Double Radio Relics in Galaxy Clusters

• Double radio relics are rare, Mpc-scale, diffuse radio sources found on opposite sides of merging galaxy clusters, indicative of shock-driven particle acceleration.
• They exhibit steep radio spectra, high fractional polarization, and arc-like morphologies that align with merger-driven shock fronts, offering precise probes of cluster dynamics.
• Combined multi-frequency observations and MHD simulations constrain key parameters such as merger geometry, acceleration efficiency, and magnetic field amplification in the intracluster medium.

Double radio relics are rare, Mpc-scale, steep-spectrum, diffuse radio sources located on diametrically opposite sides of merging galaxy clusters. They are widely interpreted as the synchrotron signatures of outward-propagating, merger-driven shock fronts in the intracluster medium (ICM), providing direct constraints on merger dynamics, particle acceleration efficiency, and plasma microphysics. Multi-frequency radio, X-ray, and lensing observations—combined with state-of-the-art magnetohydrodynamics (MHD) simulations—have established double radio relics as key probes for studying the energetics and evolution of cluster mergers, as well as the amplification of cosmic magnetic fields.

1. Physical Origin and Shock Acceleration

Double radio relics originate from bi-directional shocks generated during binary cluster mergers. The primary mechanism responsible for particle acceleration at these shocks is diffusive shock acceleration (DSA): thermal electrons are accelerated to relativistic energies as they cross the shock front multiple times. In the presence of cluster magnetic fields (typically μG-level), these electrons emit synchrotron radiation at radio wavelengths, producing elongated, arc-like relics situated at the cluster periphery.

The critical frequency for synchrotron emission from an electron with Lorentz factor γ in a magnetic field B is given by:

$$\nu_c \approx \gamma^2 \frac{eB}{2\pi m_ec}\sin\theta$$

where $e$ is the elementary charge, $m_e$ the electron mass, $c$ the speed of light, and θ the pitch angle. Radiative losses (synchrotron and inverse Compton) steepen the electron energy distribution downstream of the shock,

$-\frac{dE}{dt} \propto \gamma^2 B^2$

which leads to observable spectral index gradients along the relics.

DSA predicts a power-law energy distribution $N(E) dE \propto E^{-p}\,dE$, with the radio spectral index $\alpha = -\frac{p-1}{2}$ and $S_\nu \propto \nu^\alpha$. The Mach number $M$ of the shock controls the injection index and thus the efficiency of acceleration.

2. Observational Properties: Morphology, Spectra, and Polarization

Double radio relics are most commonly detected in galaxy clusters undergoing major mergers. They typically exhibit the following properties:

• Morphology: Extended (up to several Mpc), elongated, and arc-like structures on opposite sides of the cluster center, often perpendicular to the projected merger axis (Weeren et al., 2011, Bagchi et al., 2011).
• Spectral Index: Steep integrated spectra ($\alpha \sim -1.0$ to $-1.5$), with significant steepening toward the cluster center and further downstream from the shock, as expected from ageing of relativistic electrons (Weeren et al., 2011, Weeren et al., 2012). The integrated spectral index is typically $\sim$0.5 steeper than the injection index ($\alpha_\mathrm{inj}$) due to radiative losses.
• Polarization: Relics display high fractional polarization ($\sim$10–40%), with inferred magnetic field vectors preferentially aligned along the relic's elongation. Polarization is further modulated by Faraday depolarization effects, and RM synthesis studies reveal modest rest-frame RM dispersions ($\sim$40 rad m$^{-2}$ or less) (Stuardi et al., 2022).
• Surface Brightness Ratios: While relics in a given pair are often similar in size and brightness, pronounced asymmetries are observed, with surface brightness and luminosity ratios varying by an order of magnitude or more in some cases (Lee et al., 2021, Lee et al., 24 Oct 2025).

These properties are most easily observed at low radio frequencies (e.g., 150–600 MHz), where synchrotron losses are less severe and steep-spectrum emission is enhanced (Weeren et al., 2011).

3. Role in Mapping Merger Dynamics and ICM Physics

Double radio relics provide robust diagnostics of merger geometry, shock properties, and ICM conditions. The basic paradigm is that each relic traces an outward-propagating shock generated as two subclusters collide. The separation ($d_\mathrm{drr}$) between the relics correlates tightly with the time since collision (TSC), encapsulated by the empirical scaling:

$$\mathrm{TSC~[Gyr]} = 0.52 \cdot \frac{d_{\rm drr}}{R_{500\rm c}} - 0.24$$

with $R_{500\rm c}$ being the characteristic radius enclosing a mean overdensity of 500 times the critical density (Lee et al., 24 Oct 2025).

Hydrodynamic and MHD simulations, supplemented by weak-lensing mass mapping, have demonstrated that:

• The morphology, size, and width of double relics constrain the mass ratio (typically $\sim$2:1), impact parameter (b < 400 kpc), viewing angle (edge-on events yield thin, elongated relics), and the merger stage (typically $\sim$1 Gyr after core passage) (Weeren et al., 2011, Weeren et al., 2011, Okabe et al., 2015).
• The location and extent of the relics align closely with the collision axis, typically within $\sim$30°, and their separation is a precise probe of merger age.
• The absence of radio halo emission in some double relic systems constrains the energy density of MHD turbulence in the ICM, yielding stringent upper limits (e.g., $(\delta B/B)^2 < 10^{-6}$ at resonant wavenumbers) (Okabe et al., 2015).

4. Shock Strength, Acceleration Efficiency, and Magnetic Fields

The Mach number $\mathcal{M}$ of the merger shocks traced by double relics is a key parameter regulating particle acceleration:

$$\alpha_\mathrm{inj} = \frac{1}{2} - \frac{\mathcal{M}^2+1}{\mathcal{M}^2-1}$$

Observed injection indices (typically –0.6 to –0.7) correspond to $\mathcal{M} \sim 2.0$–4.6 (Weeren et al., 2012, Weeren et al., 2012, Lee et al., 2021). However, some X-ray analyses reveal lower $\mathcal{M}$ values ($\lesssim$2) than those inferred from radio spectra, suggesting that weak shocks alone cannot account for the observed radio luminosity in all cases, possibly requiring re-acceleration of fossil cosmic rays or projection effects (Ogrean et al., 2014, Chatterjee et al., 2023).

A steep scaling of relic radio luminosity with cluster mass ($L_\mathrm{R} \propto M^{2.83\pm0.39}$) (Gasperin et al., 2014) and consistency with models assuming nearly uniform magnetic fields ($B \sim$2 μG) suggest that both shock strength and magnetic field amplification are crucial, yet the field strength at relic locations may not scale simply with local ICM properties.

Numerical simulations find that for many systems, variations in shock dissipation and mass-weighted magnetic fields conspire to produce observed luminosity ratios and brightness asymmetries within double relic pairs; no single physical factor accounts for the diversity (Lee et al., 24 Oct 2025).

5. Diversity, Asymmetry, and Environmental Dependence

The observed diversity in size, luminosity, and morphology among double radio relic pairs reflects both underlying merger dynamics and local cluster environment:

• Some systems present highly asymmetric relics differing by factors of five in size (e.g., ZwCl 0008.8+5215 (Weeren et al., 2011)), or by an order of magnitude in surface brightness (e.g., ZwCl 1447.2+2619 (Lee et al., 2021)).
• The presence or absence of fossil cosmic-ray populations, the efficiency drop-off in weak shocks, and variations in pre-existing magnetic fields are all implicated in the observed asymmetries (Lee et al., 2021, Chatterjee et al., 2023).
• The detection of double relics in low-mass systems and supercluster environments (e.g., Abell 2108 (Chatterjee et al., 2023), Saraswati supercluster (Parekh et al., 2021)) demonstrates that merger-driven shocks can accelerate particles across a wide range of cluster masses and large-scale structure environments.

High-resolution radio imaging and improved calibration have revealed diffuse, extended emission not only confined to the relics themselves but also in the intra-cluster region between them (e.g., CIZA J2242.8+5301 (Weeren et al., 2011)), consistent with widespread turbulence and distributed acceleration.

6. Statistical Properties and Prospects for Cosmological Surveys

Comprehensive cosmological MHD simulations (e.g., TNG-Cluster, TNG300) predict that the fraction of symmetric double relic systems (where the secondary is at least 25% as bright as the primary) increases with survey depth, reaching 40% for low-luminosity systems (Lee et al., 24 Oct 2025). The simulations anticipate:

• A wide range of luminosity ratios, with many systems appearing as single relics at current sensitivity.
• Double relics align with the merger axis within ~30°, serving as robust markers of merger geometry.
• Future deep surveys (e.g., SKA) will reveal thousands of double relics, with low-mass clusters constituting the dominant population—a strong bias in current shallow observational catalogs.

The statistical scaling between relic pair separation and time since merger provides a practical tool for reconstructing cluster dynamical histories purely from radio data, with an accuracy of $\sim$0.2 Gyr.

7. Implications for Particle Acceleration and Cluster Evolution

Double radio relics offer critical constraints for plasma physics in the high-$\beta$ regime of the ICM. Their properties verify the operation of DSA at high-Mach, low-Mach, and (in some cases) re-acceleration-dominated shocks. They also probe the amplification and ordering of magnetic fields in the cluster outskirts and cosmic web, often extending beyond the cluster virial radius (Bagchi et al., 2011).

Integrated studies with multi-frequency radio, X-ray, polarization, and lensing data—combining both observational and simulation results—demonstrate that double relics are key laboratories for testing our understanding of cluster mergers and the feedback between gravitational dynamics, plasma microphysics, and non-thermal phenomena. With the advent of next-generation radio surveys and continued cross-correlation with simulations, the role of double radio relics will only expand in the reconstruction of cosmic structure formation and the physics of cosmic magnetism and particle acceleration.