Lunar Radio Images and Drift Scans
Joachim Köppen Kiel Sep 2022

Some brief explanations

This tool shows the distribution of radio brightness temperature on the face of the Moon for any lunar phase and frequency. It also displays the results of a drift scan across the centre of the Moon's disc, using an antenna with specified HPBW. These data are computed with the simple model for the heat transfer in the lunar soil.

In brief: The lunar soil is heated by the solar radiation. This heats up the top layer of a few mm thickness. Since the soil is not a solid rock, but consists of a loose mixture of dust, sand, and small pieces of rock (called 'regolith') due to the break up of the material by the constant impacts of meteroites, there is very little thermal contact between individual pieces. Hence the thermal conductivity of this material is very low, and the transport of heat from the top layer to the layers below is very slow. Thus, while the top layer can follow the solar illumination rather quickly and with a large temperature variation, the temperature of the deeper layers not only lags behind the top layers by a couple of days but also varies much less strongly.

The thermal radio emission comes mainly from a depth comparable with the wavelength. At a frequency of 1000 GHz (wavelength 0.3 mm) we see the hot top layer when under full sunshine and very cool at 'local night', but at 1 GHz (30 cm) the radio waves reach deep enough to let us observe a nearly constant temperature.

Since the Moon's face is illuminated after New Moon first on the western limb, then at the central face, and finally on the eastern limb, the region of high temperature moves across the Moon's face from West to East. At 1000 GHz the Moon looks very similar as in the optical, but at lower frequencies the delay in the heat-up makes the 'radio full moon' come later.

Technical detail: The variation of the vertical temperature profile was computed during an entire lunation for a number of lunar latitudes. From these profiles the radio brightess temperature for any frequency is computed with the assumption tanδ = 0.0143. For any pixel of the Moon's face the brightness temperature is computed from its latitude and the phase corresponding to its longitude. The darkening of the limb is due to the inclination-dependent reflection coefficient for the smooth surface between the soil (ε = 1.5) and vacuum (ε = 1).

Lunar drift scans: The scan direction angle is the angle between the scan direction and the lunar equator. This direction is indicated by a straight white line across the centre. Note that the curve is shown in the same orientation as the image. Hence in the plot the time would run from right to left. There are several options to show the data, either in terms of linear powers or in deciBel, relative to the peak value (as if you had observed the Moon from outer space) or to the background noise from the sky and the receiving system. In the latter case, you may well compare the shape of the curve with your data, by adjusting Tsys+Tsky to match the peak in your scan ... but do not try to interpret the resulting temperature as some reliable result -- this would require a proper analysis!!!

Please be aware that the drift scan curve will break into strange waves if the antenna HPBW is smaller than the pixel size. This is indicated by a yellow background in the HPBW field. Should this occur, increase the number of pixels.

The apparent width of the lunar rim depends on the beam width of the telescope, and thus its measurement can be used to determine the HPBW, even though the Moon no longer represents a point source: We measure the rim width by measuring in the drift scan the angle between a low point (say at rim level 0.15 of the maximum value) and a high point (at 0.85 of maximum). This tool allows to predict the relation between the rim width and the antenna's HPBW. For example, with level = 0.15 HPBW and rim width are nearly equal.
Hint: This tool can also be used to model the Sun above 10 GHz, by entering a frequency of 1 GHz, where the Moon also has the same top-hat brightness profile.

Hit the Enter key after changing the value in one of the input fields, to show the new image. But don't expect useful output if you enter computationally extreme or unreasonable values.

The data can be shown as a false colour image (the colour bar at right codes the temperature between minimum (black/violet) and maximum values (red)) or as a contour plot (with the user-chosen values).

Temperature in beam: gives the value when a gaussian antenna beam or the beam of an evenly illuminated circular dish (with specified HPBW) is placed at the face centre.

Please be aware that the model data displayed in LunarTemps are not exactly the same as in this tool. This is because some computational economies had to be taken in the interest of a faster display.