Deep LOFAR observations of the merging galaxy cluster CIZA J2242.8+5301
  Previous studies have shown that CIZA J2242.8+5301 (the 'Sausage' cluster,
$z=0.192$) is a massive merging galaxy cluster that hosts a radio halo and
multiple relics. In this paper we present deep, high fidelity, low-frequency
images made with the LOw-Frequency Array (LOFAR) between 115.5 and 179 MHz.
These images, with a noise of 140 mJy/beam and a resolution of
$\theta_{\text{beam}}=7.3"\times5.3"$, are an order of magnitude more sensitive
and five times higher resolution than previous low-frequency images of this
cluster. We combined the LOFAR data with the existing GMRT (153, 323, 608 MHz)
and WSRT (1.2, 1.4, 1.7, 2.3 GHz) data to study the spectral properties of the
radio emission from the cluster. Assuming diffusive shock acceleration (DSA),
we found Mach numbers of $\mathcal{M}_{n}=2.7{}_{-0.3}^{+0.6}$ and
$\mathcal{M}_{s}=1.9_{-0.2}^{+0.3}$ for the northern and southern shocks. The
derived Mach number for the northern shock requires an acceleration efficiency
of several percent to accelerate electrons from the thermal pool, which is
challenging for DSA. Using the radio data, we characterised the eastern relic
as a shock wave propagating outwards with a Mach number of
$\mathcal{M}_{e}=2.4_{-0.3}^{+0.5}$, which is in agreement with
$\mathcal{M}_{e}^{X}=2.5{}_{-0.2}^{+0.6}$ that we derived from Suzaku data. The
eastern shock is likely to be associated with the major cluster merger. The
radio halo was measured with a flux of $346\pm64\,\text{mJy}$ at
$145\,\text{MHz}$. Across the halo, we observed a spectral index that remains
approximately constant ($\alpha^{\text{145 MHz-2.3 GHz}}_{\text{across
\(\sim\)1 Mpc}^2}=-1.01\pm0.10$) after the steepening in the post-shock region
of the northern relic. This suggests a generation of post-shock turbulence that
re-energies aged electrons.
