ICM-SHOX III. The case of MACS J0018.5+1626, a radio relic that looks like a radio halo?

We present the first detailed numerical modeling of the radio emission from MACS J0018.5+1626 as part of the Improved Constraints on Mergers with SZ, Hydrodynamical simulations, Optical, and X-ray (ICM-SHOX) project. By matching X-ray, thermal and kinetic Sunyaev–Zel’dovich, optical and lensing observables to simulations, the ICM-SHOX pipeline indicates that MACS J0018.5+1626 is undergoing a binary merger close to pericenter passage and is observed along a line of sight nearly aligned with the merger axis. We perform three-dimensional magnetohydrodynamic simulations of binary cluster mergers coupled to tracer particles and a Fokker–Planck solver to model the radio emission. Exploring variations in the most likely initial conditions within the ICM-SHOX parameter space, such as the relative cluster velocity and impact parameter, we find that the resulting merger configuration consistently produces two merger-driven shocks with typical average Mach numbers $\mathcal{M}s \sim 2$–$3$ with corresponding standard deviations of $σ{\mathcal{M}} \sim 0.5$–$1.5$. Within this framework, we examine the cluster conditions under which standard diffusive shock acceleration can reproduce LOFAR observations. In particular, we discuss the possibility that the apparent radio halo seen by LOFAR arises from the superposition of two radio relics viewed nearly face-on.

💡 Research Summary

This paper presents the first detailed numerical modeling of the radio emission from the massive galaxy cluster MACS J0018.5+1626 within the framework of the Improved Constraints on Mergers with SZ, Hydrodynamical simulations, Optical, and X‑ray (ICM‑SHOX) project. By jointly fitting strong‑lensing mass maps, X‑ray surface‑brightness and temperature distributions, thermal and kinetic Sunyaev–Zel’dovich (SZ) measurements, and spectroscopic galaxy velocities, the ICM‑SHOX pipeline constrains the merger configuration to a binary collision that is currently near pericenter passage and observed almost along the merger axis.

Using these constraints, the authors perform a suite of three‑dimensional, non‑radiative magnetohydrodynamic (MHD) simulations with the moving‑mesh code AREPO. The simulation volume is a 40 Mpc cube, initially populated with ~1.15 × 10⁷ gas cells (cell mass ≈ 3.6 × 10⁷ M⊙) and 10⁷ dark‑matter particles. Six baseline MHD runs explore variations in the initial relative velocity (vᵢ ≈ 2400–3000 km s⁻¹) and impact parameter (b ≈ 100–250 kpc) consistent with the ICM‑SHOX posterior. An AREPO shock‑finder (Mach threshold Mₜₕ = 1.3) identifies two axial shocks that develop shortly after pericenter, with average Mach numbers ⟨𝓜ₛ⟩ ≈ 2–3 and standard deviations σ𝓜 ≈ 0.5–1.5. The shocks are oriented nearly face‑on to the observer, a geometry that can dramatically alter the apparent morphology of diffuse radio emission.

To model the non‑thermal radio component, the authors embed 10⁷ Lagrangian tracer particles in the MHD flow, each carrying a constant mass and a volume derived from the local gas density. The tracers are advected with the fluid and record the thermodynamic history of the gas they sample. For each tracer, the evolution of the cosmic‑ray electron (CRe) momentum distribution f(p,t) is solved with a one‑dimensional Fokker–Planck equation that includes diffusive shock acceleration (DSA) terms, radiative losses, and an escape term. The acceleration efficiency η (the fraction of shock kinetic energy transferred to CRe) is treated as a free parameter; the authors explore constant efficiencies η = 10⁻¹, 10⁻², 10⁻³ and also the Mach‑dependent prescription of Kang et al. (2007).

Synchrotron emissivities are computed from the evolved electron spectra assuming a tangled magnetic field that is initialized with a Kolmogorov power spectrum (λ₀ = 500 kpc, λ₁ = 10 kpc) and a plasma β of 100–200, leading to post‑shock magnetic field strengths of order 1–3 µG. The simulated radio maps at 144 MHz (the LOFAR Two‑metre Sky Survey band) are then compared with the observed diffuse emission, which has traditionally been classified as a central radio halo.

The key result is that, for η ≈ 10⁻², the superposition of the two nearly face‑on shock fronts reproduces both the surface‑brightness level and the elongated morphology seen in the LOFAR image, despite the apparent central location. In contrast, lower efficiencies (η ≤ 10⁻³) underproduce the observed flux, implying that additional sources of seed electrons (e.g., fossil plasma from past AGN activity) would be required to boost the DSA efficiency. The study therefore proposes that the “radio halo” in MACS J0018.5+1626 may in fact be the line‑of‑sight projection of two radio relics, challenging the conventional halo‑relic dichotomy.

Beyond this specific case, the work demonstrates the power of combining multi‑probe observational constraints with high‑resolution MHD + particle simulations to disentangle projection effects and to assess the viability of diffusive shock acceleration in massive merging clusters. The authors suggest future extensions that incorporate turbulent re‑acceleration, a realistic fossil electron population, and higher‑resolution X‑ray/SZ observations to directly map the shock geometry and to refine the acceleration efficiency estimates.