Enhanced hydrogen at the lunar poles: New insights from the detection of epithermal and fast neutron signatures

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2012je004112, 2012 Enhanced hydrogen at the lunar poles: New insights from the detection of epithermal and fast neutron signatures R. S. Miller, 1 G. Nerurkar, 1 and D. J. Lawrence 2 Received 24 April 2012; revised 2 October 2012; accepted 7 October 2012; published 21 November [1] The Lunar Prospector (LP) and Lunar Reconnaissance Orbiter (LRO) orbital neutron spectroscopy data sets represent a unique comprehensive multimission lunar resource. A rigorous statistical approach has been used to (re)analyze neutron data from both missions to provide new details regarding the relationships between the individual detector data sets, as well as a new evaluation of enhanced hydrogen deposits at the lunar poles. Using the multimission epithermal neutron data set, we find water ice distributed broadly across the poles, but showing evidence for a dependence on topographical features. A footprint averaged water equivalent hydrogen (WEH) abundance of ppm at each pole, with maxima of 131 and 112 ppm at the north and south poles, respectively, is derived from the epithermal neutron data. We also report the first definitive detection of a fast neutron signature consistent with an enhanced hydrogen hypothesis. These data suggest a highly localized distribution, consistent with Shackleton Crater, corresponding to a footprint averaged WEH abundance of If confined to this crater, this abundance yields a localized deposit of 0.7% WEH. Details of the analysis approach are presented along with spatial distribution maps showing the intriguing enhanced hydrogen deposits at the lunar poles. Citation: Miller, R. S., G. Nerurkar, and D. J. Lawrence (2012), Enhanced hydrogen at the lunar poles: New insights from the detection of epithermal and fast neutron signatures, J. Geophys. Res., 117,, doi: /2012je Introduction [2] Since the dawn of the space age two missions have provided global neutron measurements of the lunar surface. NASA s Lunar Prospector (LP) and Lunar Reconnaissance Orbiter (LRO) have contributed important information about elemental abundances on the Moon using spectrometers capable of detecting neutrons across a broad range of energies. Of particular interest have been investigations focusing on the lunar poles, where the combination of topographic features and limited solar illumination conspire to form cold traps for volatile compounds such as water [Colaprete et al., 2010; Paige et al., 2010]. [3] The two missions were motivated by different, yet complimentary, goals. Launched in 1998, LP was conceived to address lingering top-level questions in the post-apollo era. Of its five instruments, the neutron and gamma ray spectrometers (LP-NS and LP-GRS, respectively) are of interest here. They were designed to prospect the lunar regolith for elements that could help resolve open issues 1 Department of Physics, University of Alabama in Huntsville, Huntsville, Alabama, USA. 2 The Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA. Corresponding author: R. S. Miller, Department of Physics, University of Alabama in Huntsville, Optics Bldg. 300H, Huntsville, AL 35899, USA. (richard.s.miller@uah.edu) American Geophysical Union. All Rights Reserved /12/2012JE regarding lunar formation and evolution, as well investigate the presence of water in permanently shadowed craters at both poles [Feldman et al., 1998]. Both spectrometers were wide field-of-view instruments relying on orbital geometry to define the spatial footprint for lunar surface mapping. Using the LP-NS, enhanced hydrogen deposits were detected with inferred concentrations of 1.5% water equivalent hydrogen (WEH) within permanently shadowed craters [Feldman et al., 2000]. [4] Building on the success of LP and launched about a decade later, LRO was envisioned as a new beginning to an extended human presence in the solar system, starting with a return to the Moon. Instruments were therefore selected to support near-term human exploration including the selection of landing sites and resource identification. High spatial resolution mapping of polar hydrogen concentrations was a fundamental goal, requiring an instrument with surface localization capabilities better than the LP spectrometers. The Lunar Exploration Neutron Detector (LEND) was designed to meet this requirement using a suite of collimated and uncollimated detectors [Mitrofanov et al., 2010a]. [5] Both missions have produced valuable resources for lunar science and exploration. The orbital neutron spectroscopy results, however, have not been without controversy. Since before its launch, some in the lunar science community expressed concerns with the design and projected performance of the LEND instrument and in particular the effectiveness of the collimated subsystem [Lawrence et al., 2010]. The debate has continued since launch [Lawrence et al., 1of12

2 Figure 1. Plot of modeled equilibrium neutron fluxes escaping the lunar surface for a FAN material with various amounts of water added to the soil. From Lawrence et al. [2010]. 2011b; Eke et al., 2012; Mitrofanov et al., 2011], with questions raised as to the validity of the LEND data set, the analysis procedures used, and ultimately its interpretation. Resolving these issues is critical since the results will inform future lunar exploration endeavors. [6] In principle, the LP and LRO neutron data sets are complimentary and together represent a unique comprehensive resource. Both data sets include a subset of uncollimated intermediate energy neutrons, thereby enabling an important comparison. Incorporating the fast (via LP-GRS) and collimated (via LEND) neutrons should enhance the science return since each contributes a new aspect to the investigations. This comprehensive lunar neutron data set can, and should, be used to address the documented debate in an effort to resolve the discrepancies and ultimately to focus on the lunar science challenge to provide new insights and a more complete picture of the Moon. [7] With these motivations in mind the goals of this paper are threefold: (1) to evaluate the relationships among the neutron data sets and perform the necessary LP-LRO cross validation, (2) to utilize the available neutron data sets to qualitatively investigate the nature of the LEND collimated data and its usefulness to lunar science, and (3) to extract new polar hydrogen results by applying new statistical techniques to leverage the valuable the multimission neutron archive. 2. Orbital Neutron Spectroscopy [8] The leakage flux of secondary neutrons has proven to be an important remote sensing tool not only at the Moon, but also for other airless solar system bodies [Prettyman, 2006]. Orbital neutron spectroscopy is commonly divided into three distinct energy regimes, thermal (low energy), epithermal (intermediate energy), and fast (high energy), each theoretically providing complimentary elemental abundance and compositional morphology information. The process starts with fast neutrons created by cosmic ray interactions in the lunar regolith. Through moderation and/or capture processes this fast neutron flux is modified, ultimately imprinting details of the intervening material on the energy distribution and flux of the escaping neutrons. [9] Neutrons will rapidly lose energy in the presence of hydrogen due to elastic n-p interactions. This shifts some fast neutrons into the epithermal regime, and ultimately into thermal equilibrium with the regolith if the energy loss processes continue. As shown in Figure 1, the epithermal regime is the most sensitive to the abundance of hydrogen due to the efficiency of the energy loss by elastic scattering with hydrogen and absence of less efficient, competing processes such as inelastic scattering. The relative intensity between neutron energy regimes may give important stratigraphic information [Feldman et al., 1998, 2001; Prettyman, 2006; Feldman et al., 2011]. Observed neutron deficits, defined as reduced neutron count rates relative to a hydrogen-free region, are therefore indicative of energy loss and in turn suggestive of an enhanced hydrogen abundance. It is important to note that moderated (thermal) neutrons may also be captured by elements having large neutron capture cross sections, making them useful for nonhydrogen prospecting as well. [10] The comprehensive LP-LRO lunar neutron data set spans all three energy regimes. Specifically, both the LP and LRO spectrometers were sensitive to neutrons within all three energy classifications. However, due to its low counting rate and surrounding mass the LRO fast neutron data set will not be considered in this work. Details of the instruments and the individual data sets are briefly reviewed below Lunar Prospector Spectrometers [11] Lunar Prospector orbited the Moon for approximately 1.5 years beginning in January Initially placed into a 100 km circular, polar orbit, it was lowered to 30 km for the final 6 months of the mission. The LP-NS included two identical 3 He proportional counters, one covered with Sn and the other with Cd [Feldman et al., 1999]. Although both detectors were sensitive to epithermal neutrons ( ev), only the Sn-covered detector was sensitive to (thermal) neutrons with energies below the Cd cutoff at 0.4 ev. [12] Fast neutrons (0.6 9 MeV) were detected using the scintillator-based LP-GRS [Feldman et al., 1999]. This instrument incorporated a borated plastic scintillator as a charged-particle veto surrounding a BGO crystal for g ray detection. Fast neutrons were identified using a double-pulse signature: neutron moderation and signal generation in the plastic scintillator, followed by neutron capture [Genetay et al., 2003]. [13] To maximize the effectiveness of neutron observations it is important to be close to the emitting source. Therefore only data acquired during the 220 days of lowaltitude (30 km) operations are used for the analysis presented here. This includes epithermal (LP-epi) and fast neutrons (LP-fast) accumulated in 8 and 32 s intervals, corresponding to and sample intervals, respectively. All data were obtained from the Planetary Data System (PDS) public archive; data reduction details for these data sets can be found elsewhere [Maurice et al., 2004; Lawrence et al., 2006]. [14] Thermal neutrons are not used in this work since they are not a uniquely sensitive probe of hydrogen deposits. 2of12

3 Table 1. Orbital and Spatial Resolution Parameters a Data Set Altitude (km) q FoV (deg) Surface Footprint Radius (km) LP-epi LP-fast SETN CSETN a Geometric parameters were used to define fundamental spatial resolution performance of neutron data sets. Note that the CSETN resolution assumes a 100% efficient, fully collimated instrument with a field of view as defined in the table. It should also be noted that the LP spectrometer team used a modified neutron data set for their analyses of the lunar poles [Feldman et al., 1998; Maurice et al., 2004]. This hybrid epithermal-thermal data product was produced in an effort to maximize sensitivity to hydrogen relative to other elements. A second hybrid data product, consisting of all moderated neutrons (<0.5 MeV), was unique since it included neutrons from the previously unexplored highenergy epithermal (HEE) region between 100 ev and 500 kev [Genetay et al., 2003]. However, because a principle goal of this work is a direct comparison with LEND, no hybrid data products are used here. Other data corrections are described by Maurice et al. [2004] Lunar Exploration Neutron Detector [15] The Lunar Exploration Neutron Detector (LEND) is unique since it incorporates a combination of uncollimated and collimated 3 He sensors [Mitrofanov et al., 2008, 2010a]. One of the four uncollimated sensors (SETN) is configured for epithermal neutron detection (>0.4 ev), as are the four collimated sensors (CSETN). The latter are installed within a collimating module intended to provide improved spatial resolution relative to uncollimated sensors. This collimator has external layers of polyethylene and internal layers of 10 B designed to moderate and absorb neutrons incident from beyond the collimator s 5.6 field of view (half-opening angle). [16] The present analysis uses the LEND averaged science data (ALD), consisting of spatially averaged data acquired from September 2009 through September 2010 at a nominal mapping altitude of 50 km above the lunar surface. Averaged LEND data includes count rates for both uncollimated and collimated detectors, exposure times, and auxiliary housekeeping data. Archived data available at the PDS have been divided into north and south polar regions ( lat 80 ) and an equatorial region having resolutions of (14,400 grid cells, each pole) and 1 1 (57,600 grid cells), respectively Rebinned Data [17] To facilitate analysis all data sets were (re)binned using the Hierarchical Equal Area Isolatitude Pixelization (HEALPix) paradigm [Gorski et al., 2005]. This approach is advantageous for studying spatial distributions since it enables equal area binning of a sphere. Spatial resolution is defined by a grid resolution parameter N side that ultimately 2 dictates the number of pixels as N pix =12N side, with N side valid on a dyadic scale (i.e., N side =2 k, k 0). Because they are equal area, HEALPix pixels have solid p ffiffiffiffiffiffiffiffi angles W pix =4p/N pix, and an angular resolution q pix =. W pix [18] The choice of resolution parameter is driven, in part, by detector spatial resolution. Uncollimated detectors viewing a spherical body have a field-of-view half-opening angle given by q FoV = sin 1 (R m /R m + h), where h is the spacecraft orbit altitude and R m is the lunar radius, while an approximate estimate for the radius of the spatial footprint on the lunar surface is simply r = h tan(q FoV ). Table 1 gives the fundamental fields of view for each neutron data set. It should be noted that oversampling can reduce the achievable spatial resolution [e.g., Lawrence et al., 2003]. Therefore, utilizing pixels somewhat smaller than the fundamental spatial resolution is desired as long as the resulting counting statistics uncertainties do not dominate over any spatial variations. [19] Under the assumption that the CSETN is fully collimated it should have the best achievable spatial resolution of the four instruments. In principle, this would require N side = 128 (k =7,N pix = , q pix = 0.46 ) to provide a resolution just larger than that of the CSETN. However, because the spatially averaged LEND ALD data set is used here, N side =64(k =6,N pix = 49152, q pix = 0.93 ) is appropriate and selected a priori to meet the spatial resolution requirements. All LP and LRO data sets were (re)binned using this resolution parameter. 3. Neutron Count Rate Distributions [20] Global count rate distributions for the rebinned LP and LEND data sets are shown in Figure 2. Spatial variations within the maps are indicative of elemental abundance changes [Feldman et al., 1998, 2001; Prettyman, 2006] with many features, such as those associated with the nearside maria, common to all data sets. Key differences, however, do exist. For example, the LP-epi count rate shows a deficit within the maria, yet the LP-fast rate is enhanced in the same region. A visual inspection of the LEND maps show a similar deficit for the SETN data, yet the CSETN map suggests an enhancement similar to that seen in the LP-fast map. This latter observation is curious since the CSETN data is supposed to be a collimated subset of the SETN data. [21] In an effort to quantify the relationships among the data sets the 2-D global maps have been reduced to the 1-D latitude profiles shown in Figure 3. These profiles have been integrated over longitude and for clarity lunar latitude has been converted to a variable starting from equator (0 ), passing through the north and south poles (90 and 270, respectively), and returning to the equator. To more clearly illustrate variations within the individual data sets, many corresponding to specific lunar features, latitude profiles for specific 1 -wide longitude slices are shown in Figure 4. [22] As expected, a number of features are common among the data sets. For example, the two uncollimated epithermal data sets (LP-epi and SETN) have similar profiles throughout the equatorial and polar regions. In contrast, the LP-fast profile is dominated by the nearside maria apparent in the global maps, and shows a dichotomy of structure at the north and south polar regions. A quantitative analysis provides additional insights Correlation Analysis [23] The Pearson product moment correlation coefficient (1 r 1) is used to quantify the strength of the correlations between data sets, with the limits corresponding to perfect 3of12

4 Figure 2. Rebinned global maps of lunar neutron count rates. Four neutron data sets are shown: (top left) LP-epi, (top right) LP-fast, (bottom left) SETN, and (bottom right) CSETN. Note that magnitude scales differ in these global maps. anticorrelation and correlation, respectively. In this application, the correlation coefficient measures similarities in relative amplitude (or shape) only, and is not used to evaluate the physics implications of the absolute neutron rates. Coefficients obtained using the longitude-integrated latitude profiles (e.g., Figure 3) are tabulated in Table 2. Also given are the corresponding significances for the observed correlations, measured as a z score relative to the null hypothesis r =0. [24] Two highly significant correlations stand out. The first, between the LP-epi and SETN profiles, is expected since both data sets presumably sample the same lunar neutron component. Of particular note, however, is the high degree of correlation between the LP-fast and CSETN profiles. Naively, this is an unexpected result since the CSETN was intended to provide a collimated subset of epithermal neutrons, and hence should be highly correlated with the SETN and LP-epi profiles, which it is not. This strong correlation suggests a CSETN data set dominated by a nonepithermal component, a result supported visually by the global maps. [25] A benchmark for an epithermal-fast correlation is provided by the LP data sets, and is a metric for qualitative investigation of the CSETN data. This benchmark is an anticorrelation (as expected; Table 2), driven in part by the dramatic differences in the equatorial count rates that support the presence of elements having large neutron capture cross sections [Lawrence et al., 2006]. Using a linear combination of the LP data sets, the relative weights are adjusted until the LP-epi/LP-fast correlation (r = 0.6) is degraded Figure 3. Longitude-integrated latitude profiles of global lunar neutron count rates. Four neutron data sets are shown: LP-epi (gray line), LP-fast (blue line), SETN (black line), and CSETN (red line). The integration has been performed over hemispheres to show the spatial trends across the lunar surface in a one-dimensional profile. Each profile has been normalized to the average rate from equatorial latitudes ( lat 80 ), and error bars are the standard error of the mean within each binned 1 latitude interval shown. Actual counting rates are obtained by multiplying the vertical axis by the appropriate equatorial rate factor: 19.6 (LP-epi), 13.4 (LP-fast), 10.6 (SETN), and 5.1(CSETN). 4of12

5 Figure 4. Latitude profiles of global lunar neutron count rates. The profiles are shown for 10 bands of longitude circling the lunar surface that start at (top left) 0, (top right) 30, (bottom left) 60, and (bottom right) 90. Four neutron data sets are shown: LP-epi (gray line), LP-fast (blue line), SETN (black line), and CSETN (red line). Each profile has been normalized to the average rate from equatorial latitudes ( lat 80 ). Actual counting rates are obtained by multiplying the vertical axis by the appropriate equatorial rate factor: 19.6 (LP-epi), 13.4 (LP-fast), 10.6 (SETN), and 5.1(CSETN). and consistent with the LP-epi/CSETN correlation at the 90% C.L., i.e., in the range 0.24 r This qualitative approach suggests that the CSETN is not a pure epithermal sample, and is instead consistent with a model having a fast epithermal admixture ratio of 1: Although an independent sample of HEE neutrons was not included in this analysis they are also a likely, and perhaps dominant, component of the CSETN data set [Lawrence et al., 2011b; Eke et al., 2012]. [26] Similar anticorrelations, albeit at lower significances, are observed between the LP-fast/SETN and the LP-epi/ CSETN profiles. Because of the SETN s similarity to the LP-epi the former anticorrelation is expected, mimicking the one observed between the LP data sets. The latter is consistent with the high degree of correlation between the CSETN and LP-fast profiles Discussion [27] Global count rate distributions, latitude profiles, and correlation analyses are consistent with the hypothesis that the CSETN is not a collimated epithermal data set as originally intended. Rather, it has a significant nonepithermal (HEE and fast) component and may even be dominated by it. The efficiency for direct HEE or fast neutron counting using 3 He counters is low, requiring another model for their detection by LEND. Presumably these neutrons are incident from beyond the instrument s field of view, are moderated as they pass through the collimator, and subsequently detected as epithermal neutrons. Although only a detailed instrument simulation and/or laboratory calibration effort would be definitive, this model is consistent with the results outlined above. [28] Comprehensive energy- and incident angle dependent efficiencies would likely enable a deconvolution of the various neutron components, and possibly the recovery of a collimated epithermal component. In the absence of this critical performance information it is necessary to treat the CSETN data set as is, since any effort to separate the collimated and noncollimated contributions would impose unknown systematic effects and ultimately prove counterproductive. One is, therefore, forced to give up the notion of a collimated data set and its presumed benefits to spatial resolution, and utilize the data set as an uncollimated detector sensitive to a combination of fast and epithermal Table 2. Pearson Product-Moment Correlation (r) for Longitude- Integrated Latitude Profiles a LEND LEND LP LP SETN CSETN Epithermal Fast LEND SETN (4.4) 0.85 (23.5) 0.23 (4.4) LEND CSETN (3.1) 0.85 (23.8) LP epithermal (13.0) LP fast 1 a The significance (given as a z factor) for each correlation coefficient is shown in parentheses. 5of12

6 Figure 5. SETN exposure maps (orthographic projection) of the (left) north and (right) south lunar poles. neutrons. It is important to note, however, that this does not imply that the CSETN data set is unusable. On the contrary, additional efforts to characterize its performance and response will ultimately benefit neutron spectroscopy and lunar science investigations. [29] As discussed above, the choice of pixel size was driven by the assumption of an effective collimated data set. Although this assumption is not supported by the correlation analysis, the choice of pixel size will be retained for the analysis that follows. This represents a tradeoff between maximizing statistical significance (larger pixels!improved statistics) and maximizing spatial resolution (smaller pixels! improved surface mapping). The impact of this choice for polar analyses is discussed in greater detail below. 4. Polar Analysis [30] Two fundamental features are apparent in the epithermal neutron (LP-epi and SETN) latitude profiles: significant variation at equatorial latitudes and a clear reduction of the neutron count rate at the poles, with both mimicking similar features first identified by Lunar Prospector [Feldman et al., 1998, 2001]. Of particular interest here are the polar deficits. Previous analyses have provided either a general description, such as the integrated magnitude of the deficits in the polar regions that can mask topographicdependent nonuniformities [e.g., Feldman et al., 2001], or utilized a model-dependent spatial deconvolution approach [Elphic et al., 2007; Teodoro et al., 2010]. A rigorous, independent, statistical methodology appropriate for hypothesis testing [Miller, 2012] is complimentary and utilized here to infer the spatial distribution of hydrogen at the poles and its significance Likelihood Ratio Method [31] Proper determination of statistical significance and confidence intervals are often overlooked experimental challenges. In fact, approximate methods are commonly used for simplicity or to reduce computation requirements. However, the importance of using an accurate analysis methodology must take precedence over ease of use, particularly in low signal-to-noise experiments. Details of the statistical analysis framework employed here can be found elsewhere [Miller, 2012] but are briefly reviewed below. [32] Statistical techniques can incorporate the fundamental discrete statistical distributions governing particle detection experiments, including underlying uncertainties. This is critical for an accurate determination of significance. The statistical descriptions relevant to this work are based on particle counts, not rates, and therefore require the use of exposure distributions as well as the neutron rates presented above. Here exposure is defined as the amount of time the spacecraft subsatellite point is within a given pixel for a constant measurement geometry. Representative exposure maps of the polar regions showing the principle benefit of a polar orbit enhanced sampling at the poles are presented in Figure 5; similar exposures are obtained for all the data sets used here. [33] Let H o represent an hypothesis based on some a priori knowledge of a physical model containing p free parameters. Furthermore, let H represent another, more complex, hypothesis that contains q + p parameters. The likelihood ratio method (LRM) is useful when comparing the two hypotheses and determining the level of confidence that can be placed on hypothesis H compared to the null hypothesis H o. [34] Given a quantity k, the likelihood that it was drawn from each of these two parent distributions is denoted L(k H) and L(k H o ), respectively. To determine the degree with which the data may support hypothesis H over H o a likelihood ratio is computed, R ¼ LkH ð j Þ=LðkH j o Þ and since in general H incorporates hypothesis H o this ratio satisfies R 1. In a classical interpretation the statistic ð1þ 6of12

7 Figure 6. Spatial distribution of the LRM l statistic for the north polar region (latitudes greater than 80 north). All four neutron data sets are shown: (top left) LP-epi, (top right) LP-fast, (bottom left) SETN, and (bottom right) CSETN. The lunar nearside (0 longitude) is at the bottom of each polar plot. Statistically significant regions are those with l 25. An orthographic projection is shown. l =2lnR follows a c 2 distribution with q degrees of freedom if the null hypothesis is true, with H o rejected if l exceeds some predetermined critical value l c ; the confidence level is P(c q 2 < l c ). Techniques such as this have been successfully employed in a variety of scientific endeavors, including X-ray and g ray astrophysics [Cash, 1979; deboer et al., 1992]. [35] In the scenario considered here the two hypotheses correspond to dry (hydrogen-free ) regolith (H o ) and regolith with a nonzero hydrogen abundance that ultimately produce a neutron deficit (H). The likelihoods for H and H o are simply the Poisson distributions f P (k; m s ) and f P (k; m b ), respectively. Here k is the number of counts detected within a map pixel, m b the expected number of counts based on a hydrogen-free hypothesis, and m s = k. Detectors requiring background subtraction (e.g., imperfect collimation) require the Skellam, rather than the Poisson distribution [Miller, 2012]. [36] The hydrogen-free count estimate can, in principle, be obtained either from models or empirically from actual data. The latter approach is used here. Since the region of interest is poleward of 80, the average count rate is extracted from a 10 latitude band region just outside this region under the assumption that it is outside the (potentially) hydrogen-enhanced polar regions and excludes most of the equatorial latitudes having significant count rate variations. It should be noted that the results presented below are robust to this choice and do not change markedly if a latitude band between, say, is chosen instead. The resulting background, or expected, count estimate (m b ) 7of12

8 Figure 7. Spatial distribution of the LRM l statistic for the south polar region (latitudes less than 80 south). All four neutron data sets are shown: (top left) LP-epi, (top right) LP-fast, (bottom left) SETN, and (bottom right) CSETN. The lunar nearside (0 longitude) is at the top of each polar plot. Statistically significant regions are those with l 25. An orthographic projection is shown. was then obtained for each pixel by multiplying this average rate by the relevant pixel exposure. This procedure was repeated for each of the four independent data sets used in this work. [37] The difference between the two hypotheses is simply a neutron suppression factor, i.e., d =(m s m b )/m b. Therefore, with one degree of freedom (q = 1) the critical value of l corresponding to a Gaussian equivalent of 5s (chance probability of )isl c = 25, and values exceeding this threshold imply that the null hypothesis can be effectively rejected. Marginal significance, corresponding to a Gaussian equivalent of 3s, is obtained using l c =9.Itis important to note that by itself the l-statistic cannot distinguish between an enhancement (d > 1) and a deficit (d < 1), and requires additional information (e.g., m s and m b ) to do so Polar Likelihood Maps [38] Spatial distributions of the l statistic are shown in Figures 6 and 7 for the north and south polar regions, respectively. As expected, the two epithermal data sets (LPepi and SETN) show highly significant deficits centered near the poles, with asymmetries that may be indicative of morphology effects. A 2-D spatial correlation, using the Pearson product moment statistic described in section 3.1, quantifies the similarities and supports the interpretation that the two epithermal data sets have mapped map the same selenographic distribution (Tables 3 and 4). Differences in significance are accounted for by a tradeoff between the higher count rate of the LP-NS (due to lower altitude) and the additional exposure time of LEND. 8of12

9 Table 3. Pearson Product-Moment Correlation (r) for the North Polar l Statistic a LEND LEND LP LP SETN CSETN Epithermal Fast LEND SETN (23.8) 0.94 (32.4) 0.16 (3.0) LEND CSETN (19.2) 0.07 (1.3) LP epithermal (2.9) LP fast 1 a The significance (given as a z factor) for the each correlation coefficient is shown in parentheses. [39] The LP-fast data set shows a significant localized deficit slightly offset from the south pole, the first fast neutron signature detected at the lunar poles. Other associated features include a nearly symmetric circumpolar deficit just below the required significance threshold, and strong evidence supporting a fast neutron enhancement consistent with the South Pole-Aitken (SPA) basin. The spatial correlation analysis (Table 4) suggests the fast and epithermal neutron distributions are different, due in part to the SPA enhancement and the fast neutron deficit being more tightly concentrated near the pole. [40] Neither the LP-fast (north pole) nor CSETN (north or south pole) maps have features exceeding the required threshold, although it is possible that the choice of pixel size led to a reduction in significance. As discussed previously, this choice is a compromise between spatial resolution and statistical significance. To investigate if this has had a negative impact on the analysis we note that the significance of an actual resolved source will evolve with pixel size. Specifically, it will increase as pixel size is enlarged, reach a maximum when pixel size and the effective detector footprint (point spread function) are well matched, finally decrease when the pixels become larger than the physical extent of the source. This trend occurs in a predictable way for a known (or assumed) point spread function. Figure 8 shows the evolution of the most significant pixel for the LP-fast and CSETN maps as a function of pixel size. Also shown is the relative change expected for a Gaussian point spread function. Only the south pole LP-fast data set shows the required evolutionary trend while also exceeding the detection threshold at a particular scale. Therefore, we can conclude that a fast neutron signature at the south pole is real, while other features remain subthreshold. [41] Although it is tempting, one must be careful not to overinterpret the low-significance features within the LP-fast and CSETN maps. Based on significance and the pixel size evolution trends only the south pole fast neutron signature can be considered a positive detection given the significance threshold chosen a priori (l 25). It is, however, intriguing to Table 4. Pearson Product-Moment Correlation (r) for the South Polar l Statistic a LEND LEND LP LP SETN CSETN Epithermal Fast LEND SETN (26.1) 0.97 (40.8) 0.19 (3.6) LEND CSETN (24.9) 0.19 (3.7) LP epithermal (3.5) LP fast 1 a The significance (given as a z factor) for the each correlation coefficient is shown in parentheses. note the modest correlation between the CSETN spatial distribution and the epithermal maps, suggesting that this data set may yet provide statistically significant detections given additional exposure time, a prediction anticipated elsewhere [Miller, 2012]. This is certainly true at the south pole where the CSETN map mimics key features of the epithermal maps. 5. Interpretation [42] Although a detailed analysis of the l statistic (significance) maps and their relationship to lunar topography is forthcoming (R. S. Miller et al., manuscript in preparation, 2012), a cursory analysis is instructive. In addition to being a measure of significance, the l statistic is also a proxy for the actual abundance of polar hydrogen. The LRM approach characterizes the statistical significance of source pixel counts relative to an expected background, ultimately giving a direct relationship between the neutron suppression factor and the l statistic. An example of the d l relationship is shown in Figure 9, reinforcing the notion that increasing statistical significance (larger l) corresponds to a larger deficits (more negative d). The dependence of the neutron suppression factor on hydrogen (water) content of lunar regolith is also shown in Figure 9 for both epithermal and fast neutrons. [43] Using these relationships the significance maps have been converted to water content distributions. As originally proposed here, the LP and LRO neutron data sets represent a comprehensive lunar resource with maximum science return obtained by utilizing data from both missions. Comprehensive maps showing the epithermal-derived distribution of Figure 8. Evolution of the l statistic with pixel size. The maximum l statistic for the LP-fast and CSETN north and south polar distributions is shown. Only the LP-fast south pole distribution (bold line with data points) exceeds the required significance threshold (l = 25) and shows the evolution anticipated for a resolved source; LP-fast north pole and CSETN at both poles (thin lines with data points) do not show the required evolution. Also shown are the trends expected for a Gaussian point spread function on the lunar surface having a characteristic width of s = 0.35 and s =4, scaled to the maximum observed l for illustration purposes. The horizontal dashed lines at l = 9,25 represent the requirements for marginal and significant detection, respectively. See text for details. 9of12

10 Figure 9. Neutron suppression factors (d). (left) The suppression factor (%) is shown as a function of the LRM l statistic for the four equatorial counting rates corresponding to CSETN (5.1 counts/s, thick black line), SETN (10.6 counts/s, thick gray line), LP-fast (13.4 counts/s, blue line), and LP-epi (19.6 counts/s, red line). A representative exposure of 5000 s has been used; suppression factors are smaller (larger) for shorter (longer) exposures. The vertical lines at l = 9,25 represent the requirements for marginal and significant detection, respectively. (right) The suppression factor (%) is shown as a function of the weight fraction of water based on the expressions for epithermal (solid line) and fast neutrons (dashed line) given by Feldman et al. [1998]. See text for details. water ice at the lunar poles are shown in Figure 10. The multimission epithermal data set combined observed counts from the LP-epi and SETN data sets, preserving relative rates and exposures and incorporating no scaling. Specifically, total counts for each pixel were obtained by adding the number of counts, i.e., the product of count rate and exposure, from each mission data set. Only pixels meeting or exceeding the detection threshold chosen a priori have been used (l 25). [44] At the north pole the epithermal-derived water distributions appear to reach the edges of the large impact craters (e.g., Hermite, Rozhdestvenskiy, Plaskett, Byrd) but do not extend deep into them. Similar trends are apparent in the south pole maps, with the addition of a clear association with the Cabeus region. A footprint averaged WEH abundance enhancement of % (56 11 ppm) exists poleward of 80 at each pole, with maxima of 0.073% (81 ppm) and 0.065% (72 ppm) at the north and south poles, respectively. Since these are enhancements above nonpolar levels ( 50 ppm [Feldman et al., 2000, and references therein]) the polar footprint averaged WEH abundances are ppm, with maxima of 131 ppm (north) and 112 ppm (south). These epithermal-derived abundances and spatial distributions are consistent with Figure 10. Epithermal-derived polar water equivalent hydrogen (WEH) enhancement distributions for the (left) north and (right) south polar regions. The enhancements are relative to nonpolar levels (50 ppm, 0.045% WEH) and given as a percentage by weight. Spatial distributions are shown overlaid on topographical maps of the Moon made by the Lunar Reconnaissance Orbiter Camera (LROC) at a resolution of 400 m/pixel. An orthographic projection is shown. 10 of 12

11 Figure 11. Fast derived polar water equivalent hydrogen (WEH) enhancement distribution for south polar region. The enhancements are relative to nonpolar levels (50 ppm, 0.045% WEH) and are given as a percentage by weight. Spatial distributions are shown overlaid on a topographical map of the Moon made by the Lunar Reconnaissance Orbiter Camera (LROC) at a resolution of 400 m/pixel. An orthographic projection is shown. other estimates [e.g., Lawrence et al., 2006; Teodoro et al., 2010]. A detailed analysis of the hydrogen abundance maps, their relationship to lunar topography, and a comparison with previous estimates including those of LEND [Mitrofanov et al., 2010b, 2008] is forthcoming (Miller et al., manuscript in preparation, 2012). [45] In contrast to the epithermal results, the fast derived water distribution is limited to the south pole and highly localized. In fact, at the canonical map resolution level of 28 km (k =6,q pix = 0.93 ) the significance is confined to a single pixel consistent with the location of Shackleton Crater (diameter of 21 km). Unfortunately, a single pixel does not facilitate a meaningful statistical analysis. Therefore, the detection threshold was reduced to marginal significance (l 9), increasing the number of source pixels while maintaining the fundamental source significance. The resulting fast derived water distribution map has a footprint averaged WEH enhancement of %, corresponding to a final WEH abundance of ppm (Figure 11). [46] If this fast neutron-derived hydrogen enhancement is indeed confined to Shackleton crater the measured rate at orbit is different than that on the surface due to geometric instrument response factors. A forward model approach can be used to estimate the rate on the lunar surface [Lawrence et al., 2006, and references therein]. Specifically, the relationship is linear, R surf = ar orbit + b, where R orbit is the ratio of the observed (orbital) neutron count rate to a hydrogenfree region, R surf is the same ratio on the lunar surface, and a (=4.775) and b (= 3.775) are fitted parameters obtained from the forward model analysis. For Shackleton Crater we observe a 1.5% reduction in rate relative to the null hypothesis latitude band rate (13.4 counts/s) measured at orbit. This gives R surf = 0.928, corresponding to a 7.2% rate reduction on the lunar surface, and yields a WEH enhancement of 0.7% within the crater (e.g., Figure 9, right). [47] The detection of the fast neutron signature, and its colocation with Shackleton crater, is interesting and requires additional investigation. Why is this detection special? Are there other effects that could mimic a similar statistically significant result? One possibility is a local change in regolith average atomic mass, A. Although this effect does indeed lead to significant enhancements of fast neutrons in some regions, e.g., South Pole-Aitken basin, it is important to note that the feature consistent with Shackleton is a neutron deficit rather than an enhancement, and hence is suggestive of a hydrogen enhancement. Additional analyses that leverage the elemental concentrations derived from thermal neutron and orbital g ray measurements, however, will help clarify this aspect of the signature. On the other hand, if indicative of an actual localized hydrogen deposit, is this detection only the result of the good statistics near the pole (e.g., observational exposure), and if so what limits are obtained from other polar regions? Are there layering issues; that is, is there a possibility that hydrogen exists closer to surface here than other regions? What do the combined fast neutron and epithermal neutron results say about the polar regions? These questions are the focus of ongoing analysis efforts. 11 of 12

12 [48] Obviously, a collimated neutron data set would be beneficial to the polar hydrogen deposit interpretation. No effort to utilize the CSETN data set to derive water content is incorporated here since no detections met the required detection threshold chosen a priori and because of the interpretation challenge due to the multiple neutron source contributions described previously. 6. Summary [49] Multimission orbital neutron spectroscopy observations of the Moon have been used to evaluate the relationships between the LP and LRO neutron data sets, and derive hydrogen (water ice) abundance maps of the lunar poles. Treating these data as a comprehensive resource a number of useful results have been obtained. First, the uncollimated epithermal data sets from each mission are found to be well correlated, both in significance and spatial distribution, supporting a conclusion that they sample the same neutron source(s). In addition, using a robust statistical analysis methodology the significance and spatial distribution of the polar neutron deficits have been evaluated, including the first detection of a fast neutron signature. In contrast to the broadly distributed epithermal-derived polar hydrogen deposits, this fast neutron detection is highly localized and consistent with the location of Shackleton crater. Finally, a detailed evaluation of global maps and relationships between individual data sets suggests that data from the collimated instrument aboard LRO (LEND) is consistent with an admixture of both fast and epithermal neutrons, degrading the collimated aspect of this instrument and making science interpretation difficult. Although no statistically significant polar detections have been identified using this data, additional exposure time is likely to change this result. [50] Acknowledgments. This work was supported by the NASA Lunar Science Institute grant NNA09DB31A. References Colaprete, A., et al. (2010), Detection of water in the LCROSS ejecta plume, Science, 330(6003), , doi: /science deboer, H., et al. (1992), Maximum likelihood method applied to COMPTEL source recognition and analysis, in Data Analysis in Astronomy IV, edited by V. Di Gesù et al., pp , Plenum, New York. Cash, W., (1979), Parameter estimation in astronomy through application of the likelihood ratio, Astrophys. J., 228, Eke, V. R., L. F. A. Teodoro, D. J. Lawrence, R. C. Elphic, and W. C. Feldman (2012), A quantitative comparison of lunar orbital neutron data, Astrophys. J., 747, 6, doi: / x/747/1/6. Elphic, R. C., V. R. Eke, L. F. A. Teodoro, D. J. Lawrence, and D. B. J. Bussey (2007), Models of the distribution and abundance of hydrogen at the lunar south pole, Geophys. Res. Lett., 34, L13204, doi: / 2007GL Feldman, W. C., S. Maurice, A. B. Binder, B. L. Barraclough, R. C. Elphic, and D. J. Lawrence (1998), Fluxes of fast and epithermal neutrons from lunar prospector: Evidence for water ice at the lunar poles, Science, 281(5382), Feldman, W. C., B. L. Barraclough, K. R. Fuller, D. J. Lawrence, S. Maurice, M. C. Miller, T. H. Prettyman, and A. B. Binder (1999), The Lunar Prospector gamma-ray and neutron spectrometers, Nucl. Instrum. Methods, Sect. A, 422, Feldman, W. C., D. J. Lawrence, R. C. Elphic, B. L. Barraclough, S. Maurice, I. Genetay, and A. B. Binder (2000), Polar hydrogen deposits on the Moon, J. Geophys. Res., 105(E2), , doi: /1999je Feldman, W. C., et al. (2001), Evidence for water ice near the lunar poles, J. Geophys. Res., 106(E10), 23,231 23,251, doi: /2000je Feldman, W. C., A. Pathare, S. Maurice, T. H. Prettyman, D. J. Lawrence, R. E. Milliken, and B. J. Travis (2011), Mars Odyssey neutron data: 2. Search for buried excess water ice deposits at nonpolar latitudes on Mars, J. Geophys. Res., 116, E11009, doi: /2011je Genetay, I., S. Maurice, W. C. Feldman, O. Gasnault, D. J. Lawrence, R. C. Elphic, C. d Uston, and A. B. Binder (2003), Elemental content from 0 to 500 kev neutrons: Lunar Prospector results, Planet. Space Sci., 51, Gorski, K. M., E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelmann (2005), HEALPix: A framework for high-resolution discretization and fast analysis of 1011 data distributed on a sphere, Astrophys. J., 622, Lawrence, D. J., R. C. Elphic, W. C. Feldman, T. H. Prettyman, O. Gasnault, and S. Maurice (2003), Small-area thorium features on the lunar surface, J. Geophys. Res., 108(E9), 5102, doi: /2003je Lawrence, D. J., W. C. Feldman, R. C. Elphic, J. J. Hagerty, S. Maurice, G. W. McKinney, and T. H. Prettyman (2006), Improved modeling of Lunar Prospector neutron spectrometer data: Implications for hydrogen deposits at the lunar poles, J. Geophys. Res., 111, E08001, doi: / 2005JE Lawrence, D. J., R. C. Elphic, W. C. Feldman, H. O. Funsten, and T. H. Prettyman (2010), Performance of orbital neutron instruments for spatially resolved hydrogen measurements of airless planetary bodies, Astrobiology, 10(2), Lawrence, D. J., V. R. Eke, R. C. Elphic, W. C. Feldman, H. O. Funsten, T. H. Prettyman, and L. F. A. Teodoro (2011b), Technical comment on Hydrogen mapping of the lunar south pole using the LRO Neutron Detector Experiment LEND, Science, 334(6059), 1058-c, doi: /science Maurice, S., D. J. Lawrence, W. C. Feldman, R. C. Elphic, and O. Gasnault (2004), Reduction of neutron data from Lunar Prospector, J. Geophys. Res., 109, E07S04, doi: /2003je Miller, R. S. (2012), Statistics for orbital neutron spectroscopy of the Moon and other airless planetary bodies, J. Geophys. Res., 117, E00H19, doi: /2011je Mitrofanov, I., et al. (2008), Experiment LEND of the NASA Lunar Reconnaissance Orbiter for high-resolution mapping of neutron emission of the Moon, Astrobiology, 8(4), Mitrofanov, I., et al. (2010a), Lunar exploration neutron detector for the NASA Lunar Reconnaissance Orbiter, Space Sci. Rev., 150, , doi: /s Mitrofanov, I., et al. (2010b), Hydrogen mapping of the lunar south pole using the LRO neutron detector experiment LEND, Science, 330(6003), Mitrofanov, I. G., W. V. Boynton, M. L. Litvak, A. B. Sanin, and R. D. Starr (2011), Response to comment on Hydrogen mapping of the lunar south pole using the LRO Neutron Detector Experiment LEND, Science, 334, 1058, doi: /science Paige, D. A., et al. (2010), Diviner Lunar Radiometer observations of cold traps in the Moon s south polar region, Science, 330(6003), , doi: /science Prettyman, T. H. (2006), Remote chemical sensing using nuclear spectroscopy, in The Encyclopedia of the Solar System, 2nd ed., edited by L. A. McFadden, P. R. Weissman, and T. V. Johnson, pp , Elsevier, Amsterdam. Teodoro, L. F. A., V. R. Eke, and R. C. Elphic (2010), Spatial distribution of lunar polar hydrogen deposits after KAGUYA (SELENE), Geophys. Res. Lett., 37, L12201, doi: /2010gl of 12