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IV. LUNAR SUBSURFACE TEMPERATURES Kozyrev attributed his gas cloud to lunar vulcanism. In an effort to provide an alternative explanation, Fremlin (1959a) made a proposal which we now discuss. It should be emphasized that Fremlin's argument in no way depends on the validity of Kozyrev's reported observations. Portions of the Moon's surface are considered to be com- posed of dust particles in close physical contact. Because of the increase of hydrostatic pressure with depth, particle contact and hence the effective thermal conductivity also increase with depth, the derived relation for simple geometry being ke = 7 x 10"7 h1/2, (13) where ke is the effective conductivity in cal cm"* sec" C°" , and h is the depth in cm. Radioactive heat, released in the lunar in- terior, will tend to be localized at the depths of greatest thermal conductivity. The increase of temperature with depth from this cause is given by AT/Ah « J/ke, (14) where J is the heat flux due to radioactive decay in cal cm"2 sec"1. With a flux of 8.4 x 10"" cal cm"2 sec"1, Fremlin derived a temp- eration of about 750°C at a depth of 10 meters. He postulated that at some depth the temperature becomes so high that phase changes occur in the dust, volatiles being released as gases; with the re- mainder of the dust at this critical level melting and cooling. After- wards the particulate nature of the level has been destroyed, and the heat localization effect is operative henceforth only above this level. Jaeger (1959) has criticized the numerical values of conducti- vity and flux adopted by Fremlin. The high value assumed by Fremlin for the heat flux would prevent the Moon from having the tensile strength required to maintain its nonequilibrium figure, and this part of Jaeger's criticism is undeniably valid. But Fremlin (1959b) has adequately answered Jaeger's criticism of the adopted value for ke; a surface composed of both dust layers of low 22
conductivity and relatively bare rock of higher conductivity is in no conflict with microwave and eclipse observations. Taking a terrestrial value for the radioactive heat flux of J = 1. 2 x 10"" cal cm"2 sec"1âa factor of seven smaller than Fremlin's value â we find from equations (13) and (14). AT = 1.7 h1/2 C°, so that at a depth of ten meters the excess temperature is 54 C°. With J = 2. 3 x 10"' cal cm"2 sec"*, a value characteristic of chondritic meteorites, AT z 0. 33 h1/2 C°, so that at a depth of ten meters the excess temperature is 10 C°. From microwave observations it is known that the temperatures less than half a meter below the surface vary between 0° and - 70°C during a lunar day and night (Piddington and Minnett, 1949). The temperature variation is damped with depth, and at about ten meters-should be no more than a few C°. We conclude that time- constant biologically-optimum temperatures exist a few tens of meters under those areas of the Moon composed of congealed dust particles. 23
