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We measure the signal of secondary halo bias as a function of a variety ofintrinsic and environmental halo properties, and characterize its statisticalsignificance as a function of cosmological redshift. Using fixed and paired$N$-body simulations of dark-matter halos -- the \texttt{UNIT} simulation --with masses above $10^{11}M_{\odot}h^{-1}$ identified over a wide range ofcosmological redshifts ($0<z<5$), we explore the behavior of the scalingrelations among different halo properties. We include novel environmentalproperties based on the halo distribution as well as the underlying dark-matterfield. We implement an object-by-object estimator of large-scale effective biasand test its validity against standard approaches. With a bias assigned to eachtracer, we perform a statistical analysis aiming at characterizing thedistribution of bias and the signal of secondary halo bias. We show how thehalo scaling relations linking direct probes of the halo potential well do notdepend on the environment. On the contrary, links between halo mass and the socalled set of secondary halo properties are sensitive to the cosmologicalenvironment. We show that the signal of secondary bias derives statisticallyfrom secondary correlations beyond the standard link to halo mass. We show thatthe secondary bias arise through non-local and/or environmental propertiesrelated either to the halo distribution or to the properties of the underlyingdark-matter field. Properties such as the tidal field and the local Mach numbergenerates the signals of secondary bias with the highest significance. Wepropose applications of the assignment of individual bias for the generation ofmock catalogs containing the signal of secondary bias, as well as a series ofcosmological analyses aiming at mining large galaxy data sets.

Secondary halo bias through cosmic time I: Scaling relations and the connection with the cosmic web