The evolution of the halo occupation distribution in cosmic voids

The halo occupation distribution is a cornerstone in understanding galaxy formation within the large-scale structure.On the other hand, in the context of the large-scale structure of the Universe, voids are regions with singular characteristics, given their extension, the low number of objects that inhabit their interior and their own dynamics. Furthermore, the HOD of these regions exhibits significant deviations from the average, as shown by several studies in semi-analytical models, hydrodynamic simulations, and observations. This paper investigates the temporal evolution of the HOD in cosmic voids from redshift z = 0.5 to the present day. We aim to understand how the void environment shapes galaxy occupation over time and to identify the factors driving the unique HOD observed in these underdense regions. We use the MDPL2-SAG semi-analytic galaxy catalog and identify spherical cosmic voids at different redshifts. We analyze the HOD within voids across ten simulation snapshots, comparing it with the global HOD. Furthermore, we trace the evolution of z = 0 void galaxies and their host halos back in time, examining their formation times and local density evolution. Our results reveal that the HOD within voids is consistently lower than the average HOD at all redshifts considered. Tracking z = 0 void galaxies, we find that their HOD remains lower than average throughout the redshift range, with no significant redshift evolution in this relative difference. Analysis of halo formation histories shows that lower-mass void halos are younger, while massive void halos are older compared to the average. Spatially, lower-mass halos are found in the inner void regions, whereas massive halos are located closer to void boundaries. The local density of massive void halos decreases significantly towards z = 0, contrasting with the relatively stable local density of lower-mass void halos.