Models of radio halos must, in addition to explaining the radio emission itself, be capable of explaining why radio halos are rare and usually found in clusters like Coma (Hanisch 1982). Three general models for the formation of the radio emission have been proposed. Jaffe (1977) proposed that relativistic electrons diffused out of discrete radio sources to fill the cluster. Dennison (1980) presented a model in which relativistic protons were generated by cluster radio sources and then generated secondary relativistic electrons in collisions with thermal protons in the intracluster medium. Roland (1981) suggested that the magnetic fields and relativistic electrons were both generated in galactic wakes. All of these models have problems in explaining the observations (Hanisch 1982; Tribble 1991b).
More recently, Burns et al. (1992) have observed the minihalo in the Perseus cluster. They advocate a model in which the magnetic field is generated by a turbulent dynamo, and in which the cooling inflow suppresses outward diffusion of the field. The differences between Coma and Perseus are then ascribed to there being much weaker magnetic fields at large radii in cooling flow clusters.
The origin of the magnetic field in clusters is at present unclear. Jaffe (1980), Roland (1981) and Ruzmaikin, Sokoloff & Shukurov (1989) argued that galactic wakes could power a dynamo. However, Goldman & Rephaeli (1991) and De Young (1992) have shown that galactic wakes are inadequate to produce the observed fields. A more powerful energy source is required, such as cluster mergers (De Young 1992). The cluster merger could also reaccelerate energetic particles to produce the observed radio halo. Once the magnetic field has been generated it is likely to be long lived, whereas the relativistic particles responsible for the radio emission lose their energy on timescales of order 10^8 yr. Thus a more likely explanation for the lack of radio emission at large radii in Perseus is not that there is no magnetic field there, but rather that the relativistic electron population has aged and the synchrotron emission has faded from view.
In Section 2 I follow this idea, considering the formation of magnetic fields and relativistic electrons in cluster mergers. I consider the effect of cooling flows on intracluster magnetic fields in Section 3, and present simulations of cooling flow radio minihalos together with a discussion of the Burns et al. model for Perseus in Section 4. My conclusions are given in Section 5.