Comparison of images for different models

At low frequencies no ageing has taken place, so there are no differences between the models. The differences in the high frequency images are due to differential ageing of the points in the emitting region. Although this was described for the individual models, I cover it again here for all the models together.

If inverse Compton losses dominate, or if diffusion is efficient so that the current local field is not the dominant contributor to an electron's total energy losses, then the break energy and electron energy spectrum are the same everywhere. Because the magnetic field varies, the break frequency, proportional to the field strength, varies from place to place. In this case the ageing appears most rapid in the low field regions because they have the lowest break frequencies.

As the importance of local losses increases, spatial variations in the break energy and energy spectrum become more pronounced. Electrons in the stronger field regions have above average losses and the break energy is correspondingly reduced. There are now two competing effects. For a given break energy, increasing the field strength increases the break frequency. This is the same in all the models. But as the importance of local losses increases (as the inverse Compton and diffusive effects decrease), the break energy is lower in the stronger field regions. For very strong fields, corresponding to weak inverse Compton losses or little diffusion, the spatial variations in the break energy are dominant. At the other extreme, the spatial variations in break energy are unimportant. There is an intermediate regime, where the spatial variations in break frequency is minimized.

The histograms of pixel intensity (Figures 2, 4, & 6) at high frequency differ substantially between the models. In the low field, high diffusion model a long tail containing a few bright points appears. These are the last few points that have not yet aged. The histograms at high frequency for the other two cases appear rather similar - in both cases a tail of bright points is just starting to appear. There are differences, however. In the intermediate case there is little intrinsic difference in intensity, as the break frequency is reasonably independent of local conditions. These small differences are then exaggerated by the steep spectral index in this model. For the high field, low diffusion model the spectral index at high frequencies is much flatter and the evolution of the intensity histogram is driven by the strong dependence of break frequency on local conditions.

While there is not a great deal of difference between the high-frequency images for the intermediate- and high-field strength cases, the ageing will be much easier to observe in the high field strength case. This is because the shape of the spectrum (as discussed in the next section) is different - the overall intensity of the intermediate field strength image falls much more rapidly, so that sources with >> will be very faint and almost undetectable, while the high field, low diffusion sources will be much easier to observe. In addition, is much lower in the high field case, so that at a fixed time the frequency will be higher relative to the break than in the other models. The combination of these effects means that the high frequency behaviour of the high field models is most relevant to observations.

Peter Tribble,