3.2. Correlations between X-ray and radio emission
Based on the small sample of X-ray clusters known at that time, Owen (1974) argued that there was a strong correlation between the radio and X-ray luminosity of clusters. Rowan-Robinson and Fabian (1975) did not find this correlation. Bahcall (1974b, 1977a) found that the X-ray emission of a cluster was increased if a strong radio source was located near the center of the cluster. McHardy (1978a) found that strong radio sources were more likely to be located in luminous X-ray clusters than in other clusters.
As discussed above, clusters generally contain steep-spectrum radio sources. It appears that radio sources in X-ray clusters have even steeper spectra, and that r correlates with X-ray luminosity (Erickson et al., 1978; McHardy, 1978a; Cane et al., 1981; Dagkesamansky et al., 1982). This suggests that there might be a strong correlation between low frequency radio flux and X-ray luminosity (Erickson et al., 1978; Cane et al., 1981). Such a correlation is not found in larger samples of X-ray clusters (Mitchell et al., 1979; Ulmer et al., 1981). X-ray selected cluster samples from the Einstein observatory do not show a strong X-ray-radio correlation (Feigelson et al., 1982; Johnson, 1981).
A possible correlation between X-ray emission and radio emission in poor clusters has also been found (Burns et al., 1981c).
There appears to be a strong correlation between radio emission by central dominant galaxies in clusters and the presence of cooling flows, as evidenced by soft X-ray line emission or central spikes in the X-ray surface brightness (Burns et al., 1981a; Valentijn and Bijleveld, 1983; Jones and Forman, 1984; Section 5.7.2).
To summarize, at present there may be a weak correlation between X-ray and radio luminosities, and there appears to be stronger correlation between the radio spectral index r and the X-ray luminosity Lx. Because of the many interelationships between cluster properties, it is difficult to decide whether these possible correlations are primary or reflect other correlations (see Section 4.6). For example, the relationship between Lx and r may be a result of the fact that Lx correlates with cluster optical morphology (Section 4.6), as does r. Moreover, it is difficult to establish a clear causal basis for these correlations.
Costain et al. (1972) and Owen (1974) argued that the correlation between X-ray and radio emission implied that the same population of relativistic electrons produced both radio emission and X-ray emission. The radio emission is synchrotron emission; in this model the X-ray emission would be inverse Compton scattering of cosmic radiation photons by the same relativistic electrons. This 'inverse Compton' (IC) theory is described in more detail in Section 5.1.1. The IC model does require that cluster radio sources have steep spectra, as observed. However, the evidence against the IC model is now overwhelmingly strong (Sections 4.3 and Sec 5.1). Thermal emission by diffuse gas provides the main X-ray emission from clusters.
Another direct connection between the radio emitting electrons and the X-ray emitting thermal gas would be established if the thermal gas were heated by the relativistic electrons and/or any associated 'cosmic ray' nuclei. Such heating would occur through Coulomb interactions (Lea and Holman, 1978) and might be enhanced by plasma interactions (Scott et al., 1980; see Section 5.3.5 for more details). The heating is strongest for the lower energy electrons which produce very low frequency radio emission, and thus the heating requires that the radio sources in clusters have steep spectra, as observed. However, it is not clear that any ongoing heating of the thermal gas either is needed or does occur in the majority of X-ray clusters. First of all, there exist a reasonable number of strong X-ray clusters that do not have strong steep-spectrum radio sources. Second, the thermal energy per unit mass in the hot gas is roughly the same as the kinetic energy per unit mass in the galaxies. Thus the gas could have been heated initially by thermalizing its kinetic energy when it either was ejected from galaxies or fell into the cluster. In typical clusters, the cooling time in most of the gas is longer than the probable age of the cluster (the Hubble time), and no further heating of the gas would necessarily be required (Section 5.3).
A connection between the X-ray and radio luminosity of clusters might be produced if the radio emission were powered by accretion of gas which was initially part of the hot intracluster medium. In Sections 4.3 and 5.7 evidence is presented indicating that intracluster gas is cooling and being accreted by central dominant galaxies in many X-ray clusters. As mentioned previously, there is a correlation between radio emission by central dominant galaxies in clusters and the presence of these cooling flows (Burns et al., 1981a; Valentijn and Bijleveld, 1983; Jones and Forman, 1984). The further accretion of this cooling gas onto a central massive object in the galaxy might produce the radio emission.
It is likely that the most important connection between the X-ray emitting gas in clusters and the relativistic electrons that produce the radio emission is dynamical. The hot gas provides pressure forces that can control the dynamics of the plasma of relativistic electrons. The current evidence suggests that radio emission from galaxies occurs when streams or blobs of relativistic nonthermal plasma are ejected from the nucleus of the galaxy (Miley, 1980). If the pressure and density of any surrounding medium is sufficiently large, the bulk motion and expansion of the radio emitting plasma will be retarded. This could explain the absence of very large radio galaxy sources associated with clusters. Moreover, the intracluster gas may confine the radio emitting plasma and prevent its adiabatic expansion. Expansion and synchrotron emission provide two competing energy loss mechanisms for the relativistic plasma. If expansion occurs, it weakens the radio emission but generally will not affect its spectrum. If the expansion is retarded by the pressure of a confining medium, synchrotron losses become important. These losses are most important for the highest energy electrons, and thus they cause the spectrum of the radio source to steepen. This mechanism probably provides the most plausible explanation of the steep spectrum of cluster radio sources.
Additional evidence for the dynamical effect of the hot intracluster gas on radio galaxies comes from distortions in the structure of the radio source produced if the radio galaxy is moving relative to the intracluster medium, as discussed below.