The thermal emission from atmosphereless bodies, such as the Moon, Mercury, or the asteroids, is strongly affected by the roughness and porosity of their surfaces. On a rough surface effects due to multiple scattering, shadows, and mutual heating are important. The solar radiation can penetrate and heat the porous surface material to some depth, and in addition to conduction, heat is transferred by radiation. The lack of convective heat transfer within a dense atmosphere, and the very low thermal conductivity of the surface material, results in large temperature variations on rather small scales. Thus the emission is not that of a smooth flat surface, but rather the weighted sum of black body radiators at different temperatures.
The beaming is considered in the model by taking into account the effects of multiple scattered solar and thermal radiation due to the small scale surface roughness. The roughness is described by using either a Gaussian random surface, or a surface covered by hemispherical craters. In both cases the roughness is controlled by the the r.m.s. of the surface slopes.
Model thermal spectra in the range 6 to 20 micron were computed for (3) Juno. The surface is covered to 100% by spherical segment craters, and the r.m.s. of the surface slopes is controlled by the depth to diameter ratio. The diagram shows the ratio between the model fluxes, and the spectrum assuming no surface roughness.
By assuming a r.m.s. of the slopes equal to 1.0, the diagram shows the spectral flux ratio, as a function of the fraction crater coverage f.
Johan Lagerros