This paper studies how ordinary matter – gas, stars, and black-hole activity, collectively called baryons – changes the internal structure of dark-matter halos. The authors focus on the concentration–mass relation, a simple number that summarizes how centrally dense a halo is for a given mass. Using 2,048 small-box simulations from the CAMELS (Cosmology and Astrophysics with MachinE Learning Simulations) suite, they build a simulation-informed model that predicts halo concentration as a function of mass, time (redshift), and 28 varied parameters (five cosmological and twenty-three astrophysical). Their results cover halo masses from about 10^11 to 10^14.5 solar masses per h and redshifts from 0 to 3, and they report clear mass- and redshift-dependent signatures tied to different feedback processes.

To make these estimates the team used the IllustrisTNG version of the CAMELS runs, where the 28 parameters are sampled with a Sobol sequence (a way to explore many combinations evenly). Each simulation has different initial conditions. Halos were identified with the Rockstar halo finder, which groups matter in position–velocity space. Concentration was measured by fitting a standard halo profile (the Navarro–Frenk–White or NFW form) to the total matter in each halo and then computing the ratio between a halo’s outer radius and its scale radius.

At a high level, concentration is a simple summary of a halo’s radial density: higher concentration means more mass packed toward the center relative to the outskirts. The authors analyzed how that number changes when they vary things like stellar feedback (winds from exploding stars), gas cooling, and feedback from active galactic nuclei (energy from supermassive black holes), as well as broad cosmological parameters. They used a non-parametric, kernel-localized linear regression method (KLLR) to extract local trends in mass and redshift, and then distilled the results into a three-component phenomenological model. The goal of that model is to allow others to include astrophysical imprints on concentration quickly and simply.