Physical insights from the spectrum of the radio halo in MACS
  J0717.5+3745
  We present new LOFAR observations of the massive merging galaxy cluster MACS
J0717.5+3745. The cluster hosts the most powerful radio halo known to date.
These new observations, in combination with published uGMRT (300$-$850 MHz) and
VLA (1$-$6.5 GHz) data, reveal that the halo is more extended than previously
thought, with a largest linear size of $\sim2.2 \rm Mpc$. The halo shows a
steep spectrum ($\alpha_{144\,\text{MHz}}^{1.5\,\text{GHz}}\sim-1.4$) and a
steepening ($\alpha_{1.5 \text{GHz}}^{5.5 \text{GHz}}\sim-1.9$) above 1.5 GHz.
We find a strong scattering in spectral index maps on scales of 50$-$100 kpc.
We suggest that such a strong scattering may be a consequence of the regime
where inverse Compton dominate the energy losses of electrons. The spectral
index becomes steeper and shows an increased curvature in the outermost regions
of the halo. We combined the radio data with \textit{Chandra} observations to
investigate the connection between the thermal and non-thermal components of
the intracluster medium (ICM). Despite a significant substructure in the halo
emission, the radio brightness correlates strongly with the X-ray brightness at
all observed frequencies. The radio-versus-X-ray brightness correlation slope
steepens at a higher radio frequency (from $b_{144 \text{MHz}}=0.67\pm0.05$ to
$b_{3.0 \text{GHz}}=0.98\pm0.09$) and the spectral index shows a significant
anti correlation with the X-ray brightness. Both pieces of evidence further
support a spectral steepening in the external regions. The compelling evidence
for a steep spectral index, the existence of a spectral break above 1.5 GHz,
and the dependence of radio and X-ray surface brightness correlation on
frequency are interpreted in the context of turbulent reacceleration models.
Under this scenario, our results allowed us to constrain that the turbulent
kinetic pressure of the ICM is up to 10%.
