The evolution of the halo occupation distribution in cosmic voids

Context. The halo occupation distribution (HOD) is a cornerstone in understanding galaxy formation within 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 unique dynamics. Furthermore, the HOD of these regions exhibits significant deviations from the average, as shown by several studies employing semi-analytical models, hydrodynamic simulations, and observations. Aims. 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 under-dense regions. Methods. We used the MDPL2-SAG catalog and identified spherical cosmic voids at different redshifts. We analyzed the HOD within voids across ten simulation snapshots, comparing it with the global HOD. Furthermore, we traced the evolution of z = 0 void galaxies and their host halos back in time, examining their formation times and local density evolution. Results. The HOD within voids is consistently lower than the average HOD at all the redshifts considered. Tracking z = 0 void galaxies, we find that their HOD remains below average throughout the redshift range, with no significant redshift evolution. Analysis of halo formation histories shows that lower-mass void halos are younger and massive void halos 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 toward z = 0, contrasting with the relatively stable local density of lower-mass void halos.