2.5. Radio trails
Radio trails are associated with clusters of galaxies from which X-ray emission is often observed. The most probable explanation of this emission is that it is bremsstrahlung from a hot, comparatively dense thermal plasma with ne 10-3 cm-3, T 108 K exerting a fairly large pressure. Furthermore, the random (with respect to the Hubble flow) velocities of cluster galaxies are much larger than those of field galaxies. These two facts support the natural interpretation of the radio morphology of a trail as an ordinary low-power double source whose radio-emitting regions have been swept backwards by the surrounding medium. In a sense, radio trails represent a series of experiments that have been carried out on double sources, and so may prove to be especially useful in explaining them.
The beam interpretations of radio trails is straightforward. If the channel is exposed to a transverse momentum flux, the beam will be bent, perhaps through a combination of weak oblique shocks and rarefaction waves. If the motion of the galaxy with respect to the surrounding medium is supersonic, then there will be a cylindrical bow shock in front of each channel. The flow downstream will be fairly complex and, at least in some circumstances, turbulent. Conditions are then ideal for particle acceleration and field amplification close to the galaxy. We expect that the particles will subsequently cool by synchrotron radiation and by inverse Compton scattering of the microwave background. Steepening of the radio spectrum at the ends of the trails, consistent with an equipartition field strength of a few microgauss, is what is generally observed. It is possible to estimate the momentum discharge, , in the beam from the force, (~ ext V2gallW), due to the intergalactic medium, of density ext, relative velocity Vgal, striking the beam of length l and width W. The energy discharge can be estimated from the rate of increase of internal energy in the beam (~ 3/2PextAVgal) where Pext is the external thermal pressure, and A, the cross-sectional area of the trails. The mass discharge can be estimated on the basis of Faraday rotation studies. It is comforting that within the (large) uncertainties of these determinations  the power 1043 erg s-1, force 1035 dyne and mass loss ~ 1 M yr-1 approximately satisfy 2 2 (l and W are estimated from the dimensions of the radio contours). With these numbers, the velocity in the beam (~ / ) is ~ 10,000 km s-1, and the Mach number (~ (l / w)1/2) has the fairly modest value ~ 3. In particular, the beams are unlikely to be relativistic. It may be possible to perform informative gas dynamical experiments to improve these simple arguments. In particular it would be interesting to determine under what conditions the flow downstream contained a large shear, parallel to Vg, as this is probably necessary if large degrees of linear polarisation are to be achieved at the ends of the trail.
The plasmoid model of radio trails was first considered by Jaffe and Perola  who calculated the deceleration and subsequent motion experienced by pairs of gas clouds shot out into the surrounding medium. This yields the shape of the tail and, with further assumptions (e.g., that the internal energy of the cloud is predominantly in the form of relativistic electrons and magnetic fields), the variation of surface brightness and spectral index along it. The fit to the observations of 3C 129 is reasonably good, yielding plasmoid masses and velocities ~ 107 M and ~ 2000 km s-1 respectively. However the radio emission falls off less rapidly along the tail than is predicted by Jaffe and Perola's model, and so Cowie and McKee  have modified it to include the effects of thermal pressure. If the galaxy has a substantial mass loss rate, then there will be a stand-off bow shock and the plasmoid itself will not feel the full force of the intergalactic medium until it has moved some distance (~ 20 kpc). Both of these modifications can give an improved fit to the data. There is also the possibility of particle acceleration within the tail; and Pacholczyk and Scott  have identified those regions where the polarisation is comparatively low with high levels of particle-accelerating magnetic turbulence, thus accounting for the apparent association of high brightness with low polarisation and vice versa.
Observational support for in situ acceleration within the trails is provided by observations  of IC 711 which show that the time required for the galaxy to produce the observed trail, whose spectrum actually flattens at the end, exceeds by an order of magnitude the estimated cooling time.
Jaffe and Perola  also proposed an alternative model drawing an analogy with the interaction of the solar wind with the Earth's magnetosphere. They suggested that clouds of relativistic particles accelerated within the nucleus stream outwards along the polar field lines of a galactic dipole, transverse to its velocity vector. Close to the nucleus the clouds are protected, but further out the field lines will be swept backwards to form a long magnetospheric tail. This field, varying as r-3 , will be quite large within the nuclear regions and it seems difficult to avoid large radiative and adiabatic losses. Furthermore a substantial nuclear mass is called for to provide an "anchor".
There is in fact no need for any energy to be supplied by the galactic nucleus. The total power dissipated across a bow shock by the galaxy travelling through the intergalactic medium can be up to ~ 1044 erg s-1 and only 1 per cent of this (a comparable efficiency to galactic supernova remnants) need be dissipated in the form of relativistic electrons and magnetic fields to account for the radio emission. Gisler [2l] proposes that radio trails are simply radio emitting regions associated with a bow shock seen in projection. This explanation encounters some difficulty in explaining the maps of 3C 129 and 3C 83.18 because the radio features do not appear to "stand off" from the nucleus of the galaxy, and also because the contrast between high and low brightness regions may be too large to be explicable in terms of projection without postulating large departures from axisymmetry. However this remains a viable explanation for sources that are less well resolved.