3.4. Cluster radio haloes
The second type of radio morphology distinctly associated with clusters of galaxies is the cluster radio halo. They are diffuse, extended radio sources whose sizes are generally considerably larger than the cluster galaxy core radius, and smaller than the overall cluster size (for example, an Abell radius). The best studied example is Coma C, the halo source in the Coma cluster, which was first shown to be diffuse by Willson (1970), and which was studied further by Jaffe et al. (1976), Jaffe (1977), Valentijn (1978), Hanisch et al. (1979), Hanisch (1980), and Hanisch and Erickson (1980). Other clusters in which halo sources have probably been detected include A401 (Harris et al., 1980; Roland et al., 1981; but see Hanisch and Erickson, 1980), A1367 (Gavazzi, 1978; Hanisch, 1980; but this halo is considerably weaker and smaller than the others), A2255 (Harris et al., 1980), A2256 (Bridle and Fomalont, 1976; Bridle et al., 1979; but this is a very messy radio cluster), and A2319 (Grindlay et al., 1977; Harris and Miley, 1978; Andernach et al., 1980). While Ryle and Windram (1968) reported a rather large radio halo in the Perseus cluster, it does not appear to be a real source (Gisler and Miley, 1979; Jaffe and Rudnick, 1979; Birkinshaw, 1980; Hanisch and Erickson; 1980), although a smaller halo source has been reported recently (Noordam and de Bruyn, 1982).
Radio haloes do not appear to be very common, as a large number of surveys of clusters have failed to find them (Jaffe and Rudnick, 1979; Cane et al., 1981; Andernach et al., 1981; Hanisch, 1982a).
The cluster radio halos have very steep power-law radio spectra, with r 1.2. The power-law spectrum and some indications of polarization suggest that the emission process is synchrotron emission by nonthermal relativistic electrons, as in radio galaxies. The halo in Coma has a diameter (FWHM) of 1 Mpc / h50, which is typical. In Coma, the spectrum of the halo is relatively uniform spatially (Jaffe, 1977). Although the sample of known radio haloes is small, they appear to be associated with clusters of intermediate optical morphology (BM II; RS B, C, L) (Hanisch, 1982b). These clusters are relaxed, but do not have a dominant cD galaxy (an exception may be A2319). The haloes are generally associated with clusters having a regular nXD X-ray morphology (Vestrand, 1982); Vestrand notes that many of these clusters have particularly luminous and extended X-ray emission and may have unusually high X-ray temperatures (see also Forman and Jones, 1982). In making these comparisons, the unusually weak and small halo associated with A1367 has not been included.
There is currently no consensus as to the origin of these haloes. Jaffe (1977) discussed observational and theoretical constraints on the origin of the nonthermal electrons producing the emission in the Coma cluster, and proposed that the electrons originate at strong radio sources in the cluster and diffuse out to form the halo. The observed spectral index r is about 0.5 larger than the spectral indices of strong cluster radio sources; such an increase occurs if there is a steady-state between the input of relativistic nonthermal electrons and synchrotron losses. Moreover, the number of electrons produced in strong radio sources is sufficient to explain the halo radio emission if the magnetic field in the cluster is Bc 1µG, which is consistent with limits on the hard X-ray emission from clusters (Section 4.3.1). However, the halo radio emission is less strongly peaked at the cluster center than the distribution of galaxies, particularly of strong radio galaxies (Jaffe, 1977). Thus the nonthermal electrons must be transported out from the cluster core. In order that synchrotron losses should not affect the spectrum of the electrons and cause the halo radio spectrum to steepen dramatically with radius (which is not observed; Jaffe, 1977), the particles must be transported at a velocity which is 2000 km/s. Convective fluid motions of this order would be supersonic and would involve a very high rate of energy dissipation. Thus Jaffe argued that the relativistic electrons must diffuse out into the cluster.
As discussed extensively by Jaffe, a diffusion velocity 2000 km/s would greatly exceed the Alfvén velocity
in the intracluster plasma. (Here, g is the density of intracluster gas.) For typical values of the gas density from X-ray observations and the required magnetic field discussed above, vA 100 km/s. Particles that diffuse through a plasma faster than the Alfvén velocity excite plasma waves, which rapidly slow down the diffusion of the particles, and thus Jaffe argued that the Alfvén velocity acts as an upper limit on the diffusion speed of the relativistic electrons in radio halos. This velocity is much too small to allow the particles to diffuse without losses. A possible solution to this Alfvén speed limit problem, suggested by Holman et al. (1979), is that the plasma waves generated by electrons diffusing at speeds greater than vA may be damped by ions in the background thermal plasma. This would allow diffusion at speeds up to the speed of these background ions, essentially the sound speed in the intracluster gas.
Another solution to the Alfvén speed problem was suggested by Dennison (1980b). He noted that the flux of relativistic, nonthermal particles at the Earth (cosmic rays) is dominated by protons, and suggested that this might also be true in radio sources. The protons would diffuse away from cluster radio galaxies at the Alfvén speed, but suffer no significant synchrotron losses because of their rigidity. In the cluster they would collide with thermal protons and produce secondary electrons by a number of processes. These relativistic, nonthermal secondaries would then produce the observed radio haloes in this model.
Harris and Miley (1978) suggested that the radio haloes are remnants of previous head-tail radio galaxies, whose spectra have steepened due to synchrotron losses. One problem with this idea is that HTs are typically not very luminous, and the clusters with radio haloes therefore would be required to have had a large number of bright radio galaxies in the past. However, radio haloes are rare, so this may not be a serious objection.
Jaffe (1977) considered the possibility that the nonthermal electrons are accelerated to relativistic energies within the cluster by turbulence in the intracluster gas. Roland et al. (1981) suggested that the turbulence was generated by the wakes of galaxies moving through the intracluster medium. Based on the small available sample, they suggested that the luminosity of radio haloes increases with the cluster X-ray luminosity Lx (a measure of the amount of gas in the cluster) and the velocity dispersion of galaxies r, with Lhalo Lx r2. There are several problems with this hypothesis; first, unless the acceleration of relativistic electrons is very efficient, the rate of dissipation of the turbulent energy is unacceptably large (Jaffe, 1977). Second, no galactic wake has been detected as a radio source. They ought to appear as tailed galaxies without heads (no radio source in the nucleus of the galaxy).
The cluster A401 has been observed to possess a radio halo. With A399, this cluster forms a possible merging double system (Ulmer and Cruddace, 1981; Section 4.4). Harris et al. (1980) suggested that radio haloes form during the coalescence of subclusters, possibly by the acceleration of relativistic particles in shocks which form in the intracluster gas. However, there are a reasonable number of other double clusters that do not show radio haloes.
Observations of radio haloes are important to the understanding of X-ray cluster emission because the nonthermal radio-emitting electrons and X-ray emitting thermal plasma coexist and may interact. Initially, it had been suggested that the X-ray emission might be inverse Compton emission from the nonthermal electrons (Section 5.1.1). However, the frequency of occurrence of X-ray emission and rarity of radio haloes is one of the many arguments against this theory. On the other hand, the nonthermal electrons may heat the thermal plasma and contribute to the X-ray emission indirectly (Lea and Holman, 1978; Rephaeli, 1979; Scott et al., 1980; see also Sections 3.2 and 5.3.5). Vestrand (1982) has pointed out that radio halo clusters have extended X-ray emission and may have higher X-ray temperatures than nonhalo clusters; he attributes this difference to the heating of intracluster gas by nonthermal electrons.