New mysteries and challenges from the Toothbrush relic: wideband observations from 550 MHz to 8 GHz

Context. Radio relics are diffuse extended synchrotron sources that originate from shock fronts induced by galaxy cluster mergers. The actual particle acceleration mechanism at the shock fronts is still under debate. The galaxy cluster 1RXS J0603.3+4214 hosts one of the most intriguing examples of radio relics, known as the Toothbrush. Aims. To understand the mechanism(s) that accelerate(s) relativistic particles in the intracluster medium (ICM), we investigate the spectral properties of large scale diffuse extended sources in the merging galaxy cluster 1RXS J0603.3+4214. Methods. We present new wideband radio continuum observations made with uGMRT and VLA. Our new observations, in combi- nation with previously published data, allowed us to carry out a detailed high spatial resolution spectral and curvature analysis of the known diffuse radio emission sources, using a wide range of frequencies. Results. The integrated spectrum of the Toothbrush follows closely a power law over almost two orders of magnitudes in frequency, with a spectral index of −1.16 ± 0.02. We do not find any evidence of spectral steepening below 8 GHz. The subregions of the Toothbrush also exhibit near-perfect power laws and an identical spectral slopes, suggesting that observed spectral index is rather set by the distribution of Mach numbers which may have a similar shape at different parts of the shock front. Indeed, numerical simulations show an intriguing similar spectral index, indicating that the radio spectrum is dominated by the average over the inhomogeneities within the shock, with most of the emission coming from the tail of the Mach number distribution. In contrast to the Toothbrush, the spectrum of the fainter relics show a high-frequency steepening. Moreover, also the integrated spectrum of the halo follows a power law from 150 MHz to 3 GHz with a spectral index of −1.16 ± 0.04. We do not find any evidence for spectral curvature, not even in subareas of the halo. This suggest a homogeneous acceleration throughout the cluster volume. Between the "brush" region of the Toothbrush and the halo, the color-color analysis revealed emission that was consistent with an overlap between the two different spectral regions. Conclusions. None of the relic structures, the Toothbrush as a whole or its subregions or the other two fainter relics, show spectral shapes consistent with a single injection of relativistic electrons, such as at a shock, followed by synchrotron aging in a relatively homogeneous environment. Inhomogeneities in some combination of Mach number, magnetic field strengths and projection effects dominate the observed spectral shapes.