  With the advent of high-resolution, low-noise CMB measurements, the ability
to extract cosmological information from thermal Sunyaev-Zel'dovich effect and
kinetic Sunyaev-Zel'dovich effect will be limited not by statistical
uncertainties but rather by systematic and theoretical uncertainties. The
theoretical uncertainty is driven by the lack of knowledge about the electron
pressure and density. Thus we explore the electron pressure and density
distributions in the IllustrisTNG hydrodynamical simulations, and we
demonstrate that the cluster properties exhibit a strong dependence on the halo
concentration -- providing some of the first evidence of cluster assembly bias
in the electron pressure and density. Further, our work shows evidence for a
broken power-law mass dependence, with lower pressure in lower mass halos than
previous work and a strong evolution with mass of the radial correlations in
the electron density and pressure. Both of these effects highlight the
differing impact of active galactic nuclei and supernova feedback on the gas in
galaxy groups compared to massive clusters. We verified that we see
qualitatively similar features in the SIMBA hydro-dynamical simulations,
suggesting these effects could be generic features. Finally, we provide a
parametric formula for the electron pressure and density profile as a function
of dark matter halo mass, halo concentration, and redshift. These fitting
formulae can reproduce the distribution of density and pressure of clusters and
will be useful in extracting cosmological information from upcoming CMB
surveys.
