Template flux densities from a spherical dusty clump as a function of parameter m (see text).The curves are obtained for illustrative purposes from fiducial values of the input parameters: ν = 220 GHz, θ_o = R_o ∕d = 1′′, r_i = 0.01, T_o = 50 K, q = −0.4, p = −1.5. In each panel only one of these parameters is changed, as indicated in the panel itself. Dashed curves represent the approximate analytical solutions given by Eq. (9), while solid curves are obtained from the numerical model described in Sect. 2.2.