  We measure the signal of secondary halo bias as a function of a variety of
intrinsic and environmental halo properties, and characterize its statistical
significance as a function of cosmological redshift. Using fixed and paired
$N$-body simulations of dark-matter halos -- the UNIT simulation -- with masses
above $10^{11}M_{\odot}h^{-1}$ identified over a wide range of cosmological
redshifts (0<z<5), we explore the behavior of the scaling relations among
different halo properties. We include novel environmental properties based on
the halo distribution as well as the underlying dark-matter field. We implement
an object-by-object estimator of large-scale effective bias and test its
validity against standard approaches. With a bias assigned to each tracer, we
perform a statistical analysis aiming at characterizing the distribution of
bias and the signal of secondary halo bias. We show how the halo scaling
relations linking direct probes of the halo potential well do not depend on the
environment. On the contrary, links between halo mass and the so called set of
secondary halo properties are sensitive to the cosmological environment. We
show that the signal of secondary bias derives statistically from secondary
correlations beyond the standard link to halo mass. We also show that the
secondary bias arise through non-local and/or environmental properties related
either to the halo distribution or to the properties of the underlying
dark-matter field. Properties such as the tidal field and the local Mach number
generates the signals of secondary bias with the highest significance. We
propose applications of the assignment of individual bias for the generation of
mock catalogs containing the signal of secondary bias, as well as a series of
cosmological analyses aiming at mining large galaxy data sets.
