Turbulence and particle acceleration in giant radio haloes: the origin of seed electrons

About one-third of X-ray-luminous clusters show smooth, Mpc-scale radio emission, known as giant radio haloes. One promising model for radio haloes is Fermi-II acceleration of seed relativistic electrons by compressible turbulence. The origin of these seed electrons has never been fully explored. Here, we integrate the Fokker-Planck equation of the cosmic ray (CR) electron and proton distributions when post-processing cosmological simulations of cluster formation and confront them with radio surface brightness and spectral data of Coma. For standard assumptions, structure formation shocks lead to a seed electron population that produces too centrally concentrated radio emission. Matching observations requires modifying properties of theCRpopulation (rapid streaming; enhancedCRelectron acceleration at shocks) or turbulence (increasing turbulent-to-thermal energy density with radius), but at the expense of fine-tuning. In a parameter study, we find that radio properties are exponentially sensitive to the amplitude of turbulence, which is inconsistent with small scatter in scaling relations. This sensitivity is removed if we relate the acceleration time to the turbulent dissipation time. In this case, turbulence above a threshold value provides a fixed amount of amplification; observations could thus potentially constrain the unknown CR seed population. To obtain sufficient acceleration, the turbulent magneto-hydrodynamics cascade has to terminate by transit time damping on CRs, i.e. thermal particles must be scattered by plasma instabilities. Understanding the small scatter in radio halo scaling relations may provide a rich source of insight on plasma processes in clusters.