ICM-SHOX Pipeline Overview

• ICM-SHOX is a systematic computational workflow that integrates hydrodynamical/MHD simulations and multi-wavelength observables to study galaxy cluster mergers.
• The pipeline employs detailed initial condition generation, shock and cosmic-ray electron modeling, and grid-based parameter inference against observational data.
• Application to MACS J0018.5+1626 demonstrates the pipeline’s capability to reinterpret radio halo phenomena by distinguishing overlapping relic emissions in merger environments.

ICM-SHOX (Improved Constraints on Mergers with SZ, Hydrodynamical simulations, Optical, and X-ray) is a systematic computational pipeline developed for the quantitative study of galaxy cluster mergers. This framework integrates hydrodynamical and magnetohydrodynamical (MHD) simulations, synthetic observable generation, and multi-wavelength observational constraints to enable detailed inference of cluster merger parameters and interpretation of complex astrophysical phenomena, such as the distinction between radio halos and face-on radio relics. The methodology and results of the ICM-SHOX pipeline have been demonstrated in several studies, notably in the context of the merging galaxy cluster MACS J0018.5+1626 (Silich et al., 2023, Domínguez-Fernández et al., 4 Feb 2026).

1. Architecture and Core Components

The ICM-SHOX pipeline consists of five principal stages: (1) generation of merger initial conditions; (2) hydrodynamical and MHD simulation; (3) cosmic-ray electron (CRe) injection and energy evolution via tracer particles and a Fokker–Planck solver; (4) production of synthetic observables (e.g., X-ray, radio, tSZ, kSZ maps); and (5) quantitative parameter inference through comparison with multi-wavelength data (Domínguez-Fernández et al., 4 Feb 2026).

Initial Condition Generation

• Cluster parameters: Masses ($M_{500,1} = 1.15 \times 10^{15}\ M_\odot$; mass ratio $R = 1.5$), merger geometry (initial separation 3 Mpc, relative velocity $v_i$ along $x$-axis, impact parameter $b$ along $y$-axis), and observed redshift ($z=0.5456$).
• Dark matter halos: Truncated NFW density profiles with concentration parameters following Dutton & Macciò (2019).
• Gas distribution: Modified $\beta$-model (Vikhlinin et al. 2006) with cosmic gas fraction normalization ($f_\mathrm{gas} = 0.115$), and empirical core radii/slopes set to X-ray data.
• Magnetic field: Initialized as a divergence-free Gaussian random field with Kolmogorov spectrum in the 500–10 kpc scale range, plasma $\beta_p = 100$ (nominal).

Numerical Simulation

• Hydro and MHD solver: AREPO moving-mesh code with HLLD Riemann solver and Powell eight-wave divergence control.
• Domain and sampling: 40 Mpc box; initial $\sim 1.15 \times 10^7$ gas cells and $10^7$ DM particles; adaptive AMR.
• Shock detection: On-the-fly shock-finder (Schmidt et al. 2015) with $\mathcal{M}_\mathrm{th} = 1.3$.
• Outputs: Snapshots every $\Delta t = 0.02$ Gyr, up to $t_f = 1.9$ Gyr.

2. Cosmic-Ray Electron Modeling

Tracer particles ($N_\mathrm{tr}=10^7$) are advected with the flow, inheriting local gas cell properties. For each tracer passing through a shocked region, the CRe distribution function $f(p)$ is evolved with an isotropic, non-spatial Fokker–Planck equation:

$$\frac{\partial f}{\partial t} = \frac{1}{p^2} \frac{\partial}{\partial p} \left[ p^2 D_{pp} \frac{\partial f}{\partial p} + p^2 H(p) f \right] - \frac{f}{T(p)} + q(p, t)$$

where $D_{pp}$ (turbulent re-acceleration) is set to zero for pure DSA and $H(p)$ includes all (synchrotron, inverse-Compton, Coulomb, bremsstrahlung, adiabatic) losses.

• DSA injection: Mach-number dependent, with spectral index $s = 2(\mathcal{M}^2+1)/(\mathcal{M}^2-1)$, normalization set by dissipated energy: $$\Delta \epsilon_{\rm CRe, sh} = \eta(\mathcal{M}) \Delta \epsilon_{\rm sh}$$.
• Efficiency model: Both constant $\eta_0$ and Mach-dependent Kang et al. (2007) efficiencies are explored.
• Finite-difference solver: Flux-conservative Chang & Cooper (1970) scheme, logarithmic $p$ grid, timestep $dt_\mathrm{FP}=0.686$ Myr.

3. Synthetic Observable Generation

Simulated data are post-processed to yield observables directly comparable to multi-wavelength observations.

• X-ray: Photon emissivity generated via pyXSIM/APE C models (Z=0.3 $Z_\odot$, $0.5$–$7$ keV band).
• Radio synchrotron: Single-particle emissivity following Ginzburg & Syrovatskii (1965), with integration over $N(E)$ and projection along the line of sight.
• Surface brightness maps: Gaussian beam convolution to match, e.g., LOFAR resolutions (11″×5.7″ to 39″×34″).
• SZ effect:
  • Thermal SZ: $y = (\sigma_T/m_ec^2)\int n_e k_BT_e\,dl$
  • Kinetic SZ: $\Delta T/T = -(\sigma_T/c)\int n_e v_{los}\,dl$
• Spectral index mapping: $$\alpha = -[\log I_{\nu_2} - \log I_{\nu_1}]/[\log \nu_2 - \log \nu_1]$$.
• Other probes: Strong lensing mass maps, galaxy velocity catalogs.

4. Parameter Space Exploration and Inference

Parameter inference proceeds via a grid search over key merger parameters:

• Sampled parameters: $v_i \in \{2400, 3000\}$ km s$^{-1}$, $b \in \{100, 250\}$ kpc, $\beta_p \in \{100, 200\}$, $\eta_0 \in \{0.1, 0.01, 0.001\}$, plus variant Mach-dependent $\eta(\mathcal{M})$.
• Quantitative comparison: Synthetic observables—X-ray, tSZ, kSZ, radio properties (integrated flux, profile shape, spectral index), mass maps, galaxy kinematics—are compared to Chandra, LOFAR, and lensing data via summary statistics (e.g., centroid offset, shock separation, profile $\chi^2$).
• Matching criterion: Models must simultaneously reproduce all available constraints within empirical uncertainties.
• Posterior construction: Surviving models are weighted to yield posterior distributions for the best-fit parameters, such as impact parameter, epoch post-pericenter, viewing angle, and relevant plasma/gas parameters (Domínguez-Fernández et al., 4 Feb 2026).

5. Physical Results and Application to MACS J0018.5+1626

Application to MACS J0018.5+1626 provides a demonstrative instance:

• Dynamical state: Ongoing binary merger, line-of-sight near merger axis, epoch $\sim30$–$200$ Myr after pericenter.
• Shocks: Two dominant axial shocks with average Mach numbers $\mathcal{M}_s \sim 2$–$3$ (spread $\sigma_\mathcal{M} \sim 0.5$–$1.5$).
• Magnetic fields: $\beta_p=100$ yields volume-averaged $B\sim0.8$–$1\ \mu$G at shocks.
• CR injection efficiency: Consistent with modest DSA efficiency $\eta_e \sim 10^{-3}$–$10^{-2}$.
• Radio properties: Modeled flux density at 144 MHz ($\sim37.8$ mJy) and spectral index ($\alpha_\mathrm{int}\approx–1.3$ to $–1.8$) reproduce LOFAR results.
• Morphology: Two face-on radio relics overlap, producing a central, circular, $\sim1$ Mpc structure that mimics the morphology of a radio halo. Sub- or super-linear point-to-point radio–X-ray correlations (0.1–0.6 slope) are natural consequences of projected shock geometry, beam effects, and merger stage.
• Interpretation: The observed "radio halo" in MACS J0018.5+1626 can arise from the superposition of two radio relics viewed nearly along the line of sight, challenging conventional separation between radio halo and relic phenomena in cluster mergers. This result is robust to variations in Mach number, shock strength, impact parameter, viewing angle, and plausibly even efficiency model (Domínguez-Fernández et al., 4 Feb 2026).

6. Significance, Limitations, and Future Directions

The ICM-SHOX pipeline establishes a model-driven inference framework that connects idealized cluster merger physics to the full suite of modern multi-wavelength observational data. Its ability to finely map the cluster conditions and infer detailed merger geometry parameters is evidenced by its success in the MACS J0018.5+1626 case study. At the same time, a grid-based search (rather than MCMC or fully Bayesian parameter exploration) limits exhaustive exploration of parameter covariances, and assumptions such as idealized initial conditions or specific efficiency models can introduce systematic uncertainties. Future directions may include incorporating stochastic turbulence re-acceleration physics (nonzero $D_{pp}$), improved treatment of fossil electron pools, and application to a statistically significant ensemble of cluster mergers for population-level inference (Silich et al., 2023, Domínguez-Fernández et al., 4 Feb 2026).