We present deep LOFAR observations between 120 –181 MHz of the ‘ Toothbrush ’ ( RX J0603.3+4214 ) , a cluster that contains one of the brightest radio relic sources known .
Our LOFAR observations exploit a new and novel calibration scheme to probe 10 times deeper than any previous study in this relatively unexplored part of the spectrum .
The LOFAR observations , when combined with VLA , GMRT , and Chandra X-ray data , provide new information about the nature of cluster merger shocks and their role in re-accelerating relativistic particles .
We derive a spectral index of \alpha = -0.8 \pm 0.1 at the northern edge of the main radio relic , steepening towards the south to \alpha \approx - 2 .
The spectral index of the radio halo is remarkably uniform ( \alpha = -1.16 , with an intrinsic scatter of \leq 0.04 ) .
The observed radio relic spectral index gives a Mach number of \mathcal { M } = 2.8 ^ { +0.5 } _ { -0.3 } , assuming diffusive shock acceleration ( DSA ) .
However , the gas density jump at the northern edge of the large radio relic implies a much weaker shock ( \mathcal { M } \approx 1.2 , with an upper limit of \mathcal { M } \approx 1.5 ) .
The discrepancy between the Mach numbers calculated from the radio and X-rays can be explained if either ( i ) the relic traces a complex shock surface along the line of sight , or ( ii ) if the radio relic emission is produced by a re-accelerated population of fossil particles from a radio galaxy .
Our results highlight the need for additional theoretical work and numerical simulations of particle acceleration and re-acceleration at cluster merger shocks .