Secondary halo bias through cosmic time

Context. When constructing mock galaxy catalogs based on suites of dark matter halo catalogs generated with approximated, calibrated, or machine-learning approaches, assigning intrinsic properties for these tracers is a step of paramount importance, given that they can shape the abundance and spatial distribution of mock galaxies and galaxy clusters. Aims. We explore the possibility of assigning properties of dark matter halos within the context of calibrated or learning approaches, explicitly using clustering information. The goal is to retrieve the correct signal of primary and secondary large-scale effective bias as a function of properties reconstructed solely based on phase-space properties of the halo distribution and dark matter density field. Methods. The algorithm reconstructs a set of halo properties (such as virial mass, maximum circular velocity, concentration, and spin) constrained to reproduce both primary and secondary (or assembly) bias. The key ingredients of the algorithm are the implementation of individually-assigned large-scale effective bias, a multi-scale approach to account for halo exclusion, and a hierarchical assignment of halo properties. Results. The method facilitates the assignment of halo properties, aiming to replicate the large-scale effective bias, both primary and secondary. This constitutes an improvement over previous methods in the literature, especially for the high-mass end population. Conclusions. We have designed a strategy for reconstructing the main properties of dark matter halos obtained using calibrated or learning algorithms, such that the one- and two-point statistics (on large scales) replicate the signal from detailed N-body simulations. We encourage the application of this strategy (or the implementation of our algorithm) for the generation of mock catalogs of dark matter halos based on approximated methods.