The aged synchrotron spectra from electrons in a strong random magnetic field are flatter than the spectrum from the Jaffe-Perola model, and are similar to the Kardashev-Pacholczyk model spectrum. This agrees well with the recent observations of Cygnus A by Carilli et al. (1991), and explains why the observed spectra are well fit by the KP model, even though the JP model is more physically plausible.

Neglecting losses due to inverse Compton scattering, two physically distinct models can be distinguished. If the electron positions are localized then the break energy and frequency depend only on the local field strength. The resultant spectra are qualitatively similar to that of the Kardashev-Pacholczyk model, independent of whether pitch angle scattering is effective. In particular, the sharp break characteristic of the Jaffe-Perola model does not occur. Failure to observe an exponential fall off of the spectrum at high frequencies does not rule out the existence of pitch angle scattering.

The second class of models allows for electrons to move between regions of different field strength. Without pitch angle scattering, the pitch angle of an electron changes so as to keep the magnetic flux linked by the orbit constant. Such models give Kardashev-Pacholczyk type spectra but age somewhat more slowly. Strong pitch angle scattering tends to prevent diffusion between regions of different field strength, so I have considered models where the energy losses are due to some combination of the global rms field and the instantaneous local field In this case, a wide variety of spectra are possible, covering the entire range from the basic Kardashev-Pacholczyk model to the Jaffe-Perola model, depending on the diffusion efficiency.

Including inverse Compton losses gives models that are formally identical to the diffusion models. For sources in which the field is strong and the losses are dominated by synchrotron emission then the spectra should be close to the KP model. This is indeed seen in Cygnus A. For less powerful sources with weaker fields, and sources at high redshift where inverse Compton losses are greater, the spectral decline is much sharper. An interesting point is that the variation of spectral shape with field strength is not monotonic. The steepening is sharpest when synchrotron and inverse Compton losses are about equally important, as then the dependence of break frequency on field strength is weakest.

I have also considered spectral aging in sheared field configurations as suggested by Laing (1980) to explain the polarization properties of edge-brightened double sources. Again, spectra similar to those of the three dimensional models resulted.

In summary, realistic magnetic field configurations can give a spectrum without the sharp break of the JP model. The resultant spectra are very similar to the KP spectrum. The observation of such a spectrum does not imply that the electron pitch angles remain constant. I conclude that the JP model is probably correct, as would be expected, and that the sharp break in the JP model is smoothed out because there is a range of break frequency corresponding to the range of field strength. The sharp break should become more pronounced for sources with lower field strengths when inverse Compton losses are more important.

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Peter Tribble,