Parameter dependence

From Fig. 1, we see that the result is indeed insensitive to the precise choice of . Furthermore, most of the magnetic energy comes from sources with luminosities L~, or a little fainter. These are all luminous, well studied sources. We are not integrating over a poorly determined part of the luminosity function, so that the result we get is reliable. If the luminosity function declines at low luminosities, it will make no difference to the result. It is always possible that there is a new population of fainter sources that might make a contribution, but this will only increase the derived energy density. (In fact, we know this to be the case - the spiral galaxy population has been neglected in this paper.)

From Fig. 2, we see that as long as the upper redshift limit exceeds about 3, the result is again insensitive to the precise value chosen. Most of the magnetic energy is accumulated in the redshift interval 1--3, which is not surprising as the space density of radio sources peaks in this redshift range. In particular, most of the magnetic energy had been accumulated by redshift unity, so that high redshift clusters should already contain strong fields.

There is evidence to suggest that this is indeed the case: the powerful sources used in studies of the depolarization asymmetry (Laing 1988; Garrington et al. 1988; Garrington, Conway & Leahy 1991; Tribble 1992) are surrounded by strongly magnetized haloes at z~1--2. Work by Welter, Perry & Kronberg (1984) and Perry, Watson & Kronberg (1993) on the integrated Rotation Measures of high redshift quasars led to the conclusion that there are widespread and significant magnetic fields in objects at z~0.5--2.

At even higher redshifts, Carilli, Owen & Harris (1994) show that the radio galaxies 0902+343 and 4C41.17, at redshift 3.4 and 3.8 respectively, are embedded in strongly magnetized Faraday screens. This is not in conflict with Fig. 2, as sources at these high redshifts will be located at the highest peaks in the density fluctuation field, which are highly clustered (Bardeen et al. 1986), so that they will be in cluster environments that will be made up of previous generations of structure that could have been magnetized by earlier radio sources. The magnetic energy generated at very early times will be localized to the most overdense, most quickly evolving regions, which are just those places where we expect the observed sources to be found.

• On to section 5.2