduced with significant confidence at the $\sim5-6\sigma$ level.