  Halos of similar mass and redshift exhibit a large degree of variability in
their differential properties, such as dark matter, hot gas, and stellar mass
density profiles. This variability is an indicator of diversity in the
formation history of these dark matter halos that is reflected in the coupling
of scatters about the mean relations. In this work, we show that the strength
of this coupling depends on the scale at which halo profiles are measured. By
analyzing the outputs of the IllustrisTNG hydrodynamical cosmological
simulations we report the radial- and mass-dependent couplings between the dark
matter, hot gas, and stellar mass radial density profiles utilizing the
population diversity in dark matter halos. We find that for the same mass halos
the scatters in the density of baryons and dark matter are strongly coupled at
large scales ($r>R_{200}$); but the coupling between gas and dark matter
density profiles fades near the core of halos ($r < 0.3 R_{200}$). We then show
that the correlation between halo profile and integrated quantities induces a
radius-dependent additive bias in the profile observables of halos when halos
are selected on properties other than their mass. We discuss the impact of this
effect on cluster abundance and cross-correlations cosmology with
multi-wavelength cosmological surveys.
