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Ultra-low frequency observations (<100 MHz) are particularly challengingbecause they are usually performed in a low signal-to-noise ratio regime due tothe high sky temperature and because of ionospheric disturbances whose effectsare inversely proportional to the observing frequency. Nonetheless, theseobservations are crucial to study the emission from low-energy populations ofcosmic rays. We aim to obtain the first thermal-noise limited (~ 1.5 mJy/beam)deep continuum radio map using the LOFAR Low Band Antenna (LBA) system. Ourdemonstration observation targeted the galaxy cluster RX J0603.3+4214 (the"Toothbrush" cluster). We used the resulting ultra-low frequency (58 MHz) imageto study cosmic-ray acceleration and evolution in the post shock region, aswell as their relation with the presence of a radio halo. We describe the datareduction we have used to calibrate LOFAR LBA observations. The resulting imageis combined with observations at higher frequencies (LOFAR 150 MHz and VLA 1500MHz) to extract spectral information. We obtained the first thermal-noiselimited image from an observation carried out with the LOFAR LBA system usingall Dutch stations at a central frequency of 58 MHz. With 8 hours of data, wereached an rms noise of 1.3 mJy/beam at a resolution of 18" x 11". Theprocedure we have developed is an important step forward towards routinehigh-fidelity imaging with the LOFAR LBA. The analysis of the radio spectrashows that the radio relic extends to distances of 800 kpc downstream from theshock front, larger than what allowed by electron cooling time. Furthermore,the shock wave started accelerating electrons already at a projected distanceof <300 kpc from the crossing point of the two clusters. These results can beexplained if electrons are reaccelerated downstream by background turbulencepossibly combined with projection effects.

Reaching thermal noise at ultra-low radio frequencies: the Toothbrush radio relic downstream of the shock front