The application of the adiabatic compression scenario to the radio relic in the galaxy cluster Abell 3411-3412

Although radio relics are understood to originate in intracluster shock waves resulting from merger shocks, the most widely used model for describing this (re-)acceleration process at shock fronts, the diffusive shock acceleration (DSA) model, has several challenges, including the fact that it is inefficient at low shock Mach numbers. In light of these challenges, it is worthwhile to consider alternative mechanisms. One possibility is the adiabatic compression by a shock wave of a residual fossil electron population which has been left over from a radio galaxy jet. This paper applies this model to the relic hosted in the merging galaxy cluster Abell 3411-3412, where a radio bridge between the relic and a radio galaxy has been observed, with the aim to reproduce the spatial structure of the spectral index of the relic. Four scenarios are presented, in which different effects are investigated, such as effects behind the shock front and different shock strengths. The results show that the adiabatic compression model can reproduce the observed spectral indices across the relic for a shock Mach number that is lower than the value required by the DSA-type modelling of this relic and is in accordance with the values derived from X-ray observations, if other mechanisms, such as an expansion phase or post-shock turbulence, are effective behind the shock front.