  The excess emission seen in spectral energy distributions (SEDs) is commonly
used to infer the properties of the emitting circumstellar dust in
protoplanetary and debris discs. Most notably, dust size distributions and
details of the collision physics are derived from SED slopes at long
wavelengths. This paper reviews the approximations that are commonly used and
contrasts them with numerical results for the thermal emission. The inferred
size distribution indexes are shown to be greater and more sensitive to the
observed sub(mm) spectral indexes than previously considered. This effect
results from aspects of the transition from small grains with volumetric
absorption to bigger grains that absorb and emit near to their surface,
controlled by both the real and the imaginary part of the refractive index. The
steeper size distributions indicate stronger size-dependence of material
strengths or impact velocities or, otherwise, less efficient transport or
erosion processes. Strong uncertainties remain because of insufficient
knowledge of the material composition, porosity, and optical properties at long
wavelengths.
