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

Diffuse synchrotron radio sources associated with the intra-cluster medium of galaxy clusters are of special interest at high redshifts to understand the magnetization and particle acceleration mechanisms. El Gordo (EG) is the most massive galaxy cluster at high redshift (0.87), hosts a radio halo and a double radio relic system. We aim to understand the role of turbulence in the origin of the diffuse radio emission by combining radio and X-ray observations. We observed EG with the Upgraded GMRT at 0.3 - 1.45 GHz and obtained the integrated spectra, spatially resolved spectral map, and scaling relations between radio and X-ray surface brightness. We constructed a density fluctuation power spectrum for the central 1 Mpc region using Chandra data. 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 $-1.0\pm0.3$ with a possible steepening beyond 1.45 GHz. All the relics have spectral indices of $-1.4$ except the extension of the east relic which has $-2.1\pm0.4$. The radio and X-ray surface brightness point-to-point analysis at bands 3 and 4 show slopes of $0.60\pm0.12$ and $0.76\pm0.12$, respectively. The spectral index and X-ray surface brightness show an anti-correlation. The density fluctuations peak at $\sim 700$ kpc with an amplitude of $(\delta \rho/\rho) =0.15\pm0.02$. We derive the 3D turbulent Mach number of $\sim$ 0.6 from the gas density fluctuations power spectrum, assuming all the fluctuations are attributed to turbulence. The derived properties of EG are in line with the low redshift clusters indicating that fast magnetic amplification proposed in high redshift clusters is at work in EG as well. We have discussed the consistency of the obtained results with the turbulent re-acceleration which might be representative of high redshift merging clusters.