In-situ acceleration of subrelativistic electrons in the Coma halo and the halo's influence on the Sunyaev-Zeldovich effect

The stochastic acceleration of subrelativistic electrons from a background plasma is studied in order to find a possible explanation of the hard X-ray (HXR) emission detected from the Coma cluster. We calculate the necessary energy supply as a function of the plasma temperature and of the electron energy. We show that, for the same value of the HXR flux, the energy supply changes gradually from its high value (when emitting particle are non-thermal) to lower values (when the electrons are thermal). The kinetic equations we use include terms describing particle thermalization as well as momentum diffusion due to the Fermi II acceleration. We show that the temporal evolution of the particle distribution function has, at its final stationary stage, a rather specific form: it cannot be described by simple exponential or power-law expressions. A broad transfer region is formed by Coulomb collisions at energies between the Maxwellian and power-law parts of the distribution function. In this region the radiative lifetime of a single electron differs greatly from the lifetime of the distribution function as a whole. For a plasma temperature of 8 keV, the particles emitting bremsstrahlung at 20-80 keV lie in this quasi-thermal regime. We show that the energy supply required by quasi-thermal electrons to produce the observed HXR flux from Coma is one or two orders of magnitude smaller than the value derived from the assumption of a nonthermal origin of the emitting particles. This result may solve the problem of rapid cluster overheating by nonthermal electrons. We finally predict the change in Coma's SZ effect caused by the distortions of the Maxwellian electron spectrum, and we show that evidence for acceleration of subrelativistic electrons can be derived from detailed spectral measurements.