The impact of baryons on the internal structure of dark matter haloes from dwarf galaxies to superclusters in the redshift range 0<z<7

We investigate the redshift evolution of the concentration-mass relationship of dark matter haloes in state-of-the-art cosmological hydrodynamic simulations and their dark-matter-only counterparts. By combining the IllustrisTNG suite and the novel MillenniumTNG simulation, our analysis encompasses a wide range of box size ($50 - 740 \: \rm cMpc$) and mass resolution ($8.5 \times 10^4 - 3.1 \times 10^7 \: \rm M_{\odot}$ per baryonic mass element). This enables us to study the impact of baryons on the concentration-mass relationship in the redshift interval $0<z<7$ over an unprecedented halo mass range, extending from dwarf galaxies to superclusters ($\sim 10^{9.5}-10^{15.5} \, \rm M_{\odot}$). We find that the presence of baryons increases the steepness of the concentration-mass relationship at higher redshift, and demonstrate that this is driven by adiabatic contraction of the profile, due to gas accretion at early times, which promotes star formation in the inner regions of haloes. At lower redshift, when the effects of feedback start to become important, baryons decrease the concentration of haloes below the mass scale $\sim 10^{11.5} \, \rm M_{\odot}$. Through a rigorous information criterion test, we show that broken power-law models accurately represent the redshift evolution of the concentration-mass relationship, and of the relative difference in the total mass of haloes induced by the presence of baryons. We provide the best-fit parameters of our empirical formulae, enabling their application to models that mimic baryonic effects in dark-matter-only simulations over six decades in halo mass in the redshift range $0<z<7$.