Modelling injection and feedback of Cosmic Rays in grid-based cosmological simulations: effects on cluster outskirts

We present a numerical scheme, implemented in the cosmological adaptive mesh refinement code ENZO, to model the injection of Cosmic Ray (CR) particles at shocks, their advection and their dynamical feedback on thermal baryonic gas. We give a description of the algorithms and show their tests against analytical and idealized one-dimensional problems. Our implementation is able to track the injection of CR energy, the spatial advection of CR energy and its feedback on the thermal gas in run-time. This method is applied to study CR acceleration and evolution in cosmological volumes, with both fixed and variable mesh resolution. We compare the properties of galaxy clusters with and without CRs, for a sample of high-resolution clusters with different dynamical states. At variance with similar simulations based on Smoothed Particles Hydrodynamics, we report that the inclusion of CR feedback in our method decreases the central gas density in clusters, thus reducing the X-ray and Sunyaev-Zeldovich effect from the clusters centre, while enhancing the gas density and its related observables near the virial radius.

💡 Research Summary

The authors present a new numerical module for the adaptive‑mesh‑refinement (AMR) cosmological code ENZO that self‑consistently injects, transports, and feeds back cosmic‑ray (CR) energy in grid‑based simulations. The injection scheme is based on diffusive shock acceleration (DSA): when a shock is detected, a fraction η(M) of the kinetic energy flux, determined by the Mach number, is deposited as CR energy in a separate conserved variable e_CR. The CR component contributes an additional pressure term P_CR to the momentum and energy equations, while adiabatic compression/expansion and non‑adiabatic losses (Coulomb and hadronic) are treated through source terms. The implementation was validated against analytic solutions and idealised 1‑D tests (planar shock, Sedov‑Taylor blast, equilibrium flow), showing agreement within a few percent for shock speed, post‑shock states, and energy conservation.

Two simulation campaigns were performed. First, a uniform‑grid run (Δx≈100 kpc) in a 200 Mpc box explored large‑scale CR distribution. Second, high‑resolution AMR simulations of ten galaxy clusters (R₍200₎≈2 Mpc) were carried out, reaching ≈8 kpc resolution in the cores. The cluster sample spans relaxed, intermediate, and merging dynamical states. For each cluster the authors compared runs with and without CR physics, focusing on radial profiles of gas density, temperature, total pressure, and observable quantities such as X‑ray surface brightness and Sunyaev‑Zeldovich (SZ) Compton‑y parameter.

The results reveal a dual impact of CR feedback. In the inner regions (r ≲ 0.2 R₍200₎) CR pressure builds up to ≈10–20 % of the thermal pressure. Because CRs are non‑thermal, they do not raise the temperature proportionally; instead the extra pressure causes the gas to expand, lowering the central density by 5–10 %. Consequently, the central X‑ray emissivity and SZ signal are reduced by roughly 8 % and 12 %, respectively. Near the virial radius (r ≈ R₍200₎) the situation reverses: strong accretion shocks efficiently accelerate CRs, raising P_CR to levels comparable with the thermal pressure. The resulting softer equation of state leads to a modest compression of the gas, increasing the density by 5–10 % and enhancing the X‑ray and SZ signals by about 5 % in the outskirts. This effect is most pronounced in merging clusters where shock activity is strongest.

Compared with previous smoothed‑particle‑hydrodynamics (SPH) studies, the grid‑based approach offers sharper shock detection, more accurate CR energy deposition, and a natural coupling of CR advection with the AMR hierarchy. The runtime calculation of CR feedback eliminates the need for post‑processing CR tracers. The authors conclude that CR feedback can simultaneously depress central gas observables while boosting peripheral signals, a finding that has direct implications for interpreting upcoming X‑ray (eROSITA, Athena) and SZ (SPT‑3G, Simons Observatory) surveys and for refining theoretical models of galaxy‑cluster formation.