On the accuracy of dark matter halo merger trees and the consequences for semi-analytic models of galaxy formation

Galaxy formation and evolution models, such as semi-analytic models, are powerful theoretical tools for predicting how galaxies evolve across cosmic time. These models follow the evolution of galaxies based on the halo assembly histories inferred from large $N$-body cosmological simulations. This process requires codes to identify halos ("halo finder") and to track their time evolution ("tree builder"). While these codes generally perform well, they encounter numerical issues when handling dense environments. In this paper, we present how relevant these issues are in state-of-the-art cosmological simulations. We characterize two major numerical artefacts in halo assembly histories: (i) the non-physical swapping of large amounts of mass between subhalos, and (ii) the sudden formation of already massive subhalos at late cosmic times. We quantify these artefacts for different combinations of halo finder (SUBFIND, VELOCIRAPTOR, HBT-HERONS) and tree builder codes (D-TRESS+DHALO, TREEFROG, HBT-HERONS), finding that in general more than $50\%$ ($80\%$) of the more massive subhalos with $>10^{3}$ ($>10^{4}$) particles at $z=0$ inherit them in most cases. However, HBT-HERONS, which explicitly incorporates temporal information, effectively reduces the occurrence of these artefacts to $5\%$ ($10\%$). We then use the semi-analytic models SHARK and GALFORM to explore how these artefacts impact galaxy formation predictions. We demonstrate that the issues above lead to non-physical predictions in galaxies hosted by affected halos, particularly in SHARK where the modelling of baryons relies on subhalo information. Finally, we propose and implement fixes for the numerical artefacts at the semi-analytic model level, and use SHARK to show the improvements, especially at the high-mass end, after applying them.