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

¹ Institute of Astronomy, National Central University, Chung-Li 32054, Taiwan
² I. E. Tamm Theoretical Physics Division, P. N. Lebedev Physical Institute, 117924 Moscow, Russia e-mail: dogiel@lpi.ru
³ INAF - Osservatorio Astronomico di Roma, via Frascati 33, 00040 Monteporzio, Italy
⁴ Department of Physics, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
⁵ Moscow Institute of Physics and Technology, Institutskii lane, 141700 Moscow Region, Dolgoprudnii, Russia

Received: 23 August 2005
Accepted: 19 September 2006

Abstract

Aims.The stochastic acceleration of subrelativistic electrons from a background plasma is studied in order to find a possible explanation of the hard X-ray emission detected from the Coma cluster.

Methods.We calculate the necessary energy supply as a function of the plasma temperature and of the electron energy, and we show that, for the same value of the hard X-ray flux, the energy supply changes gradually from its high value for the case 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.

Results.We show that the temporal evolution of the particle distribution function has, at its final stationary stage, a rather specific form. This distribution function 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 functions. In this region the radiative lifetime of a single quasi-thermal 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  keV lie in this quasi-thermal regime. We show that the energy supply required by quasi-thermal electrons to produce the observed hard X-ray 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 raised by Petrosian (2001): while Petrosian's estimates are correct for nonthermal particles, they are inapplicable in the quasi-thermal range. We finally analyze the change in Coma's Sunyaev-Zeldovich effect caused by the implied distortions of the Maxwellian spectrum of electrons, and we show that evidence for the acceleration of subrelativistic electrons can, in principle, be derived from detailed spectral measurements.