Correlations of Dark Matter, Gas and Stellar Profiles in Dark Matter Halos

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.