4.3. Low frequency radio emission as a tracer of extragalactic magnetic fields

Cosmic rays serve as particularly effective `illuminators' of intergalactic magnetic fields at low radio frequencies. This is because of the relatively high spectral density of synchrotron radiation at low frequencies, reflecting the high value of (typically 2.4-3) which defines the power law distribution of cosmic ray electron energies: N(E) ~ E<sup>-</sup> (cf equation (1.1)). The critical frequency (near which most of the synchrotron radiation is emitted) is related to E by <sub>C</sub> = (3 eB sin / 4 m<sup>3</sup> c<sup>5</sup>)E<sup>2</sup> (Pacholczyk 1970). An advantage of observing at the lowest possible radio frequencies is that we preferentially detect the lowest energy CR electrons, which survive the longest to `keep illuminating' the associated magnetic field.

To calculate the longest possible loss time for a CR electron, we define a `cosmic background-equivalent' magnetic field, B_bge for which a CR electron's energy loss rate by synchrotron radiation (E / t |B|² E²) equals that due to inverse Compton scattering off the microwave background radiation (E / t) _bg E² where _bg = 4.8 × 10^-13(1 + z)⁴ erg cm^-3. Thus, for B B_bge, the energy density of the magnetic field (B² / 8) equals that in the cosmic background radiation (_bg). For z << 1, to which we restrict the present discussion, B_bge 3 × 10^-6 G. Larger magnetic field strengths will cause shorter, synchrotron radiation-dominated lifetimes, whereas for B < B_bge a CR electron's loss rate, being dominated by inverse Compton scattering, will depend only on its energy and _bg (cf Rees 1967, Pachoczyk 1970 for a discussion of the basic radiation processes).

We can write an expression for the inverse Compton-dominated lifetime, _max, for synchrotron-radiating CR electrons which are observed at a frequency , expressing the electron energy in terms of and B, as

(4.1)

where (|B| / |B_bge| 1). The Factor (|B| / |B_bge|)^1/2, is probably not far below unity as suggested by recently measured ICM field values. Thus we see that the maximum `fossil lifetime' of relativistic electrons scales to first order by ^-1/2. Observing frequencies of interest are approximately between 20 MHz and 400 MHz: below 20 MHz, refraction and absorption by the ionized component of the interstellar medium and/or the ionosphere become important. Above ~ 400 MHz, the emissivity becomes too low for the most sensitive detection of diffuse intergalactic synchrotron emission. In addition, the higher energy electrons, which radiate on average at higher frequencies, are less likely to have propagated to large distances from their acceleration sites because of their shorter loss times. Observing frequencies below 20 MHz are conceivable from space, if one is restricted to high galactic latitudes.

Until recently both the low resolution, and difficulties with earthbound and solar interference and ionospheric phase fluctuations, have prevented accurate imaging at frequencies below ~ 300 MHz. To distinguish true diffuse intergalactic synchrotron emission from a blend of discrete extragalactic radio sources, an angular resolution of 1' or better is required. This, at = 75 MHz for example, requires a well-filled antenna array (to achieve the required image quality), which extends to 30 km or more. Furthermore, interference suppression and phase irregularities in the ionosphere need to be eliminated, which require compute-intensive data processing techniques. These requirements are being fulfilled for the first time (by the NRAO VLA recently outfitted to low frequencies, the Giant Meter Wave Telescope (GMRT) at Pune, India, and the Westerbork Synthesis Radio Telescope (WSRT) in the Netherlands), a development which opens new possibilities for the detection of large scale 10 magnetic fields. Relation (4.1) shows that radio images at 30 MHz could show diffuse, magnetized intergalactic gas in the local universe which was produced 10⁹ years ago, on the assumption that |B| is not much different from |B_bge|. Such observations could give clues from the local Universe to the evolution of magnetic field strength over a significant period of cosmic time in such systems, e.g. in old, extended radio source lobes. An important complement will be sensitive imaging of diffuse x-ray emission which is produced by the inverse Compton mechanism (see also section 5.4.2).

Figure 13 shows a WSRT image at 326 MHz published by Kim et al (1989) of the 326 MHz intergalactic synchrotron emission surrounding the Coma cluster of galaxies, which may be prototypical of the type of radiation which could be imaged in future at much lower frequencies. They found emission extending beyond the Coma cluster, indicating an extended, magnetized region on a supercluster scale. Measurements of this type do not yield the field strength directly (equation (l.l)), but the assumption of equipartition between particle and magnetic density gives field strengths of ca 2 × 10^-7(1 + k)^2/7 G in the region in Kim et al's observations which is well outside of the cluster core. (k is the ratio of CR proton to electron energies, usually estimated at between 10 and 100.)

Figure 13. Radio image showing 326MHz emission along in intergalactic `bridge', which appears to connect the Coma cluster of galaxies [Coma C) with the Coma A complex of radio emission (source: Kim et al 1989).