Weak background sources could also lead to small fluctuations. Generally, the number of cells must be large enough to reduce the noise below this level, so that an upper limit may be set on the field scale size. The observed fluctuations will be the cell to cell fluctuations reduced by averaging over the number of cells in the beam, both along the line of sight and in the plane of the sky. The intrinsic fluctuation level for a spectral index of unity is 1.1, so that for a depth of 640 kpc, the field scale size must be less than 16 kpc. This simple minded estimate agrees with that obtained by taking the modelled emission in a box smoothed to the required resolution, and is shown in Fig.
Error bars are the fluctuation levels calculated from the simulated halos.
The long dashed line shows the upper limit on the contrast in the Coma radio halo, leading to an upper limit on the field scale size. A second method is to calculate the fluctuations in my models with the same profile as the Coma radio halo, in the same way as for the observational data. I show, in Fig. 4, the fractional fluctuations of the simulations as a function of the scale size. Again, the scale length of the field must be less than about 15 kpc. This conclusion is also obtained by comparing the simulations presented in this paper with the map of Kim et al.