

Paper: 
Theoretical Modeling of Radiative Transfer in Planetary Regoliths 
Volume: 
196, Thermal Emission Spectroscopy and Analysis of Dust, Disks, and Regoliths 
Page: 
213 
Authors: 
Hapke, Bruce; Hale, Amy Snyder 
Abstract: 
The status of theories of thermal emission from particulate media, such as planetary regoliths, is discussed. When the particles are large compared with the wavelength, models based on the radiative transfer equation (RTE), which assumes that the particles scatter independently, appear adequate. Geometric optics can be used to calculate the optical properties of the particles, because diffraction by individual particles is effectively nonexistent. The emissivities of individual particles can display spectral features with high contrast. However, multiple scattering greatly reduces the contrast, decreasing the usefulness of the thermal IR for remote compositional identification. The maximum in the spectral emissivity does not occur exactly at the Christiansen frequency, where the real refractive index equals unity, but at a nearby frequency in a reststrahlen band where the dominant particle scattering process is changing from volume scattering to surface scattering. Thus, the emissivity maximum should more properly be refered to as the Christiansen ``feature'' rather than ``frequency''. In order to calculate the spectral emissivity and subsurface temperature distribution, the RTE for visible and thermal radiation must be solved simultaneously with the heat transfer equation. Such solutions intrinsically include the radiative conductivity and the solid state greenhouse effect. Examples of steady state and timedependent solutions are given. The status of thermal emission models is much less satisfactory when the particle size is comparable to or smaller than the wavelength. The use of the RTE is questionable then because this equation intrinsically assumes that the particles scatter independently, but coherent effects between the particles do not allow them to be independent scatterers. Unfortunately, this is the size range that occurs in most situations involving thermal emission from planetary regoliths. 



