Spectral age modelling of the `Sausage' cluster radio relic

CIZA J2242.8+5301 is a post-core passage, binary merging cluster that hosts a large, thin, arc-like radio relic, nicknamed the `Sausage', tracing a relatively strong shock front. We perform spatially-resolved spectral fitting to the available radio data for this radio relic, using a variety of spectral ageing models, with the aim of finding a consistent set of parameters for the shock and radio plasma. We determine an injection index of $0.77^{+0.03}_{-0.02}$ for the relic plasma, significantly steeper than was found before. Standard particle acceleration at the shock front implies a Mach number $M=2.90^{+0.10}_{-0.13}$, which now matches X-ray measurements. The shock advance speed is $v_\mathrm{shock}\approx2500$ km s$^{-1}$, which places the core passage of the two subclusters $0.6-0.8$ Gyr ago. We find a systematic spectral age increase from $0$ at the northern side of the relic up to $\sim60$ Myr at $\sim145$ kpc into the downstream area, assuming a $0.6$ nT magnetic field. Under the assumption of freely-ageing electrons after acceleration by the `Sausage' shock, the spectral ages are hard to reconcile with the shock speed derived from X-ray and radio observations. Re-acceleration or unusually efficient transport of particle in the downstream area and line-of-sight mixing could help explain the systematically low spectral ages.