Lunar Radio Temperatures
Joachim Köppen DF3GJ ... Kiel, Dec 2020
This tool shows the radio brightness temperatures at various microwave frequencies, computed with a simple model for the thermal behaviour of lunar soil, heated by the solar radiation during an entire month (as in DUBUS 2/2020, p.74). It also displays some observed data. [Collected references to the literature are at the very bottom of this page.]
The lunar soil at a patch in the the middle of the lunar disk is modelled as a
column of material whose physical properties do not change with depth below the
surface: the density is ρ = 3.33 g/cm³
(mean value of entire Moon), specific heat c = 840 Ws/kgK (basalt rock),
and thermal conductivity of K = 0.003 W/mK (basalt powder), hence
γ = 1/√Kρc
= 456 in cgs units. Dielectric constant ε = 1.5 (basalt powder)
and electric loss tan δ = 0.0143 (basalt powder)
The surface is illuminated by the Sun, whose elevation varies during one month.
The incident power (solar constant 1.3 kW/m²) is transported to deeper layers
by thermal conduction. At the phase of First Quarter, the Sun rises above this patch.
Full Moon is 7.375 days later. According to its temperature, each soil layer emits
thermal radiation, part of which emerges from the surface due to the transparency
of the material, specified by its loss tangent.
The red curve refers to this surface patch at the centre of the lunar disc, the blue curve is the (approximated) average over the entire face of the Moon.
This rather primitive model is not intended to provide an exact model for the lunar surface. The parameters were not tuned to attempt to match any observed radio data. Its principal role is to demonstrate that already a basic model is able to provide satisfactory explanations of the phase-varying temperatures at various frequencies. Therefore it gives physically consistent and quite reliable predictions for lunar radio fluxes.
The controls of this script are the choice of the frequency, text fields to enter the plotting limits for the temperatures, radio buttons to switch on/off the display of available measured data, and a button to output the model numerical data of the current frequency as a table just below this button, from where it can be copied with the mouse and pasted into a text editor for further use. The mouse position indicates the plot values at the current place of the mouse.
The choice for the frequency also contains the option to interpolate the data to any frequency supplied by the user. A yellow frequency field indicates that the value is outside the range of validity for this model.
One may also try to make a Fitcurve with the function T(phase) = M + A * cos(phase-P) which is shown in magenta. This rather simple function captures the essential monthly variation, which may often suffice for an application. Enter the parameters and hit the Enter key.
Observed data are from various studies of the monthly variation of lunar surface temperature as well as from single measurements (References below the plot). For each study we list the wavelength or frequency and the width of the antenna beam. Red symbols are for small regions on the lunar disc, blue symbols refer to measurements of the whole lunar disc. Dotted curves are authors' fits of their data.
Some of the original observation papers are not very easily accessible, being hidden in some reports. Here are a few papers which list a number of other observations: