The magnetic energy content of radio sources

A powerful radio source contains an enormous amount of magnetic energy and flux. For the purposes of this paper a radio source is a volume containing relativistic particles and magnetic fields. I am primarily concerned with the radio lobes. The particles lose energy by radiation and fade quickly, while the magnetic field decays on a substantially longer timescale. There is then a volume V containing strong magnetic fields that gets mixed with the gas surrounding the source. If the source has original dimension D_0 (where V = D_0^3) and initial field strength B_0, then if we conserve magnetic flux and have a final field strength B then we can fill a volume of side D = D_0 (B_0/B)^1/2.

It is probably more valid to conserve energy than magnetic flux, as the source achieves rough pressure equilibrium with its surroundings and evolves at roughly constant pressure thereafter. Radio sources are confined by an external medium that prevents them from expanding and suffering catastrophic adiabatic expansion losses (Gull & Northover 1973; Longair, Ryle & Scheuer 1973). The pressure in the source is similar to that in the external medium (Arnaud et al. 1984), so that the magnetic energy does not expand into free space to fill the volume of the cluster but must rather be mixed into the medium. We can then fill a volume of size D where

B_0^2 D_0^3 = B^2D^3 --> D = D_0(B_0/B)^2/3. (1)

More details of how the magnetic energy contained in the lobes is distributed into the intracluster medium are discussed in Section 6.

As a very rough calculation, we can consider a ``typical'' high redshift radio source (Daly 1992), with a 35microGauss field in a cylindrical volume of length 150 kpc and radius 15 kpc. Assuming conservation of magnetic flux, this can give a 1microGauss field over a cube 280 kpc on a side. There is sufficient magnetic energy to give a 1microGauss field over a volume a little over 500 kpc on a side. To put this another way, this is an energy of 1.5x10^52 J which is a fairly typical energy for a luminous radio source.

For a specific example, consider the radio galaxy Cygnus A. Although very luminous for a nearby source, Cygnus A may not be atypical of high redshift radio sources. The two lobes of Cygnus A are about 30 kpc across and contain a field (from equipartition arguments) of about 50microGauss. The magnetic energy in these lobes is equivalent to a 1microGauss field in a volume 500 kpc on a side. The point is clear - a single radio source can contain sufficient magnetic energy to magnetize the entire core of a galaxy cluster.

These large energy contents are not restricted to the ultra-luminous sources. More extended lower luminosity sources can contain as much energy as Cygnus A, because although more diffuse they are substantially larger. For example, the radio galaxy 3C234 (Alexander 1987) has a field strength (from minimum energy arguments) of between 5 and 10microGauss, in a cylinder almost 500 kpc long and about 40 kpc in diameter. This gives enough energy to fill a volume of between 250 and 400 kpc on a side with a 1microGauss field, depending on which end of the range of minimum energy fields is taken.

Similar calculations can be performed for other radio sources, leading to similar results. During the lifetime of a cluster, it will have contained several radio sources, not all as luminous as the powerful high redshift radio quasars. We must now integrate over all the sources a cluster and its predecessors has contained throughout its history.

Peter Tribble,