We consider a Swiss Cheese model with a random arrangement of LemaitreTolman-Bondi holes in Lambda CDM cheese. We study two kinds of holes with radius r(b) = 50 h(-1) Mpc, with either an underdense or an overdense centre, called the open and closed case, respectively. We calculate the effect of the holes on the temperature, angular diameter distance and, for the first time in Swiss Cheese models, shear of the CMB. We quantify the systematic shift of the mean and the statistical scatter, and calculate the power spectra. In the open case, the temperature power spectrum is three orders of magnitude below the linear ISW spectrum. It is sensitive to the details of the hole, in the closed case the amplitude is two orders of magnitude smaller. In contrast, the power spectra of the distance and shear are more robust, and agree with perturbation theory and previous Swiss Cheese results. We do not find a statistically significant mean shift in the sky average of the angular diameter distance, and obtain the 95% limit vertical bar Delta D-A/(D) over bar (A)vertical bar less than or similar to 10(-4). We consider the argument that areas of spherical surfaces are nearly unaffected by perturbations, which is often invoked in light propagation calculations. The closed case is consistent with this at 1 sigma, whereas in the open case the probability is only 1.4%.

Context. During their lifetimes, galaxy clusters grow through the accretion of matter from the filaments of the large-scale structure and from mergers with other clusters. These mergers release a large amount of energy into the intracluster medium (ICM) through merger shocks and turbulence. These phenomena are associated with the formation of radio sources known as radio relics and radio halos, respectively. Radio relics and halos are unique proxies for studying the complex properties of these dynamically active regions of clusters and the microphysics of the ICM more generally. Aims. Abell 3667 is a spectacular example of a merging system that hosts a large pair of radio relics. Due to its proximity (0.0553) and large mass, the system enables the study of these sources to a uniquely high level of detail. However, being located at Dec = -56.8 degrees, the cluster could only be observed with a limited number of radio facilities. Methods. We observed Abell 3667 with MeerKAT as part of the MeerKAT Galaxy Cluster Legacy Survey. We used these data to study the large-scale emission of the cluster, including its polarisation and spectral properties. The results were then compared with simulations. Results. We present the most detailed view of the radio relic system in Abell 3667 to date, with a resolution reaching 3 kpc. The relics are filled with a network of filaments with different spectral and polarisation properties that are likely associated with multiple regions of particle acceleration and local enhancements of the magnetic field. Conversely, the magnetic field in the space between filaments has strengths close to what would be expected in unperturbed regions at the same cluster-centric distance. Comparisons with magnetohydrodynamic cosmological and Lagrangian simulations support the idea of filaments as multiple acceleration sites. Our observations also confirm the presence of an elongated radio halo, developed in the wake of the bullet-like sub-cluster that merged from the south-east. Finally, we associate the process of magnetic draping with a thin polarised radio source surrounding the remnant of the bullet's cool core. Conclusions. Our observations have unveiled the complexity of the interplay between the thermal and non-thermal components in the most active regions of a merging cluster. Both the intricate internal structure of radio relics and the direct detection of magnetic draping around the merging bullet are powerful examples of the non-trivial magnetic properties of the ICM. Thanks to its sensitivity to polarised radiation, MeerKAT will be transformational in the study of these complex phenomena.