MACS J1149 radio maps at 30 × 30 resolution. In all the panels, the contour levels are [±3, 6, 12, ...] × σ. Top left: 144 MHz LOFAR map (σ ∼ 0.30 mJy beam −1 ). Top right: 323 MHz GMRT map (σ ∼ 0.30 mJy beam −1 ). Bottom left: 1.5 GHz JVLA (D array) map (σ ∼ 45 µJy beam −1 ). Bottom right: 144 MHz LOFAR contours (after the subtraction of the embedded sources) overlaid on the X-ray image of Fig. 1.

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... clear whether this diffuse emission belongs to the relic or the source itself. As discussed by Giovannini et al. (2020), the orientation of 'J' is expected to be perpendicular to the merger axis, if it is a relic induced by the merger shock. Therefore, they proposed that 'J' might be a radio filament associated with the merger and not a relic. Fig. 6 shows the 30 × 30 resolution maps at 144 MHz (top left), 323 MHz (top right), and 1.5 GHz (bottom left), that we used to consistently measure the flux density of the halo. For the first time, we have deep radio maps of the halo at both high and low frequency and a more reliable measure of the spectrum can be performed. In all these ...

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... these images, the diffuse emission extends up to ∼ 400 (∼ 2.6 Mpc) along the NW-SE direction, even though it is fully recovered only at 144 MHz. The morphology of the halo emission is similar at 144 MHz, 323 MHz, and 1.5 GHz. It has a projected NW-SE length of ∼ 200 (∼ 1.3 Mpc) and is interconnected with the relic. In the bottom right panel of Fig. 6 we overlay the LOFAR contours (after the subtraction of the sources embedded in the halo) on the X-ray image of Fig. 1. The radio emission of the halo is co-spatial with the X-ray emission of the ICM, as typically observed in galaxy ...

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... and S 1500 = 2.0 ± 0.5 mJy, respectively. The resulting spectrum across 144 and 1500 MHz is reported in Fig. 8. We fitted the flux density values with a single power law, obtaining a spectral index of α 1500 144 = 1.49 ± 0.12. We iterated the measures in different regions of the halo (in particular, within the brightest X-ray counterpart; see Fig. 6, bottom right), consistently finding an average α ∼ 1.5 everywhere and thus confirming that MACS J1149 is a steep spectrum radio halo. We notice that Bonafede et al. (2012) measured S 323 = 29 ± 4 mJy and S 1500 = 1.2 ± 0.5 mJy (α 1500 323 = 2.1), whereas Giovannini et al. (2020) obtained S 1500 = 0.9 ± 0.1 mJy. The inconsistency of ...

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... typically found in radio halos, the non-thermal emission in MACS J1149 roughly follows the thermal one (Fig. 6, bottom right). The left panel of Fig. 10 shows the radio (I R ), and X-ray (I X ) surface brightness radial profiles, extracted in circular beamsize annuli (we used the LOFAR image at 19 × 15 resolution) and normalised at their respective maxima. We notice that I R decreases with the radius slower than I X ...

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... The ratio of CRp and thermal energy budget required to match the observed radio emission assuming a pure hadronic model is shown in Fig. 11 as a function of B 0 . We also show the ratio of the thermal (ε ICM ) and non-thermal (ε CR + ε B ) energy budget, integrated within maximum radii of 2.2r c and 2.5r c , where the halo is clearly visible (see Fig. 6). For typical values of B 0 < 10 µG in galaxy clusters (e.g. Bonafede et al. 2010), an untenable ε CR /ε ICM > 1 is required. The CRe energy budget declines with increasing B 0 , however the minimum (ε CR + ε B ) /ε ICM is reached for unusually high values of the magnetic field B 0 ∼ 25 µG. Moreover, the CRe energy budget is still ...