The heat flow of the Moon: influence of long term orbital signals

In the past decades, numerous efforts have been made to estimate planetary heat flows [1]. Planetary cooling is what drives the evolution of a planet, and the measured heat flow constrains models of both thermal evolution and planetary bulk composition. As part of the Apollo program, heat flow experiments were carried out during Apollo 15 and 17 missions. These experiments measured both surface and subsurface temperatures, and analysis of the 4 years of data provided estimates of the near surface temperature gradient, thermal diffusivity, thermal conductivity and heat flow [2]. A striking result was the large difference in measures between the two experiments: 21 and 16 mWm−2 at Apollo 15 and 17 landing site, respectively. This variation has been explained by differences in radioactive elements abundance between the two regions. Unfortunately, both landing sites are on the edge of an anomalous thorium-rich geochemical province, the Procellarum KREEP terrane, and this has made estimation of the Moon’s global heat flow difficult [3]. Langseth and coworkers analyzed the heat flow experiment data in two steps [2]. First, the thermal diffusivity was calculated from the attenuation of the annual thermal wave’s amplitude with depth. Density and thermal capacity from returned samples were then used to deduce the thermal conductivity. The annual signal, due to the eccentricity of the Earth’s orbit about the Sun, and the daily thermal waves were then subtracted from the temperature profile to estimate the mean temperature gradient, and the heat flow was finally calculated by multiplying the mean thermal gradient and thermal conductivity. As an example, it can be seen from Figure 1 that the Apollo time series appear to possess a modulation of the annual signal that was not considered in the original analysis. As shown below, this is likely a result of the 18.6 years precession of the lunar nodes which has previously been neglected. A long-term temperature increase is also observed in the data that is still not well understood. Here we deal with the question of whether or not this long term increase could be a result of the 18.6 year precessional signal. Furthermore, whether the modulation of the annual signal seen in Figure 1 affects the estimation of the thermal diffusivity or not will be investigated. To do so, we use a thermal model of the lunar regolith that takes into account both thermal conduction and the radiative transport of energy [4]. Figure 1: Apollo 15 surface temperature evolution during the complete span of the mission. Plotted are the maximum temperatures encountered during each lunation as inferred from the thermocouples suspended about the lunar surface. We can see an increase of 2K in the amplitude of the annual thermal wave during this three years period.