Latitude variation of the subsurface lunar temperature: Lunar Prospector thermal neutrons

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. E5, 5046, doi: /2001je001497, 2003 Latitude variation of the subsurface lunar temperature: Lunar Prospector thermal neutrons R. C. Little, 1 W. C. Feldman, 1 S. Maurice, 2 I. Genetay, 2 D. J. Lawrence, 1 S. L. Lawson, 1 O. Gasnault, 1 B. L. Barraclough, 1 R. C. Elphic, 1 T. H. Prettyman, 1 and A. B. Binder 3 Received 30 March 2001; revised 11 January 2002; accepted 19 August 2002; published 29 May [1] Planetary thermal neutron fluxes provide a sensitive proxy for mafic and feldspathic terranes and are also necessary for translating measured gamma-ray line strengths to elemental abundances. Both functions require a model for near-surface temperatures and a knowledge of the dependence of thermal neutron flux on temperature. We have explored this dependence for a representative sample of lunar soil compositions and surface temperatures using the Monte Carlo N-Particle Code (MCNP 2 )(MNCP is a trademark of the Regents of the University of California, Los Alamos National Laboratory). For all soil samples, the neutron density is found to be independent of temperature, in accord with neutron moderation theory. The thermal neutron flux, however, does vary with temperature in a way that depends on, the ratio of macroscopic absorption to energy-loss cross sections of soil compositions. The weakest dependence is for the largest (which corresponds to the Apollo 17 high-ti basalt in our soil selection), and the largest dependence is for the lowest (which corresponds to ferroan anorthosite, [FAN] in our selection). For the lunar model simulated, the depth at which the thermal neutron population is most sensitive to temperature is 30 g cm 2. These simulations were compared with the flux of thermal neutrons measured using the Lunar Prospector neutron spectrometer over the lunar highlands using a subsurface temperature profile that varies with latitude, l, as Cos 1/4 l. Model results assuming equatorial temperatures of 200 and 250 K are in reasonable agreement with measured data. This range of equatorial temperatures is not inconsistent with the average temperature measured below the diurnal thermal wave at the equator, T meas = 252 ± 3 K [Langseth and Keihm, 1977]. INDEX TERMS: 5410 Planetology: Solid Surface Planets: Composition; 5464 Planetology: Solid Surface Planets: Remote sensing; 6225 Planetology: Solar System Objects: Mars; 6250 Planetology: Solar System Objects: Moon (1221); 6297 Planetology: Solar System Objects: Instruments and techniques; KEYWORDS: Lunar Prospector, thermal and epithermal neutrons, subsurface lunar temperature, MCNP, lunar soil compositions Citation: Little, R. C., et al., Latitude variation of the subsurface lunar temperature: Lunar Prospector thermal neutrons, J. Geophys. Res., 108(E5), 5046, doi: /2001je001497, Introduction [2] The information content of thermal neutrons from planetary surfaces stems from several parameters that shape equilibrium neutron flux distributions. These parameters in turn, reflect three major processes that control the shapes of neutron energy distributions; 1) the neutron production rate by galactic cosmic rays, 2) their moderation to lower energy through primarily elastic energy-loss collisions, and 3) their absorption at thermal energies. The first process can be eliminated by construction of the ratio of thermal to epithermal neutron fluxes. This ratio is then determined by only one parameter, the ratio of the macroscopic absorption to energy-loss cross sections of surface soils. The variation of 1 Los Alamos National Laboratory, Los Alamos, New Mexico, USA. 2 Observatoire Midi-Pyrénées, Toulouse, France. 3 Lunar Research Institute, Tucson, Arizona, USA. Copyright 2003 by the American Geophysical Union /03/2001JE this parameter for a variety of soils found on planetary surfaces is large (amounting to more than two orders of magnitude). It thereby provides a sensitive discriminator between high-iron basaltic and low-iron feldspathic lithologies and also to the presence of minute amounts of hydrogen (having a detection threshold of about 20 ppm) [Feldman et al., 1991, 2000a, 2000b, 2001]. [3] Knowledge of thermal neutron distributions also has another important application. A well-developed technique to determine the composition of surface soils is to measure the intensity of gamma-ray lines stemming from the absorption of thermal neutrons [Reedy et al., 1973; Lawrence et al., 1998]. One example is the Fe(n,g) reaction that produces and 7.63 MeV gamma-ray lines, which are readily measurable. Translation of these line strengths to Fe abundance requires knowledge of the neutron number density. This quantity, in turn, can be determined from a measurement of the flux of thermal and epithermal neutrons that leak outward from planetary surface layers to space. Although measurement of these 12-1

2 12-2 LITTLE ET AL.: LATITUDE VARIATION OF SUBSURFACE LUNAR TEMPERATURE thermal neutron data can be modeled very well by a Cos 1/4 l temperature law. All results are summarized in section 5. Figure 1. Data used for neutron source distributions: (a) the energy spectrum and (b) the depth dependence of the source intensity (1 g cm 3 ). neutron fluxes for planetary exploration is straight forward using a variety of techniques [Feldman et al., 1991, 1998], the translation of these fluxes to useful information requires knowledge of the physical temperature of surface layers and a knowledge of its effect on the flux of escaping neutrons. [4] We address this last problem in the present study by simulating the equilibrium neutron flux distributions for a variety of depth-dependent temperature profiles and soil chemistries using the Monte Carlo N-Particle (MCNP) code developed at Los Alamos [Briesmeister, 1997]. The computational technique applied in our simulations is first presented in section 2. The parameter range of our simulations is also presented there. The results of the simulations and their analysis in terms of the relationship between thermal-neutron flux intensities and the depth distribution of temperatures for a representative sample of chemistries is given in section 3. In section 4, these results are compared with counting rates measured using the Lunar prospector neutron spectrometer, LPNS, over a large area stretching from the equator to the pole that is dominated by highland terrane. This terrane is generally anorthositic, approximated here by ferroan anorthosite (FAN). As will be shown, the LP 2. Simulations 2.1. Neutron Transport Simulations [5] Monte Carlo transport simulations were performed with Versions 4XU [Hendricks, 1999] and 4C [Hendricks, 2000] of MCNP. The neutron energy spectrum and depthdistribution used in the current study were obtained from previous calculations [Drake et al., 1988] and are plotted in Figures 1a and 1b. This spectrum and depth-distribution represent an intermediate result in the complete simulation of neutron flux spectra, in that the calculation only includes neutron production by galactic cosmic ray protons and their transport to energies below 10 MeV. Subsequent transport to develop an equilibrium spectrum and its depth distribution was carried out using MCNP. [6] Six lunar soil compositions were modeled: Apollo 11 (AP11), Apollo 12 (AP12), Apollo 17 (AP17), Luna 20, ferroan anorthosite (FAN), and Apollo 17 high-ti basalt (AP17HiTiBa). In each case we used nominal weight fractions of SiO 2,TiO 2,Al 2 O 3, FeO, MgO, CaO, Na 2 O, Mn, Sm, and Gd [Haskin and Warren, 1991]. In all cases, we used a soil density of 1 g cm 3. [7] Neutron cross sections were all based on ENDF/B-VI evaluations [Rose, 1991]. For all but isotopes of Sm and Gd, the MCNP cross sections were from the ENDF60 library [Hendricks et al., 1994]. MCNP cross sections for 7 isotopes of Sm and 7 isotopes of Gd were prepared specifically for this study. All cross sections were processed at room temperature. [8] Calculations for each soil composition were performed at four constant temperatures: 100, 200, 300, and 400 degrees Kelvin. Additional calculations were performed for a FAN composition at extra constant temperatures and using four depth-dependent temperature profiles. Two of the profiles used the two extreme members of the thermal wave at the lunar equator as modeled by Vasavada et al. [1999] (see their Figure 4a). The last two were linearly increasing and decreasing, respectively, temperature profiles that connected 400 K (100 K) at the surface to 100 K (400 K) at a depth of 100 g cm 2. Several profiles are summarized in Figure 2. [9] The temperature-dependence of cross sections in MCNP is handled by modifying the elastic scattering cross section using a free-gas model. Similarly, kinematics are modeled based on free-gas theory. Absorption cross sections are not modified, based on the assumption of an inverse dependence on neutron velocity (1/v). Although this approximation fails for isotopes with large resonances at low neutron energies, such as 149 Sm and 157 Gd, we did not believe it necessary to generate cross sections broadened to various temperatures. [10] Detailed neutron leakage spectra were calculated from to 10 4 MeV. All simulations used a minimum of 650,000 source neutrons. Typical running times were 4 hours on a Sun Ultra Detector Response Simulations [11] The detailed leakage spectra calculated by MCNP were used in combination with detector energy-response functions to arrive at total simulated thermal and epithermal counting rates.

3 LITTLE ET AL.: LATITUDE VARIATION OF SUBSURFACE LUNAR TEMPERATURE 12-3 Figure 2. A schematic drawing of eight of the depthdependent temperature models that were used to simulate surface neutron fluxes. The vertical line represents the depth at which the two linear models give fluxes that equal the depth-independent models. [12] The specific detectors considered were those comprising the Lunar Prospector (LP) neutron spectrometer (NS). Thermal and epithermal neutrons are measured from lunar orbit using two 3 He-filled gas proportional counters and associated electronics [Feldman et al., 1999]. One of the counters is covered with a 0.63-mm-thick sheet of Cd and used to determine the epithermal counts. The other detector is wrapped with Sn; the difference in counting rates from the two detectors yields the thermal counts. [13] The detector energy-response functions used in this study are from previous calculations [Feldman et al., 2000b] and are shown in Figure 3. Using these response functions with the calculated MCNP spectra allows us to arrive at simulated thermal and epithermal counting rates for each combination of soil composition and temperature distribution at the lunar surface. Monte Carlo statistical uncertainties in all simulations ranged between about 0.4% and 1.4%, depending on the assumed composition and the depth below the surface. [14] An additional step was included to compare the thermal neutron flux simulated for FAN at the lunar surface to the measured flux normalized to an altitude of 40 km. Liouville s theorem was used for this purpose using simulated neutron orbits that accounted for lunar gravity [Feldman et al., 1989]. The full energy-angle response function of the Lunar Prospector 3 He counters, simulated using MCNP, was then used to calculate counting rates in the reference frame of the Lunar Prospector spacecraft (see Feldman and Drake [1986] for details). 3. Results 3.1. Neutron Flux as a Function of Temperature [15] The energy distribution of the neutron flux at the lunar surface can be described by a single power law in the epithermal range, and a Maxwellian in the thermal range [Feldman et al., 2000b]. The relative amplitudes of each of the components depend on composition and temperature. [16] Of the six lunar soil compositions investigated, the FAN results showed the largest dependence on temperature (see Figure 4a). The reason for this is that FAN has minimal concentrations of highly absorbing materials. Therefore, the thermal neutrons are best able to equilibrate with the target nuclei at velocities (neutron energies) representative of the medium. [17] The least dependence of calculated neutron flux on temperature was observed for the Apollo 17 high-ti basalt case (see Figure 4b). This composition includes substantial amounts of Fe and Ti. The large absorption cross sections of these materials tend to offset the thermal neutron dependency on scattering kinematics, and hence on material temperature Thermal and Epithermal Counting Rates [18] As described in section 2, we convolved the MCNP calculated neutron leakage spectra with thermal and epithermal detector response functions to obtain thermal and epithermal counting rates for each model. A plot of the temperature-dependence of the resulting thermal neutron counting rates is shown in Figure 5a. Note again that the FAN results show the most dependence on temperature of the six lunar soils considered. The range of variation of thermal counts for FAN between T = 100 K and 400 K was about 25%. This range is far less than what might be expected for a pure thermal population having a constant density (100% because the flux of a thermal population is proportional to T 0.5 ). The reason for the reduced sensitivity of thermal counting rates to temperature is that the flux of epithermal neutrons fills in the energy range vacated by the thermal population as T decreases. [19] In Figure 5b, we plot the temperature-dependence of the epithermal neutron counting rates. Finally, the temper- Figure 3. Thermal and epithermal detector response functions used to convert calculated flux spectra to counting rates.

4 12-4 LITTLE ET AL.: LATITUDE VARIATION OF SUBSURFACE LUNAR TEMPERATURE Figure 4. Calculated neutron leakage spectra: (a) for FAN and (b) for Apollo 17 high-ti basalt. In both cases, results are shown for 100, 200, 300, and 400 degrees Kelvin. ature-dependence of the ratio of the thermal to epithermal count rates is shown in Figure 5c. [20] Delta () is a convenient parameter to describe neutronic properties of a material. We define it as the ratio of macroscopic absorption ( a ) to energy-loss cross sections (x s ), ¼ a =x s ; where x is the average energy lost by a neutron per collision. We have determined for each of the six lunar compositions modeled in this paper and they are given in Table 1. Using these values, and the results of Figure 5c, we Figure 5. Temperature-dependent counting rates for the compositions considered: (a) thermal counting rates, (b) epithermal counting rates, and (c) the ratio of thermal to epithermal counting rates.

5 LITTLE ET AL.: LATITUDE VARIATION OF SUBSURFACE LUNAR TEMPERATURE 12-5 Table 1. Macroscopic Cross Sections for Lunar Soils a Composition s x s a AP17 high-ti basalt AP AP AP LUN FAN a All cross sections are in units of cm 2 g 1. are able to develop a power law in temperature that describes the relationship between and the ratio of the thermal to epithermal neutron counts. It is given by ¼ AT=E ð Þ½Therm=Epi ð Þ ð1þ Š PT=E AT=E ð Þ ¼ 0:3896 T : ð2þ PT=E ð Þ ¼ 2:1785 T 0:11455 ð3þ These relations are shown in Figure 6. The goodness of the fits (R = for equation 2 and R = for equation 3) show that if the material temperature is known, and the thermal and epithermal counting rates are measured, then can be determined. [21] After is determined, it is possible to go two steps further to construct relationships that will allow a removal of the temperature bias of measured thermal neutrons from planetary surfaces to determine neutron number density. Using the present simulations, the relations to construct temperature-corrected thermal fluxes are ½Thermal FluxŠ ¼ RðThermÞ*AðTherm; ð Þ ð4þ ÞT P therm; AðTherm; Þ ¼ 0: :3597 ð5þ words, given a surface composition, measured neutron fluxes can be used to determine the spatial profile of nearsurface temperatures. The Moon is an excellent place to apply this technique. Large portions of its surface in the lunar highlands are feldspathic, which to a good approximation can be modeled as ferroan anorthosite (FAN) [Haskin and Warren, 1991; Feldman et al., 2000b]. Comparison of measured counting rates with those simulated for assumed temperature profiles can then be used to constrain the parameters of these profiles. This possibility is exploited in the next section to determine the latitude variation of the lunar temperature at a depth of about 20 cm (which is 30 g cm 2 for an assumed density of 1.5 g cm 3 ). [23] For our FAN composition, we performed additional constant temperature profile calculations at 25, 50, 150, 250, and 350 K. The low-energy portions of neutron flux spectra that were simulated for FAN depth-independent temperatures between 25 K and 400 K are shown in Figure 8a. We note that all energy profiles coalesce above about 1 ev to a dependence that is close to E 1, where E is the neutron energy. Below this energy, the thermal components diverge according to their temperature, T. Their shapes in the neighborhood of the peak flux are closely Maxwellian, characterized by hardened temperatures, T, that are close to, but larger than, T [see, e.g., Feldman et al., 2000a]. The hardened temperature is the energy at which the flux distribution peaks. Here kt varies between ev and about 0.05 ev, and k is Boltzmann s constant. [24] The portions of energy spectra between 0.3 and 3 ev are expanded in Figure 8b. Inspection shows a monotonic variation of spectra with increasing temperature, which is considerably less than that seen at lower energies in Figure 8a. Although small, we verified that this effect is real by inspecting the temperature-dependent cross sections of oxygen, which contributes about 46% by mass to average lunar compositions. PðTherm; Þ ¼ 0: :1353 ; ð6þ where R(Therm) is a factor that translates simulated thermal fluxes to measured counting rates. The relations that allow a determination of neutron number density are ½Density=CðHeSnÞŠ ¼ RN ð Þ*AðN; ÞT PN; ð Þ ð7þ AN; ð Þ ¼ 1 þ 1:391ðÞ 1:1147 ð8þ PN; ð Þ ¼ 0:041835ð þ 0:25Þ 1:8369 ; ð9þ where C(HeSn) is the counting rate measured using the tincovered 3 He gas proportional counter aboard Lunar Prospector. Figures 7a (R = 0.992) and 7b (R = 0.998) show how well equations 7 through 9 reproduce data calculated in this study Application to the Lunar Highlands [22] In the foregoing discussions, MCNP simulations were conducted for an assumed temperature profile for a variety of near-surface compositions. This procedure can be inverted if the composition of surface layers is known a priori. In other Figure 6. Power law constants relating delta (the ratio of macroscopic absorption to energy-loss cross sections) to the ratio of thermal to epithermal neutrons.

6 12-6 LITTLE ET AL.: LATITUDE VARIATION OF SUBSURFACE LUNAR TEMPERATURE In addition, inspection of Figure 5b shows that the temperature-dependence of the simulated epithermal neutron fluxes does not depend significantly on composition. Equation 11 can therefore be used to correct all measured fluxes of epithermal neutrons for latitude-varying, diurnallyaveraged temperatures. 4. Comparison With Lunar Prospector Thermal Neutron Data 4.1. Depth-Dependent Temperature Simulations [26] In order to apply these simulations to Lunar Prospector measurements, we need first to determine the depths Figure 7. Power law constants relating the neutron density to the sum of the thermal and epithermal counting rates (measured using the LP HeSn sensor). The power law index is shown in Figure 7a, and the power law amplitude is in Figure 7b. [25] Simulated counting rates for thermal and epithermal neutrons in FAN at a depth of 20 g cm 2 below the surface are shown in Figures 9a and 9b, respectively. The solid lines in each figure give the best fitting quadratic and linear functions, respectively, C therm ¼ 0:0314 þ 5: T 4: T 2 ; C epi ¼ 0:0270 þ 3: T; ð10þ ð11þ where C therm and C epi are proportional to the thermal and epithermal counting rates and T is the temperature in degrees Kelvin. Inspection shows that both fits are quite good (R = in Figure 9a and R = in Figure 9b). Figure 8. Neutron flux spectra simulated using MCNP for a FAN composition and temperatures ranging between 25 K and 400 K. The flux spectra between ev and 10 ev are given in Figure 8a, and an exploded version between 0.3 ev and 3 ev is given in Figure 8b. Only a small number of symbols for each plot that delineate the different temperature flux distributions are included to enhance clarity.

7 LITTLE ET AL.: LATITUDE VARIATION OF SUBSURFACE LUNAR TEMPERATURE K that were all independent of depth. These simulations were presented in section 3. The next two assumed a linear temperature profile that ranged between 100 (400) K at the surface and 400 (100) K at 100 g cm 2 below the surface. These profiles were illustrated in Figure 2. Counting rates simulated for the LP thermal detector at the surface for each of these six profiles are shown in Figure 10. The straight line in the figure gives the best fitting power law to the four constant temperature simulations (R = 0.998). This power law was inverted for the thermal counting rates simulated for the two linear temperature models, to give an effective temperature that characterized these two simulations. The two solid diamond symbols are positioned accordingly in Figure 10. They are seen to lie very close to the constant T = 200 K and 300 K locations for the linearly increasing and decreasing (with increasing depth) models, respectively. Both models cross over at the same physical depth, given by the vertical line in Figure 2. We conclude that the effective depth sampled by thermal neutrons measured above the surface is centered at about 30 g cm 2 below the surface. If we assume a soil density of 1.5 g cm 2,this depth corresponds to about 20 cm. [27] More realistically, the temperature of the lunar soil will be at its extreme (minimum or maximum) at the surface and will then vary with depth until reaching some constant value. To explore this effect, we performed two additional calculations with FAN wherein the temperature was varied to mimic the depth-dependence of the diurnal thermal wave Figure 9. Simulations of the thermal and epithermal counting rates at a depth of 20 g cm 2 below the surface using the LPNS for an assumed FAN composition and constant depth-dependent temperatures that range between 25 K and 400 K. The thermal rates are given in Figure 9a, and those for the epithermal rates are in Figure 9b. The solid lines are the best fitting quadratic and linear functions, respectively. below the lunar surface at which measurements of leakage neutrons above the surface are sensitive. Such a determination is critical because subsurface temperatures are known to vary strongly with depth near the surface [Langseth and Keihm, 1977]. Simulations have shown that most of this dependence occurs within the top two cm (which corresponds to 3 g cm 2 at a density of 1.5 g cm 3 ) of regolith [see, e.g., Vasavada et al., 1999, and references therein]. We used several simulations to determine the depth sensitivity. The first four assumed temperatures of 100, 200, 300, and Figure 10. Predicted thermal counting rates at the surface for the eight models schematically represented in Figure 2. The solid line is the best fitting power law to the four depthindependent models. The solid diamonds give the two linear, depth-dependent temperature profiles in Figure 2, and the solid squares give the thermal wave extremes simulated by Vasavada et al. [1999].

8 12-8 LITTLE ET AL.: LATITUDE VARIATION OF SUBSURFACE LUNAR TEMPERATURE Figure 11. A map of the thermal neutrons measured using the LPNS during the low-altitude portion of the LP mission. envelope using the calculation by Vasavada et al. [1999]. These profiles were also illustrated in Figure 2. The results are given in Figure 10 by the two solid square symbols. We note that both yield about the same flux at the surface. This result indicates that measurement of thermal neutrons from orbit sample the subsurface temperature below the thermal wave of subsurface soils (at least for thermal skin-depths similar to the Vasavada et al. calculation), in agreement with the conclusion reached from our linear depth-dependent temperature simulations Latitude Dependence of the Subsurface Lunar Temperature Profile [28] Lunar Prospector flew in a circular polar orbit and took data for over 18 months. During this time, as the moon rotated under the orbit, the LP neutron spectrometer sampled all times of day for each location. A map of LP thermalneutron counting rate data measured at low altitude (normalized to 40 km above the surface) is given in Figure 11. Here a 32 s counting interval was used, and the data were registered in equal-area surface elements corresponding to a square latitude-longitude box at the equator but smoothed to a 40 km diameter resolution element using a Gaussian smoothing procedure. Note that there is a large stretch of terrain on the far side (120 East longitude to 120 West longitude and the equator to the north pole) that has uniformly high thermal counting rates. This situation also holds on the front side of the Moon between 100 W and 80 E longitude from 60 S latitude to the south pole. An analysis of thermal and epithermal neutron data showed that most of this back-side highland terrain can indeed be modeled by a FAN composition [Feldman et al., 2000b]. It therefore qualifies for use in determining the latitude dependence of subsurface temperature by applying the simulations in section 3 to measured thermal neutron counting rates. Latitude averages of thermal counting rates are shown by the circle (northern latitudes) and square (southern latitudes) symbols in Figure 12. All latitude samples were averaged according to their absolute value (north and south latitudes were overlain) and the vertical lines give the standard deviations of counting rates within all longitudes in each latitude band. The apparent deviation near 30 degrees in the measured data from a Cos 1/4 l latitude-dependence results from the fact that we did not remove data from Mare Moscoviense. [29] The overlays in Figure 12 give two simulations of counting-rates in orbit at 40 km altitude for assumed temperature models. A Cos 1/4 l latitude-dependent temperature law was chosen for this purpose to conform to the latitude variation of local-noon surface temperatures measured using the Clementine LWIR experiment [Lawson et al., 2000]. Comparison of the two curves for T o = 200 and 250 K, respectively, with the data shows both the goodness of fit and the sensitivity of the procedure to variations in assumed equatorial temperature. The models were normalized to each other at the equator. The reasonable qualitative agreement between the measured data and the simulated count rates reinforces the validity of the results of our modeling of the temperature-dependent neutron behavior. 5. Summary and Conclusions [30] We have used MCNP to explore the temperaturedependence of galactic cosmic ray induced neutron leakage from several typical lunar soil compositions. As expected, the neutron number density at the surface is independent of temperature. However, the neutron flux at the surface is a function of temperature; the variation of thermal neutron flux with temperature depends inversely on the ratio of macroscopic absorption to energy-loss cross sections. The range of variation of thermal neutron flux for a FAN composition was found to be about 25% over the temperature range from 100 to 400 degrees Kelvin. The effective temperature derived from thermal neutrons measured at the surface corresponds to a depth of about 30 g cm 2, which is a physical depth of 20 cm for a density of 1.5 g/cm 3. This depth is below most of the thermal wave envelope on the Moon [see, e.g., Vasavada et al., 1999] so that thermal

9 LITTLE ET AL.: LATITUDE VARIATION OF SUBSURFACE LUNAR TEMPERATURE 12-9 [33] Acknowledgments. Work at Los Alamos was carried out under the auspices of the U.S. Department of Energy and financial support from NASA through Lunar Research Institute. Support for S. Maurice was provided by the Observatoire Pic Midi. Figure 12. Comparison of the latitude-dependent measurements of thermal fluxes above a broad band of highlands on the Moon with simulated counting rates using a Cos 1/4 l temperature model. neutron fluxes measured at orbit should not respond to diurnal variation of surface temperatures. This result is also confirmed by two of our depth-dependent temperature simulations that were designed to match the profiles modeled by Vasavada et al. [1999]. [31] Lunar Prospector thermal and epithermal neutron data were then compared with simulated flux variations expected for a model of subsurface lunar temperatures that vary with latitude as Cos 1/4 l. Awide band of longitudes centered in the highlands on both sides of the Moon from the equator to the poles, was used for this purpose. This choice was made to create a database that had a composition that was generally feldspathic (approximated here by FAN) but as independent of latitude as was possible. The fit of the model with measured thermal neutron counting rates is reasonable. [32] The average temperature at depths below the thermal wave was measured at both the Apollo 15 and Apollo 17 landing sites to be between 249 and 255 K [Langseth and Keihm, 1977]. The agreement of simulated with the measured latitude-dependent thermal counting-rate profile is within the uncertainties of the present neutron analysis. Although our uncertainties are large, the present results are encouraging because they represent the first attempt to correlate neutron measurements in orbit with temperature profiles of the moon. 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Prettyman, Diagnostic Applications Group, Applied Physics Division, Los Alamos National Laboratory, X-5, P.O. Box 1663, Mail Stop, F663, Los Alamos, NM 87545, USA. (rcl@lanl.gov) A. B. Binder, Lunar Research Institute, 9040 South Rita Road, Tucson, AZ 85747, USA. I. Genetay and S. Maurice, Observatoire Midi-Pyrénées, 14 avenue Edouard Belin, Toulouse, France.