## Abstract

Critical comments from Lawrence *et al*. are considered on the capability of the collimated neutron telescope Lunar Exploration Neutron Detector (LEND) on NASA’s Lunar Reconnaissance Orbiter (LRO) for mapping lunar epithermal neutrons, as presented in our paper. We present two different analyses to show that our previous estimated count rates are valid and support the conclusions of that paper.

The major advantage of the collimated neutron telescope Lunar Exploration Neutron Detector (LEND) on board NASA’s Lunar Reconnaissance Orbiter (LRO) compared with the previous neutron spectrometer (NS) on Lunar Prospector is the ability of LEND to measure spatial variations of lunar neutrons within a narrow field of view (FOV) (*1*, *2*). The count rate of neutrons within the FOV is our “signal” for such lunar mapping, and all other counts in the collimated sensors are “background” (*1*, *2*). According to our paper (*3*), the count rate of the collimated sensors is about 5 counts per second (cps), with a signal about 1.5 to 1.9 cps and a background about 3.1 to 3.5 cps. The main criticism of our paper by Lawrence *et al*. (*4*) is based on the estimation of a much larger background that was nearly equal to the total count rate of the collimated sensors. If that were the case, LEND could not detect a significant number of neutrons within its FOV, and it would not be able to map neutrons with the required spatial resolution.

In our analysis of the LEND mapping capabilities (*1*, *2*), we took into account neutrons at all energies corresponding to the collimated signal and all the components of background on lunar orbit. Lawrence* et al.* (*4*) have focused on one particular component of background, which is associated with the partial transparency of the collimator for high-energy epithermal (HEE) neutrons from the Moon. This component was presented in (*4*) as a new background that was missed in our paper (*3*), but that is not correct. We estimated a count rate about 0.3 cps for neutrons of all energies, including the HEE.

In (*4*), the count rate for freely propagating HEE neutrons was estimated as 2.25 cps, which is about 7 times higher than our estimation. To get this value, Lawrence* et al.* (*4*) performed a numerical simulation of LEND-type sensors for HEE neutrons from soils with different atomic mass. They found that the count rate of HEE neutrons should be about 10% higher for maria than for highlands. Then, using NASA Planetary Data System (PDS) data, they found a difference of about 0.25 cps between the maximum count rate of maria and the mean count rate for highlands. Using these values, they found 2.25 cps for the background from propagating HEE neutrons.

We disagree with two statements in (*4*). The first one is related to the count-rate values they used. The statistics of the counts are low, and one must average data over large areas to properly estimate the difference between maria and highlands. However, Lawrence* et al. *(*4*) compared the maximum count rate in one area with the mean count rate in another. We found the difference between mean count rates for maria and highlands to be 0.143 cps compared with the 0.25 cps of (*4*), and we found the difference between the mean count rates of fast neutrons for maria and highlands to be 12.9% (*5*). Using these values, we estimate 1.1 cps (*5*) as the contribution of fast neutrons into the total count rate of the collimated sensors, which is smaller by a factor of 2 than the value of 2.25 cps presented in (*4*). Interestingly, note 12 of (*4*) also presents the option of a smaller estimation of 1.3 cps for the same component of the HEE background, which is quite close to our estimation of 1.1 cps.

This estimation of 1.1 cps is still much larger than our original value of 0.3 cps for neutrons transmitted thru the collimator. The difference is due to fast neutrons that are back-scattered off the spacecraft into the LEND sensors. This effect of back-scattering was described (*6*) as part of the total spacecraft-related background of about 2.8 cps. Our second disagreement concerns the Lawrence *et al*. (*4*) statement that they found a new component of background (2.25 cps). In reality, they were dealing with a part of the total spacecraft-related background (2.8 cps), which had already been taken into account in (*3*).

Our analysis above follows the same approach as used in (*4*), but used adjusted values. We can take another approach and use the LEND observational data for a more comprehensive study of the signal and background components of the collimated sensors. To characterize the global variations of neutrons, we use Orbital Phase Profiles (OPP) of counts averaged over two lunar hemispheres (centered on 0° and 180°) versus orbit phase ϕ. Such profiles were used by the NS team on Lunar Prospector as a generic signature of spatial variations of lunar neutrons (*7*). After correcting for contributions from thermal and fast neutrons, the relative variation of OPPs for true counts of epithermal neutrons should be the same for the omnidirectional neutron sensor and for the collimated sensors. Therefore, one may propose the equationOPP_{etn}^{(omni)}(ϕ) = OPP_{etn}^{(col)}(ϕ) (1)for properly normalized OPPs (*8*). Eq. 1 may be transformed into another one (*8*), which contains only directly measured OPPs together with two free parameters α and β, which define fractions of the background due to thermal and fast neutrons, respectively, into the total counts of omnidirectional and collimated sensors. In such representation, Eq. 1 is used for searching for the best-fitting values for these fractions. This procedure determines the background and true counts of epithermal neutrons for the omnidirectional and collimated sensors (*8*). The resultant profiles for these counts OPP_{etn}^{(omni)}(ϕ) and OPP_{etn}^{(col)}(ϕ) are in good agreement with each other (Fig. 1), as required by Eq. 1. Moreover, these profiles are shown to be consistent with the OPP of independently measured epithermal neutrons by NS of Lunar Prospector (Fig. 1). The signal count rate of the collimated sensors is 1.6 cps and the background component from the fast neutrons in these sensors, the main point of this response, is found to be 1.1 cps, in agreement with our independent estimate presented above.

## References and Notes

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To estimate the difference in counts between maria and highlands, we selected the box M (maria) as 10° S to 45° N and 65° E to 0° and another box H (highlands) as 45° S to 45° N and –90° E to 90° E. We used LEND PDS data to estimate the average count rates of collimated sensors for M and H boxes as
*r*_{M}= 5.244 ± 0.002 cps and*r*_{H}= 5.101 ± 0.001 cps. The difference is Δ*r*_{MH}= 0.143 ± 0.002 cps. We also use LEND PDS data to estimate the average background-subtracted count rates of fast neutrons for M and H boxes as*q*_{M}= 0.648 ± 0.001 cps and*q*_{H}= 0.574 ± 0.001 cps. So, the relative difference of fluxes of fast neutrons between M and H is Δ*q*_{MH}/*q*_{H}= 0.074/0.574 = 0.129. Therefore, assuming, as was done in (*4*), that the difference Δ*r*_{MH}= 0.143 cps is related to the contribution of fast neutrons into the counts of the collimated sensors, and dividing 0.143 cps by 0.129, one may estimate the count rate of these particles as 1.1 cps. - ↵
See section 6 of the supporting online material for (
*3*). - ↵
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The suggested physical Eq. 1 may be presented on a form that is based on measured OPPs from four different sensors of LEND for thermal, epithermal-omnidirectional, epithermal-collimated, and fast particles [see (
*2*) for details]. All OPPs are used in normalized form with the average value equal to 1. For the omnidirectional sensor of epithermal neutrons, one has the expression: (Eq. 2) OPP^{(omni)}(ϕ) = (1 – α) OPP_{epi}^{(omni)}(ϕ) + α OPP^{(therm)}(ϕ), which takes into account the background component of thermal neutrons, which may propagate through the partially transparent shield of Cd around this sensor (*2*). For the collimated sensors, one has another expression: (Eq. 3) OPP^{(col)}(ϕ) = (1 – β) OPP_{epi}^{(col)}(ϕ) + β OPP^{(fast)}(ϕ), which takes into account the background component of fast neutrons in the collimated sensors. Substituting Eq. 2 and Eq. 3 into Eq. 1, one has: (Eq. 4) (1 – α)^{−1}OPP^{(omni)}(ϕ) – α (1 – α)^{−1}OPP^{(therm)}(ϕ) = (1 – β)^{−1}OPP^{(col)}(ϕ) – β (1 – β)^{−1}OPP^{(fast)}(ϕ). This expression was used for the fitting procedure based on the Pearson criteria for comparison of left and right sides of Eq. 4 for each interval of phase angle, when fitting parameters change between 0 and 1. Statistical uncertainties of the measured OPP are properly taken into account for this fit. When the best-fitting parameters are found, one gets the curves for OPPs for true counts of epithermal neutrons at omnidirectional and collimated sensors (Fig. 1). They are in very good agreement with each other. A similar procedure was applied to PDS data from NS of Lunar Prospector, and OPP was created for true counts of epithermal neutrons of this instrument. The shape of this OPP is very similar to curves for LEND (Fig. 1), which supports good consistency between the data of these two instruments provided they are similarly presented.