Brightness temperature vs. size (left column) and size vs. frequency (right column) relations for model atmospheres (see text) with different power-law slopes for the density profile (α, top), temperature profile (β, middle), and ionisation (γ, bottom). The two dashed lines indicate the range of the observed slopes of the size vs. frequency relation (η). Standard parameters are given in Table 3. We vary α from 5 (blue) to 9 (red) in steps of 0.5. We vary β from 0.3 (blue) to 1.5 (red) in steps of 0.2 and include the grey atmosphere model (dark blue). We vary γ from 2 (blue) to 12 (red) in steps of 1.