I therefore take a simple model in which a constant magnetic field is simply compressed while being flux frozen. I also take the high energy particle density to be constant, assuming diffusion to be efficient. 1 shows the synchrotron profiles for three values of the spectral index.
Steeper spectra give smaller halos, as the dependence of emissivity on field strength is stronger.
The resulting profiles, especially if a realistic spectral index is chosen, look very similar to the radial profile of the Perseus cluster given by Burns et al. In the case of the Perseus cluster, Burns et al. Note, however, that a realistic spectral index will also improve the fit of the models of Burns et al. to the data.