Exploring the statistical properties of double radio relics in the TNG-Cluster and TNG300 simulations

TL;DR

This work uses the TNG-Cluster and TNG300 cosmological MHD simulations to statistically characterize double radio relics and their connection to cluster merger histories. By modeling shock-driven radio emission and identifying relic pairs, the authors show that relic axes generally align with the collision axis and that the time since collision correlates with relic separation, enabling ~0.2 Gyr precision in TSC estimates from double relics. The study finds a broad range of luminosity ratios among relic pairs, with no single parameter setting the brightness asymmetry; however, after applying a luminosity cut, the symmetric fraction aligns with observations (~30%), providing a testbed for plasma acceleration models. Projection effects and survey depth are shown to strongly influence detectable double relics, and forecasts for SKA imply a substantial rise in detectable double relics, especially from low-mass clusters, guiding expectations for future radio surveys.

Abstract

Double radio relics, pairs of diffuse radio features located on opposite sides of merging galaxy clusters, are a rare subclass of radio relics that are believed to trace merger shocks and provide valuable constraints on plasma acceleration models and merger history. With the number of known double relics growing in recent and upcoming radio surveys, statistical analyses of their properties are becoming feasible. In this study, we utilize the cosmological magnetohydrodynamics zoom-in simulations TNG-Cluster, in combination with TNG300-1, to examine the statistical properties of double radio relics. The simulated double relic pairs exhibit a wide range of luminosity ratios, broadly consistent with the observations. We find that the two relics in a given double system often differ significantly in their shock properties and magnetic field strengths. This diversity implies that the observed brightness asymmetry in the pair cannot be explained by a single factor alone, but instead reflects an interplay of multiple physical parameters. Nevertheless, double radio relics tend to align with the collision axis within $\sim30^{\circ}$ and their separation ($d_{\rm drr}$) correlates tightly with the time since collision (TSC) as ${\rm TSC~[Gyr]} = 0.52 d_{\rm drr}/R_{500\rm c} - 0.24$, allowing it to be inferred with an accuracy of $\sim0.2~\rm Gyr$. With the statistical samples of simulated radio relics, we predict that low-mass clusters will constitute the dominant population of double radio relic systems detected with upcoming surveys such as SKA. These results demonstrate that double radio relics can serve as robust probes of merger dynamics and plasma acceleration, and that simulations provide critical guidance for interpreting the large samples expected from next-generation radio surveys.

Figures (16)

• Figure 1: Radio luminosity at $1.4\rm~GHz$ of radio relics identified in the TNG-Cluster (black) and TNG300 (blue) simulations, and in observations (red). The x- and y-axes show the luminosities of the primary and secondary relics, respectively. The luminosity of the secondary relic is marked with an upper limit when it is undetected. The dashed and dotted lines mark luminosity ratios of $1$ and $1/4$, respectively. The top panel shows the cumulative fraction of symmetric double relics with the primary relic luminosity above the given threshold, where symmetric double relic systems are defined as those with a luminosity ratio $>1/4$. The fraction of symmetric relics increases with a lower luminosity threshold.
• Figure 2: Fraction of symmetric double radio relics with $L_{\rm 1.4GHz,2}/L_{\rm 1.4GHz,1}>0.25$ in radio relic systems as a function of cluster mass. The black line shows the fraction from simulated radio relics in TNG-Cluster and TNG300, the red line represents observations, and the blue line shows the symmetric fraction of simulated relics with $L_{\rm 1.4GHz,1}>10^{24}\rm~W~Hz^{-1}$. The simulated radio relics yield a symmetric fraction comparable to that observed after applying the luminosity cut.
• Figure 3: Ratio of the largest linear size between the primary and secondary relics as a function of their luminosity ratio in TNG-Cluster (black) and TNG300 (blue). Observed radio relics are shown as red points. While the overall size ratio broadly follows the luminosity ratio, many secondary relics exhibit a larger extent than their primary counterparts.
• Figure 4: Ratio of the average shock properties between the primary and secondary relics compared to their luminosity ratio from TNG-Cluster and TNG300. From left to right, the net shock-dissipated energy ($E_{\rm diss,2}/E_{\rm diss,1}$), the mass-weighted average magnetic field strength ($B_{2}/B_{1}$), and the mass-weighted average Mach number ($\mathcal{M}_2/\mathcal{M}_1$) are shown as a function of the luminosity ratio. The color scale represents the number density of simulated systems in each bin. The cyan dashed line indicates the analytical relation between radio emissivity and the underlying cell properties, assuming a spectral index of $\alpha=-0.5$. The shock properties display broad variation, indicating that no single parameter alone determines the luminosity ratio.
• Figure 5: Cumulative fraction of the relative angle between the collision axis and the vector connecting the centers of the double radio relics (top) or the center of the primary relic (bottom) from TNG-Cluster and TNG300. Color show subsamples with simple merger geometries, selected as head-on mergers ($d_{\rm peri}/R_{\rm 500c} < 0.2$), major mergers ($M_{\rm sub}/M_{\rm main} > 0.3$), and isolated mergers. The results show that relic axes can typically constrain the collision axis within $\hbox{$\sim$}30^{\circ}$.