Double radio relics and the radio halo in the high-redshift galaxy cluster El Gordo with the Upgraded GMRT

Context. Diffuse synchrotron radio sources that are associated with the intracluster medium of galaxy clusters are of special interest at high redshift for understanding the magnetization and particle acceleration mechanisms. Aims. El Gordo is the most massive galaxy cluster at high redshift (z = 0.87). It hosts a radio halo and a double radio relic system. We aim to understand the role of turbulence in the origin of its diffuse radio emission by combining radio and X-ray observations. Methods. We observed El Gordo with the Upgraded GMRT at 0.3-1.45 GHz and obtained the integrated spectra, the spatially resolved spectral map, and the scaling relations of the radio and X-ray surface brightness. We constructed a density fluctuation power spectrum for the central 1 Mpc region using Chandra data. Results. The radio halo and the double relics are detected at all the bands, and in addition, we detect an extension to the eastern relic. The radio halo has a spectral index of -1.0 +/- 0.3 with a possible steepening beyond 1.45 GHz. All the relics have spectral indices of -1.4, except for the extension of the east relic, which has -2.1 +/- 0.4. The radio and X-ray surface brightness point-to-point analysis at bands 3 and 4 show slopes of 0.60 +/- 0.12 and 0.76 +/- 0.12, respectively. The spectral index and X-ray surface brightness are anticorrelated. The density fluctuations peak at similar to 700 kpc at an amplitude of (delta rho/rho) = 0.15 +/- 0.02. We derived a 3D turbulent Mach number of similar to 0.6 from the gas density fluctuation power spectrum under the assumption that all the fluctuations are attributable to turbulence. Conclusions. The derived properties of El Gordo agree with those of low-redshift clusters. This indicates that the fast magnetic amplification that was proposed for high-redshift clusters is at work in El Gordo as well. We discuss the consistency of our results with turbulent reacceleration, which might be representative of high-redshift merging clusters.