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In order to understand certain observed features of arc-like giant radio relics such as the rareness, uniform surface brightness, and curved integrated spectra, we explore a diffusive shock acceleration (DSA) model for radio relics in which a spherical shock impinges on a magnetized cloud containing fossil relativistic electrons. Toward this end, we perform DSA simulations of spherical shocks with the parameters relevant for the Sausage radio relic in cluster CIZA J2242.8+5301, and calculate the ensuing radio synchrotron emission from re-accelerated electrons. Three types of fossil electron populations are considered: a delta-function like population with the shock injection momentum, a power-law distribution, and a power-law with an exponential cutoff. The surface brightness profile of radio-emitting postshock region and the volume-integrated radio spectrum are calculated and compared with observations. We find that the observed width of the Sausage relic can be explained reasonably well by shocks with speed $u_s sim 3times 10^3 kms$ and sonic Mach number $M_s sim 3$. These shocks produce curved radio spectra that steepen gradually over $(0.1-10) u_{rm br}$ with break frequency $ u_{rm br}sim 1$ GHz, if the duration of electron acceleration is $sim 60 - 80$ Myr. However, the abrupt increase of spectral index above $sim 1.5$ GHz observed in the Sausage relic seems to indicate that additional physical processes, other than radiative losses, operate for electrons with $gamma_e gtrsim 10^4$.
The existing theoretical framework for the energies stored in the synchrotron-emitting lobes of radio galaxies and quasars doesnt properly account for the curved spectral shape that many of them exhibit. We characterise these spectra using parameters
Moderately strong shocks arise naturally when two subclusters merge. For instance, when a smaller subcluster falls into the gravitational potential of a more massive cluster, a bow shock is formed and moves together with the subcluster. After pericen
We study the conditions required for the production of the synchrotron maser emission downstream of a relativistic shock. We show that for weakly magnetized shocks, synchrotron maser emission can be generated at frequencies significantly exceeding th
On the largest scales, the Universe consists of voids and filaments making up the cosmic web. Galaxy clusters are located at the knots in this web, at the intersection of filaments. Clusters grow through accretion from these large-scale filaments and
Collisionless shocks with low sonic Mach numbers, $M_{rm s} lesssim 4$, are expected to accelerate cosmic ray (CR) protons via diffusive shock acceleration (DSA) in the intracluster medium (ICM). However, observational evidence for CR protons in the