Conclusions

The structure of radio synchrotron emission from a volume containing a random magnetic field can change radically as the relativistic electron population ages. The changes are smallest when instantaneous and average losses are similar in magnitude, as when synchrotron and inverse Compton losses are equally important or when diffusion allows some motion of electrons between regions of differing field strengths. When the energy losses are independent of position, as when inverse Compton losses are dominant or diffusion is efficient, ageing substantially increases the contrast between the light and dark areas of the image. When local losses are dominant, so that inverse Compton losses are small or diffusion is not efficient, bright points at low frequencies fade most rapidly to leave holes in the image at high frequencies.

The image changes will be most apparent in high field sources. There are two reasons for this, in addition to the obvious fact that these sources tend to be more luminous. First, the break frequency is lowest in these sources so that observations are at a higher frequency relative to the break. Second, the shape of the integrated spectrum means that the overall luminosity of the high field, low diffusion model falls much more slowly at frequencies above the break than in the intermediate and low field models, which will have faded very substantially at any frequency more than a few times the break frequency.

As the source ages, the polarization from points in the image tends to increase, although this increase is not always simple and monotonic. The increase in polarization is relatively small for the intermediate field case, but the fractional polarization climbs almost to unity for weak and strong fields. The polarization angle changes with frequency, the angle deviating more from the initial (low frequency) position angle with increasing frequency. For the high field case, the polarization position angle rapidly becomes totally uncorrelated with its initial value. In reality, the magnetic field configuration in powerful radio sources is probably highly sheared (Laing 1980) so that the polarization angle is determined by the shear and does not vary with frequency. We would still expect to see variations in polarization angle with frequency in weaker sources and cluster radio haloes where a random magnetic field would be a better description of the field structure.

Spectral ageing naturally and inevitably increases the intensity contrast in radio images. Spectrally aged radio images generally show high emission peaks on a faint background. The discussion of this paper has nowhere considered the shape of the filaments, which is related to the structure of the field, but it has shown that high contrast emission does not necessarily have to involve instabilities in the radiating plasma. If filaments are the result of spectral ageing they will be ubiquitous, arise on the ageing timescale, and the bright regions will have flatter spectra than their surroundings at high frequencies.

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Peter Tribble, peter.tribble@gmail.com