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Recent radio observations with Low-Frequency Array (LOFAR) discovered diffuseemission extending beyond the scale of classical radio halos. The presence ofsuch mega halos indicates that the amplification of the magnetic field andacceleration of relativistic particles are working in the cluster outskirts,presumably due to the combination of shocks and turbulence that dissipateenergy in these regions. Cosmological magnetohydrodynamical (MHD) simulationsof galaxy clusters suggest that solenoidal turbulence has a significant energybudget in the outskirts of galaxy clusters. In this paper, we explore thepossibility that this turbulence contributes to the emission observed in megahalos through second-order Fermi acceleration of relativistic particles and themagnetic field amplification by the dynamo. We focus on the case of Abell 2255and find that this scenario can explain the basic properties of the diffuseemission component that is observed under assumptions that are used in previousliterature. More specifically, we conduct a numerical follow-up, solving theFokker--Planck equation using a snapshot of a MHD simulation and deducing thesynchrotron brightness integrated along the lines of sight. We find that avolume-filling emission, ranging between 30 and almost 100% of the projectedarea depending on our assumptions on the particle diffusion and transport, canbe detected at LOFAR sensitivities. Assuming a magnetic field $B\sim0.2\mu$G,as derived from a dynamo model applied to the emitting region, we find that theobserved brightness can be matched when $\sim$1% level of the solenoidalturbulent energy flux is channeled into particle acceleration.

Efficiency of turbulent reacceleration by solenoidal turbulence and its application to the origin of radio mega halos in cluster outskirts