Using a Monte Carlo model, we analyze the evolution of the vapor plume emanating from the Lunar Crater Observation and Sensing Satellite (LCROSS) impact into Cabeus as seen by the Lyman Alpha Mapping Project (LAMP), a far-ultraviolet (FUV) imaging spectrograph onboard the Lunar Reconnaissance Orbiter. The best fit to the data utilizes a bulk velocity between 3.0 and 4.0 km/s. The fits to the light curve comprised of Hg, Ca, and Mg are not strongly dependent on the temperature. In contrast, the best fit to the light curve from H2 and CO corresponds to a 500 K thermal velocity distribution. The LAMP field of view primarily encounters particles released at low angles to the horizontal and misses fast moving particles released at more vertical angles. The isotropic model suggests that 117 ± 16 kg H2, 41 ± 3 kg CO, 16 ± 1 kg Ca, 12.4 ± 0.8 kg Hg, and 3.8 ± 0.3 kg Mg are released by the LCROSS impact. Additional errors could arise from an anisotropic plume, which cannot be distinguished with LAMP data. Mg and Ca are likely incompletely volatilized owing to their high vapor temperatures. The highly volatile components (H2 and CO) might derive from a greater mass of material. To agree with predicted abundances by weight of 0.047%, 0.023%, 11%, 0.28% and 3.4% for H2, CO, Ca, Hg, and Mg, respectively, the species would be released from 250,000 kg, 180,000 kg, 140 kg, 4400 kg, and 110 kg of regolith, respectively. This is consistent with the relative volatility of these species.
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 In the coldest regions of the Moon where sunlight does not shine, volatiles may be frozen within the lunar regolith for billions of years [Watson et al., 1961; Arnold, 1979]. The darkness of these permanently shadowed regions (PSRs) is the quality that produces the cold temperature that can trap volatiles for extremely long times [e.g., Vasavada et al., 1999]. However, that darkness also makes the volatiles within PSRs difficult to detect, identify, and quantify.
 The Lunar Crater Observation and Sensing Satellite (LCROSS) experiment revealed the composition of those volatiles by lofting material out of a permanently shadowed crater into the sunlight where they could finally be spectroscopically analyzed [Colaprete et al., 2010]. LCROSS performed a controlled impact experiment into Cabeus crater, which is one of the coldest craters on the Moon [Paige et al., 2010]. The impact occurred at 11:31 UT on 9 October 2009, when the 2300 kg Centaur stage of the Atlas V launch vehicle hit the moon at 2.5 km/s [Colaprete et al., 2010].
 One of the observers was the Lyman Alpha Mapping Project (LAMP) onboard the Lunar Reconnaissance Orbiter (LRO) [Gladstone et al., 2010a, 2010b]. With sensitivity in the far-ultraviolet (FUV), LAMP is sensitive to a different set of species than were observed by the LCROSS shepherding spacecraft (SSC) in the UV/VIS and IR. LAMP also had an orthogonal field of view to the LCROSS SSC, thus observes a physically different region of the vapor plume. In this paper, we model the evolution of the gases that LAMP observed after the LCROSS impact using a Monte Carlo model developed for the lunar exosphere [Crider and Vondrak, 2000]. We model a broad range of parameter space covering the initial velocity vectors of the vapor when the plume becomes collisionless to determine a scenario that fits the observations by LAMP.
 LRO's orbit was adjusted such that it would fly past the LCROSS site 90 s after the Centaur impact [Gladstone et al., 2010a]. Onboard LRO, LAMP measured the FUV emissions over the limb of the Moon prior to impact, during the impact, and on several subsequent orbits. On 9 Oct 2009, LRO's orbital plane was approximately in the noon-midnight plane such that the pass near Cabeus went from day to night over the south pole. Before the spacecraft reached the south pole, LRO rolled 80° off-nadir in the plane perpendicular to the orbital motion of LRO such that LAMP's line of sight (LOS) was aimed just above the limb of the Moon toward the dusk side. The slit of LAMP's imaging spectrograph was oriented along the local vertical. The pointing was fixed such that LAMP watched the limb perpendicular to the trajectory of LRO as the motion of LRO carried the spacecraft past the LCROSS impact site. In this configuration, the observed signal in the field of view (FOV) evolved due to both the changing position of the field of view of the spacecraft and the temporal evolution of the gas cloud.
 The LAMP instrument is an FUV imaging spectrograph with a passband of 57–196 nm [Gladstone et al., 2010b]. The spectral resolution is 2.8 nm. Its 21 spatial pixels measure photons within the 0.3° × 6.0° FOV. Projected to the closest distance of the impact, the slit viewed a ∼10 km altitude span above the surface, centered at 33 km altitude above the impact site.
 LAMP detected strong emissions off of the lunar limb in the southern hemisphere immediately following the LCROSS impact [Gladstone et al., 2010a]. Because LRO performed the same maneuver to roll to a limb view for eight orbits surrounding the LCROSS impact, subtraction of background UV-bright stars was possible. Gladstone et al. compared the counts observed during the LCROSS orbit to those observed on the prior two orbits. They found that most of the excess attributable to the LCROSS vapor plume came in the wavelength range of 180–190 nm. Weaker emissions were observed from 130 to 170 nm. Gladstone et al. [2010a] present the spectrum with counts integrated over the entire slit and during the times from 30 to 60 s post-impact. They fit the spectrum with lines from numerous atomic and molecular species and find the spectrum can be fit by a combination of Mg, Ca, Hg, CO, and H2.
 In addition, Gladstone et al. [2010a] produce LAMP light curves divided into the wavelength ranges 130–170 nm and 180–190 nm (Figure 1). The slit-integrated count rate begins to increase 30 s after impact, at which time the LOS had a closest approach of 115 km from the impact site. The light curve peaks strongly at 45 s after impact, when the LOS has a closest approach of 80 km from the impact site. For the 180–190 nm range, the light curve then drops off quickly to the background level 65 s after impact. A small secondary peak is observed when the LOS passes vertically above the impact site at t = 90 s. For the 130–170 nm range, the light curve falls off more slowly after the peak.
3. Modeling the Data
 We use a Monte Carlo model to simulate the evolution of the vapor plume after the LCROSS impact [Hurley, 2011]. The model follows gaseous atoms and/or molecules on ballistic trajectories under the influence of lunar gravity over time similar to in the works of Arnold  and Butler . This treatment of particle motion assumes that the vapor is collisionless, which is not appropriate at very early times after the impact. However, within the first second after impact and at approximately 1 km radius, the vapor becomes collisionless. The analysis is done for all greater times and distances. Thus, using the collisionless model is equivalent to simulating the evolution of the vapor from the point it becomes collisionless, and the collisional period is not specifically modeled in this work. The work presented here assumes that all of the particles are released simultaneously. Although a prolonged release of volatiles is possible and can be included in the model, the narrow peak in Figure 1 suggests that such a scenario is inconsistent with LAMP data.
 The primary input to the model is the starting velocity vector for each individual particle at its release. We use a two-component velocity. The first component is a thermal velocity that is randomly drawn from a Maxwellian distribution at the user-provided temperature. The thermal velocity is assumed to have an isotropic distribution in direction. The second component is a non-thermal velocity, a user-provided bulk speed. The same magnitude of the bulk speed is assigned to each particle in a run, and the bulk speed direction is radially outward over the upward hemisphere.
 The model provides the position and velocity of particles at 1 s time steps with which one can calculate line-of-sight (LOS) column densities. The Monte Carlo treatment in a collisionless exosphere allows each species to be calculated separately and the results to be co-added, for a range of initial conditions. In addition, if a prolonged source exists, one can co-add time-shifted results in the expected proportions to simulate the production rate.
 Here we present the results from model runs varying the two components to the initial velocity in a systematic way for each of the species observed by LAMP. The model results are compared to LAMP data to determine the initial velocity that best reproduces the data. Further, we estimate the mass of each species released by the LCROSS impact using model runs by scaling the modeled column density for a modeled known mass release to the observed column density.
3.1. LAMP, 180 nm – 190 nm
Gladstone et al. [2010a] attribute the emissions observed by LAMP from 180 to 190 nm to resonantly scattered sunlight by elemental mercury (at 184.95 nm), with minor contributions from calcium (at 188.32 nm) and magnesium (at 182.79 nm). Owing to the high oscillator strength of the Hg line, the signal from Hg comprises about 77% of the counts, although the estimated number density of Hg from the spectrum is only 10% of the total Mg, Ca, and Hg column [Gladstone et al., 2010a]. We initially model the observations by simulating only the Hg, since it contributes most to the signal. Hg is quite heavy, therefore has a low thermal velocity. Thus, the non-thermal properties (i.e., the bulk velocity) dominate over the thermal effects for Hg, clearly establishing the role of non-thermal properties in the evolution of the vapor plume.
 One scenario was easily ruled out for Hg. A purely thermal, isotropic expansion of Hg did not reproduce the LAMP time series. For a purely thermal Hg vapor plume, LAMP would have observed the peak column density 90 s after impact (Figure 2). Furthermore, the temperature required to get the signal into the LAMP FOV in time was unreasonably high. Therefore, a non-thermal velocity function like a bulk ejection velocity is required to fit the LAMP observations [Hurley, 2011]. In Figure 2, top, we show the model output for LOS column density of Hg seen from the LRO perspective for a release temperature of 1000 K added to an assumed bulk velocity of 0, 2, 3, 4, and 5 km/s. The thermal velocity of Hg (201 AMU) at 1000 K is on the order of 100 m/s. The vapor cloud expands at the bulk velocity, with the thickness of the shell determined by the thermal velocity. Thus, we can use the observation of the Hg light curve from LAMP to determine the bulk velocity from the LCROSS impact by comparing Figure 2, top, to the LAMP data shown in Figure 1, top. In the data, the peak is observed 40–44 s after impact. For the model runs, the peak occurs at 38 s for a 4 km/s bulk velocity and at 46 s for a 3 km/s bulk velocity. Thus the bulk velocity we infer is 3.5 km/s from the linear fit to the peak time as a function of velocity. The bulk velocity is imparted by the rarefaction shock and should be independent of constituent mass, but likely depends on the details of how quickly each volatile is released.
 We show the effect of temperature on the modeled time series of the LOS column density in Figure 2, bottom. We take 3.5 km/s bulk velocity runs for 5 different temperatures (200, 500, 1000, 2000, and 3000 K) of Mg, choosing Mg because its lighter mass results in a greater temperature effect than for Hg. The higher temperature simulation results in a broader peak that begins to rise slightly earlier than for lower temperatures. Similarly, the higher temperature simulation falls off after the peak more slowly. The most significant effect is that the peak column density is lowest for the higher temperature simulation with the same amount of material released. These simulations all consist of the same number of particles. When a higher temperature is imposed, there is a larger spread in velocities. Thus, the particles get spread out more in the high temperature simulations. From Figure 2, bottom, the peak LOS column density for the 200 K simulation is more than double than that from the 3000 K simulation for the same mass of material released in the simulations, i.e., about twice as much material would need to be released at 3000 K to produce the same peak column density as for material released at 200 K.
 We explored the parameter space of bulk velocity, temperature, and relative abundance of Hg, Mg, and Ca. We required that the bulk velocity and the temperature vary in the same way for all three elements to limit the number of free parameters, i.e., there are not separate temperatures and bulk velocities for the separate species in a single model run. Performing regressions, we present the reduced goodness of fit, χ2/ν, where ν is the number of data points, as a function of temperature and bulk velocity in Figure 3, left. The goodness of fit is most strongly influenced by the bulk velocity. The favored bulk velocity is from 3.5 to 4.0 km/s. Thus we find that any bulk velocity in that range would be consistent with the LAMP observations. The model fits the data better for higher temperatures, although the difference is not dramatic. Composition and temperature are secondary effects. In producing Figure 3, left, relative abundance was constrained to reproduce the LAMP spectrum. However, in other simulations, the relative abundances of Hg, Mg, and Ca were allowed to vary. Figure 3, right, shows the reduced χ2/ν goodness of fit as a function of composition for the 3.7 km/s 2250 K model runs. The color scale is the same for both panels. Compositional effects on the goodness of fit to the light curve are comparable to temperature effects. In Figure 3, right, the diamond indicates the composition as constrained by the spectrum. In the velocity range where reduced χ2/ν is minimized, the composition producing the best fit to the time series was dominated by Ca, with ∼10% of Hg by mass. For slower bulk velocity or lower temperature, increasing the amount of Mg in the plume somewhat improves the fit to the light curve. As the temperature increases, the amount of Hg needed to produce the best fit increases, although it never exceeds 25% of the relative abundance.
 The model light curve assuming the relative abundances determined by spectral analysis for the 3.7 km/s, 2250 K run, together with the LAMP observations, appears in Figure 4. The light curve from each element is shown separately to show the effect of the g-factor (a measure of the rate at which solar photons are scattered for a given transition) and the species mass on the light curve. The cumulative curve in red approximately fits the timing of the observations for the main peak. It starts to rise a little after the rise in the data. Also, it does not fall off quite as fast as the data. The preference for a higher temperature is because higher temperatures help broaden the peak. Still, the peak is not quite broad enough. An effective broadening would also result from allowing a range of bulk velocities. A small range of bulk velocities combined with a lower temperature could provide a broader peak at the top; yet allow a rapid fall off after the peak. A small spread in the effective bulk velocity (i.e., the non-thermal velocity used in the collisionless model) might arise during the collisional phase of the expansion.
 A secondary peak is observed as the LOS passes the impact site, at t = 90 s. This peak is about 10% of the count rate of the main peak. Figure 2 indicates that a purely thermal release produces a peak at the impact site. If we allow for a two-component cloud that incorporates both a purely thermal (i.e., zero bulk velocity) component and a component with 3.7 km/s bulk component, we can reproduce the secondary peak at closest approach. The purely thermal component might represent material that diffuses out of the warm regolith soon after the impact. A prolonged source is also possible for this component. Note that spectral analysis has not been done for the time period surrounding the secondary peak. If the peak is due to only one element, the mass of material released with a thermal distribution at 1000 K that would produce that peak is 2 kg, 5 kg, or 2 kg for Hg, Ca, or Mg, respectively.
 Until now, we have assumed that the angle of release of the particles is isotropic, i.e., a hemisphere expanding radially outward. Some physical impact scenarios call for a preferred angle of ejection, for example the upside-down lampshade of solid ejecta. Note that the vapor in the plume does not follow the same trajectories as the solid ejecta. We now investigate whether some degree of anisotropy is consistent with LAMP data. Figure 5 shows a dynamic histogram of the release angle of the particles in LAMP's FOV as a function of time from an isotropic, 3.7 km/s bulk velocity, 2250 K model run. Angle is measured from the local horizontal. The particles that reach the FOV of LAMP are mostly confined to angles close to the horizontal. At 30 s after impact, the particles entering LAMP's FOV were ejected at 5°–25° from the horizontal. As LRO approaches the impact site, the LOS encounters particles that were emitted at a greater range of angles (and are at a larger range of distances along the LOS). The LAMP LOS mainly crosses particles that were released at angles < 35° from the local horizontal during the peak. Particles released at angles closer to vertical than 35° (measured from the horizontal) ascend to altitudes above the LAMP LOS before the LOS reaches that position on the Moon and are never observed by LAMP. In fact, the FOV does not encounter any particles ejected with angles > 35° until 44 s after impact. The FOV does not encounter any particles ejected at 45° until 57 s after impact. Thus, LAMP data cannot constrain material released at angles > 45°.
 For a hollow body impactor like LCROSS, Schultz et al. [2010b] predict an enhancement to the high-angle (nearly vertical) plume. Any anisotropy in the form of a high-angle plume would lead to an increase in the total amount of material released compared to the model estimates provided here. For a gas dynamic distribution, densities are greatest at angles near the horizontal [e.g., Korycansky et al., 2009]. As such, the total amount of material released would be lower than the model estimates provided here.
 In the model run presented in Figure 5, the angle of ejection of particles encountering the LAMP FOV bifurcates into two branches. One branch appears for particles ejected at higher angles as time progresses because the LOS is approaching the impact site, allowing these particles to enter the FOV. The form of the more vertical branch of model particles can be reproduced with simple geometric assumptions. The dashed line sloping upward to the right in Figure 5 represents the angle of release for the particle that moves on a straight line from the impact site to the LOS at the center of the LAMP slit in the plane perpendicular to the LOS. There are model particles in the field of view above that dashed line because the slit has a size of about 10 km projected at that distance. In addition, the geometric assumption used for the dashed line does not account for the curved trajectory under the influence of lunar gravity. In the model run, the number of particles in this branch is high from 30 to 45 s after impact. The number of particles then decreases as a function of time because the high angle particles have already ascended above the FOV of LAMP.
 Also shown in Figure 5 are lines relating the angle at which a particle had to be released to reach the LOS at that time for a fixed initial velocity (i.e., vector sum of thermal and non-thermal component). These lines trace out the lower branch of particles from the model run. Again, these lines were produced by geometric assumptions and neglect gravity. At any given time, the particles in the FOV that are released at the most vertical angle are the slowest moving. The particles seen by LAMP that are fastest moving are released at angles closer to the horizontal. There is no way to determine what angle is associated with the particles in the FOV based on the data. However, these traces provide a reference using the model run in Figure 5. The gray line in Figure 5 shows the particles with an initial velocity at the lunar escape speed, 2.38 km/s. The simulation shows that more than half of the particles' speeds are higher than the escape speed; thus, most of the LCROSS-released vapor is not expected to have returned to the Moon. According to the model run, all of the particles LAMP observes in the first 40 s after impact escape from the Moon. Beginning at 40 s after impact, or after the passage of the main peak, some of the particles in the FOV do not escape the Moon. These are from the slower moving end of the distribution.
3.2. LAMP, 130 nm – 170 nm
 The Lyman Alpha Mapping Project also identified the fluorescence spectrum of H2 gas as it looked over the limb near the impact site in the two minutes after the LCROSS Centaur impact [Gladstone et al., 2010a]. Incorporating fluorescence of CO into the spectrum provided an excellent fit to the spectral data in the wavelength range 130–170 nm. Gladstone et al. [2010a] considered only purely thermal scenarios of H2 alone to fit the light curve and determined that the 1000 K H2 simulation provided the best fit to the observed 130–170 nm count rate. Now we investigate other possibilities including a bulk speed and a component of CO contributing to the light curve.
 As discussed in the accompanying paper [Hurley, 2011], the low mass of H2 allows its thermal and bulk velocities to be comparable. Figure 6 demonstrates how the H2 cloud is not substantially morphologically different in the non-thermal bulk simulation (Figure 6, bottom) than in the purely thermal simulation (Figure 6, top). Unlike heavier species where the bulk velocity results in a shell of material, H2 retains its highest density in the central region of the plume for a bulk velocity of a few km/s. Progressing to higher bulk velocity from top to bottom in Figure 6, one can see that the peak density is higher for lower bulk velocity. Likewise the cloud diameter is smaller for lower bulk velocity. Therefore the start time for the LAMP fluorescence light curve would reflect the combination of the thermal and non-thermal velocity.
 We investigate the fit to the LAMP 130–170 nm light curve using model runs with isotropic angular distribution of H2 and CO released at a range of temperatures from 200 to 3000 K and at a range of bulk velocities from 0 to 5 km/s. The reduced χ2 for the fits are shown in Figure 7 as a function of temperature and velocity. Like for the Hg/Mg/Ca analysis, velocities > 4 km/s do not provide a good fit to the data. However, the best fit occurs at slower bulk velocity for H2/CO at 3.0–3.5 km/s than for Hg/Mg/Ca at 3.5–4.0 km/s. There is more compatibility with the data for any bulk velocity < 4 km/s than for the 180–190 nm data. For lower bulk velocities, the best fit requires higher initial temperature. In essence, this occurs because the sum of thermal and non-thermal velocity remains about the same for H2 in the plume.
Gladstone et al. [2010a] analyzed the spectrum to determine the abundances of H2 and CO. They found that the column density of H2 is about 27 times that of CO by number in the interval from 30 to 60 s after impact. The observed mass of H2 is 1.9 times the observed mass of CO. For each combination of bulk velocity and temperature, we tried a range of mixtures of H2 and CO. The χ2 given in Figure 7 is from the mixture that gave the lowest χ2 of all of the relative abundances. The overlying contours show the percentage of H2 that produced the best fit in Figure 7. Note that for low temperatures and low velocity, the best fit comes from an entirely hydrogen gas cloud. Trending toward the upward right corner of high velocity and high temperature, increasingly greater fractions of CO are required to produce the best fit. In order to reproduce the spectrum from 30 to 60 s, the relative abundance by mass of H2 is 66% of the combined H2 and CO mass [Gladstone et al., 2010a]. Therefore the region from 60 to 70% H2 is expected in Figure 7. The range spanning 400 K–1200 K and 3.7 km/s–2.7 km/s provide a good fit to both the spectrum and time series. The overall best fit to the spectrum and time series comes for the model with a bulk velocity of 3.25 km/s and temperature of 500 K.
 The reason that there is a high dependence on composition for this wavelength range is because the light curve for CO is quite different than the light curve for H2. As for Hg, Mg, and Ca, the CO light curve is highly dependent on the bulk velocity. In contrast, the H2 light curve has both temperature and velocity dependencies. Thus, at bulk velocity below 3 km/s, the presence of CO reduces the goodness of fit. In Figure 8, we show the light curves for H2 and CO separately for a 3.25 km/s bulk and 500 K. The H2 light curve (dotted line) begins its rise and peaks about 15 s earlier than CO (dashed line). The H2 light curve falls off slowly on its own, but adding some CO influences the light curve after the peak and on toward closest approach at 90 s after impact. The model light curve for the combination 66%/34% H2/CO appear together with the LAMP data in Figure 8.
 The comparable nature of the thermal and bulk velocity for H2 in this circumstance makes many scenarios for H2 appear very similar to the limited field of view of the LAMP observations. The simulations with exactly the same conditions as the Hg/Mg/Ca best fit are not the best fit here even with the broad range of satisfactory parameter space for H2/CO. H2 and CO are molecules and have additional degrees of freedom compared with the elemental species. This could account for the lower energy partition into translational velocity of H2/CO in the plume than for the elemental counterparts.
3.3. Abundances in the Plume
 Reanalysis has led to a revision the column densities observed by LAMP [Gladstone et al., 2011]. Table 1 displays the new estimates of average LOS column density from 30 to 60 s for each of the five species. The revision was done to correct a mistake in the application of the g-factors as a function of wavelength for Ca, Mg, Hg, and CO. The corrected column density values are decreased by a factor of about 5.5 from the values published by Gladstone et al. [2010a]. However, the initial abundances by weight reported [Gladstone et al., 2010a] were referenced to a predicted plume of total content 10,000 kg, which was revised to 3150 kg [Colaprete et al., 2010] and relatively increases the determined abundances by a factor of 3.2. The combined result is that the current best estimates of soil mass abundance are about 1.7 times less than the values published by Gladstone et al. [2010a].
Table 1. Estimated Mass of Gaseous Species Released by the Centaur Impact Including the Amount in the FOV, a Simple Geometric Scaling of That Amount, and the Best Fit of the Isotropic Model Runs From Figures 9 and 10
Revised Column Density (cm−2)
Amount Observed in FOV (kg)
Geometric Scaling of Amount Observed (kg)
Best Fit Isotropic Model (kg)
117 ± 16
41 ± 3
16 ± 1
12.4 ± 0.8
3.8 ± 0.3
 LAMP's field of view is much smaller than the vapor plume, and so it only samples a small fraction of the plume. Furthermore, the modeling presented here has shown that the count rate observed by LAMP is dependent on the specific physical parameters of the gas when it becomes collisionless. We apply results from the model to scale the observed quantities of gas to the amounts of gas that were released in total. A range of initial conditions (temperature, relative abundance) can reproduce the timing of the light curve. We use the information we have from modeling and a few simplifying assumptions to estimate total amounts of each observed species ejected from the LCROSS impact.
 The model output is normalized to give the LOS column density in any look direction per kg of that species released. To determine the scaling that produces the best fit to the data, we conduct a regression. Figure 9 shows the inferred total mass of Hg, Mg, and Ca that had to be released isotropically at 3.7 km/s in order to reproduce the observed LOS column density as a function of the modeled temperature. Here we have constrained the relative proportions to reproduce the relative proportions of Hg, Mg, and Ca in the spectrum taken from 30 to 60 s. Inspecting the total mass from the model for an initial bulk velocity of 3.5–4.0 km/s, we find 12.4 ± 0.8 kg of Hg, 16 ± 1 kg Ca, and 3.8 ± 0.3 kg Mg. The errors are 1-σ uncertainties from averaging over the 72 model runs in that bulk velocity and temperature range. It is important to note that these uncertainties do not include differences for anisotropic distributions of vapor. Thus the actual uncertainties are greater than the given values. These values are summarized in Table 1.
 Similarly, for H2 and CO, we simulate the total mass release needed to reproduce the observations in Figure 10. Here, we show the mass from the model as a function of the temperature and bulk velocity in the model. However, when constraining the model to reproduce the observed spectrum, the best fits occur in a region around 500 K, 3.25 km/s sloping to higher bulk velocity and lower temperatures to lower bulk velocity and higher temperatures. Contours of the lowest χ2 from the fit to the time series while constraining the relative abundance are superimposed in white to focus attention on the region where the fit to the time series and spectrum was best. Placing a limit on the valid area of the plot inside the outermost contour displayed, we compute the average and 1 standard deviation for the mass released from model runs inside that velocity and temperature range. The isotropic model suggests that 117 ± 16 kg of H2 was released by the LCROSS impact. Correspondingly, the amount of CO released based on the modeling is 41 ± 3 kg. Again, the uncertainties do not include variations that anisotropy would produce. In a gas dynamic scenario, densities are greatest at angle close to the horizontal, i.e., angles preferentially selected for by LAMP's FOV. Thus in a hydrodynamic distribution the total mass released would be less than these values.
 One can compare the modeled mass release to the actual amount of material observed by LAMP. The size of LAMP's field of view projected on the central plane of the vapor plume is 2.5 km2. The size of the cloud is on the order of 65–130 km radius during the 30–60 s interval [Hurley, 2011]. Thus the hemispheric projection of the vapor plume covers ∼15000 km2. LAMP's field of view is 1e-4 of the total cloud area (and is decreasing in time). Integrating over the path of the field of view, LAMP samples 780 km2 on approach to the impact site. With a small field of view, the observed mass underestimates the amount of material released but puts a lower limit on the amount of these species released. Based purely upon the observed signal from LAMP and assuming the particles in the cloud are motionless, the total count rate gives the results: 0.12 kg (Hg); 0.16 kg (Ca); 0.04 kg (Mg) 0.70 kg (CO); and 1.33 kg (H2) as lower limits for the release of these materials.
 As an alternative to the modeling, we can use scaling arguments to adjust the observed columns of material to derive total abundance in the plume. Scaling the observed count rate by the along-track distance to the impact site and assuming constant density along a hemisphere at that radius, we calculate the “scaled observed” values in Table 1. In this calculation, we also consider the relative velocity of LRO to the cloud expanding at ∼3.5 km/s. The scaled values are very close to the model predictions for Hg, Mg, and Ca. The problem with this calculation for H2 and CO is that it assumes that the fractional count rate for H2 and CO is constant over time, which is inconsistent with the simulations (see Figure 8). Therefore, the model predictions have a better physical basis for being accurate than the predictions from geometric scaling. Both the model predictions and the mass released that we derive from scaling have additional errors associated with the isotropic assumption.
 After using model-data comparisons to infer the initial temperature, bulk velocity, and mass of Hg, Mg, Ca, CO, and H2 released by the LCROSS impact, we put the results into context of the environment at the permanently shadowed regions of the Moon. First, we discuss the release of volatiles from the impact. Next we discuss the implications of this research on determining the abundance and distribution of these species within the regolith of Cabeus. We compare the results to predicted and measured abundances in Cabeus.
 The Centaur impactor was a cylindrical, hollow body that had to compress and collapse as it hit the Moon. A shock wave propagated through the projectile and the target. In the target, the shock collapsed the pore space and heated the frozen regolith, which could have released volatiles. The frictional heating of grains moving relative to one another is enough to mobilize low temperature volatiles like CO and H2. Hayne et al.  estimate that a 60 m2 area a few mm deep was heated to 950 K due to the LCROSS impact. A rarefaction wave traveled out of the target material, excavating ejecta from the crater. Schultz et al. [2010a] estimate that the resulting transient crater measured 25–30 m in diameter, much larger (by 8–12 times) than the area warmed to 950 K. In addition, volatiles could have been lofted into the sky on regolith grains that are ejected from the crater. Once the regolith grains are in sunlight and warm, the volatiles they contain may sublime or become photodissociated. Estimates of the mass of ejecta that reached sunlight (i.e., achieved an altitude above 800 m to rise over the shadow from the rim of Cabeus) range from 1200 kg to 6000 kg [Colaprete et al., 2010; Schultz et al., 2010a; Hayne et al., 2010]. The observations are consistent with laboratory simulations of hollow hyper-velocity impactors on regolith that produce a low angle ejecta curtain and a fast, high angle component [Schultz et al., 2010b].
 The amount of volatiles at a given location and time will be quite different depending on the release scenario. The timing of the passage of the volatiles from LAMP's perspective requires that a non-thermal, prompt process was responsible for their release. Sublimation and photoionization mechanisms are inconsistent with the LAMP data because neither of these prolonged sources produces a narrow peak. Simulations that include a ∼3.5 km/s bulk velocity are the most consistent with all of the observations. This speed is faster than the tens of m/s that would be expected for subliming vapor.
 For the initial second after impact, the vapor cloud is dense enough to be collisional. During the collisional phase, the density is constant throughout the cloud. That gives the velocity profile a linear function with radius. Our model assumes a collisionless cloud, which becomes appropriate within the first second after impact and at distances greater than 1 km. The initial conditions used in the model to reproduce the data reflect the conditions of the vapor plume when it transitions to the collisionless regime. Once the gas becomes collisionless, the gas continues on a ballistic trajectory with the particles on the outside edge of the cloud with the highest starting velocity and the particles in the interior with the lowest velocity. The narrow ejecta peak LAMP observed indicates that the cloud became collisionless very quickly, allowing only a very small distribution of velocities.
Zel'dovich and Raizer  show that the vapor emitted promptly on impact has an expansion velocity about 3 times the mean thermal velocity. Our simulations suggest that a bulk velocity of ∼3.5 km/s is required to reproduce the observations. Given the species and temperatures that reproduce the observations, the mean thermal velocity used in the simulations is on the order of several hundred m/s. Thus, the bulk velocity is slightly higher than three times the mean thermal velocity in the simulations. However, temperature is not well-constrained by the simulations (see Figure 3). Also, the thermal velocity varies with the inverse square root of the atomic weight, yet one temperature and one bulk velocity are assumed for multiple species.
 Molecular species H2 and CO are seen in the vapor plume. In the case of the LCROSS impact, CO and H2 must be stored in the regolith as molecules or have a rapid formation process catalyzed by sudden mobility on the grain surface in order to be released as quickly and in as much quantity as observed. H2 and CO are extremely low temperature volatiles, and are not expected even with the 40K surface temperature in Cabeus [Paige et al., 2010]. Zhang and Paige  estimate that CO ice will sublimate at the rate of 1 mm/Gyr at 18 K. The temperature in Cabeus could allow ices deposited by a cometary impact to persist for long periods of time while they slowly sublime away. The volatilization of any ice would have to be extremely fast for the molecules to be accelerated to the bulk velocity by the rarefaction shock. Alternatively, the molecules may exist as trapped gases onto grains, possibly enhanced by defects due to radiation damage. If this is the case, the blisters containing the trapped gas molecules could open from the impact, allowing the gas to diffuse out. Again, assimilation into the outer shell of the vapor plume would have to be rapid. Alternatively, the grain defects could induce a weak dipole in the adsorbed CO and H2, which slightly increases its thermal stability from that of ice, yet leaves it readily available for desorption.
 It is likely that some hydrogen exists as adsorbed water on the surfaces of regolith grains as individual molecules or clusters [Hibbitts et al., 2011]. It is also possible that the hydrogen that comprises the observed H2 could have been on surfaces of grains prior to impact and released as H2. In giant molecular clouds, formation of H2 is catalyzed by adsorption to dust grains in the presence of pre-existing adsorbed OH [Duley and Williams, 1986]. Cazaux and Tielens [2004, 2010] model adsorption-catalyzed H2 formation on silicate grains considering thermal hopping and quantum tunneling using both chemisorption and physisorption sites. At 40 K, all of the physisorption sites should be vacant while chemisorption sites remain stable. Temperature programmed desorption rates for a fractional monolayer of chemisorbed hydrogen peak just at temperatures between 400 and 500 K. This process could occur on the Moon in PSRs, and the sudden mobility of the volatiles from the LCROSS impact could have spurred rapid production and release of H2 from hydrogen atoms chemisorbed on grain surfaces. Duley and Williams  predict that OH-catalyzed formation of H2 gas is exothermic, leaving the gas molecule with 0.1–0.2 eV in translational energy and an excited vibrational state. The velocity of H2 associated with 0.1 eV is 3.1 km/s, which is similar to the non-thermal velocity inferred by the analysis in section 3.2. However, the reaction considered by Duley and Williams occurs at 10 K, considerably colder than the temperature of Cabeus.
4.2. Energy Budget
 The impact of the 2300 kg LCROSS Centaur at 2.5 km/s carries 7.2e9 J of kinetic energy. Laboratory and model studies of impacts suggest that the kinetic energy of an impactor is partitioned into kinetic energy and internal energy of both the projectile and target [e.g., O'Keefe and Ahrens, 1977]. Most impact studies use higher velocity impactors. Similarly, the extreme cold of the target material and the low temperature volatiles released by the impact differ from the typically studied impact problem. Thus the actual partition of energy from the LCROSS impact into Cabeus is unknown a priori. Schultz et al. [2010a] interpret observations from the SSC to be consistent with a target with high porosity and high volatility. A large partition of energy went into compressing the target, driving material downward, and vaporizing volatiles, all of which acted to suppress the optical flash.
 From our model, we calculate the combined kinetic energy of the modeled H2, CO, Hg, Mg, and Ca. We estimate that a total of 190 kg of these 5 constituents were released. Note that this is not the total vapor released from the impact because there are other species of volatiles LAMP did not detect due to a lack of strong lines in the FUV. Colaprete et al.  reported ∼150 kg of volatiles comprised of H2O, H2S, NH3, SO2, C2H4, CO2, CH3OH, CH4, and OH in the plume from spectroscopic analysis. Killen et al.  reported sodium in the plume. However, at 3.5 km/s, the kinetic energy of the modeled species from LAMP alone is 1.2e9 J, or already about 17% of the total available energy. It is surprising that the kinetic energy in the 5 species LAMP could detect in the vapor cloud would amount to such a large fraction of the total available energy considering that other species were also released by the impact. Because the timing of the observations constrains the velocity of the vapor, this suggests that the mass inferred by the model calculations is too high. Using only the observed masses from Table 1 (i.e., not extrapolating from the small FOV of LAMP), the total energy of particles crossing LAMP's FOV is 1.4e7 J or 0.19% of the incident energy. However, a significant amount of material is certainly outside of LAMP's FOV. Thus, the isotropic assumption may not be appropriate. Given the bias of LAMP's FOV toward particles released at angles low to the horizontal, an anisotropy where low angle ejecta dominate would artificially increase the modeled total mass released, possibly explaining some of the excess in the mass estimate. LAMP data cannot be used to resolve this issue.
 Alternatively, there could be an energy source that is unaccounted for, e.g., leftover fuel in the Centaur or chemical energy stored in the lunar regolith. For example, if the H2 observed is formed as it is released using the OH-catalyzed H atom recombination mechanism proposed by Duley and Williams , the exothermic reaction is sufficient to provide its translational kinetic energy. Because the majority of mass observed by LAMP was H2 (about 60%), this provides considerable relief to the energy budget.
 There is material that is ejected in the solid phase at lower speeds that has kinetic energy [Shuvalov and Trubetskaya, 2008]. Colaprete et al.  observed an estimated ∼3150 kg of solid ejecta moving at ∼50 m/s. Additional material is released but not observed because it does not reach sunlight. However, even using 6000 kg, the higher estimated mass reaching sunlight from Schultz et al. [2010a], the kinetic energy of the solid component is a negligible fraction of the available energy.
 Energy from the impact also has to go into internal energy, raising temperatures. Standard specific heats of rock and ice are 800 J/kg/K and 2100 J/kg/K, respectively. Hayne et al.  estimate that 30–200 m2 of material to depth of a few mm was initially heated by the impact to 950 K. For regolith of density 1.8 g/cm3 and 0.5 cm, the mass of regolith heated to 950 K is 270–1800 kg. For 1,000 kg of rock heated from 50 K to 950 K, the energy consumed into heating is 0.72e9 J, which is 10% of the available energy budget, without including energy for phase changes. The energy balance would be helped if a lower mass of regolith is heated to 1000 K, or the same mass heated to a lower average temperature. A lower mass of heated regolith would imply higher regolith percentages of the observed species.
 In addition, energy from the impact has to go into vaporization of the observed materials. The energy from the Centaur projectile is insufficient for bulk vaporization of the silicate target material [Zel'dovich and Raizer, 1966; Melosh, 1989; Schultz et al., 2010a]. However, considerably less energy is needed to vaporize the highly volatile constituents of the lunar cold trap of Cabeus than to vaporize rock. Table 2 shows the heat of vaporization for the 5 species LAMP observed. To vaporize the modeled amounts of Hg, Mg, Ca, CO and H2 requires 0.147e9 J, or 2% of the energy budget. LAMP observed H2, CO, and Hg, which are highly volatile species. Refractory elements Mg and Ca were also observed by LAMP for the first time in the lunar exosphere. Since Mg and Ca have both been detected in the exosphere of the planet Mercury [Bida et al., 2000; McClintock et al., 2009] and are present in high abundance in the lunar regolith [McKay et al., 1991], their release is not surprising.
Table 2. Parameters Relating to the Abundance in the Source Regolith for the Volatiles
Modeled Amount Released (kg)
Heat of Vaporization (kJ/mol)
Boiling Point (K)
Abundance in 3150 kg Regolith (wt %)
Predicted Abundance (wt %)
Required Mass of Regolith From Predicted Abundance (kg)
 In section 3.3, the model relates the observed amount of each species to the total amount of each species that is released. The next step is to relate the amount released to the mass of regolith from which it is derived to determine its abundance within the regolith in the Cabeus cold trap. Determining the volume of regolith from which the gases are derived is a problem requiring a hydrodynamic simulation, which is not done here. Instead, here we present previous expectations of abundances and determine the associated volume of regolith the modeled release would need for the amount released to match the expectations. These are all uncertain values, owing to the uncertainties with the vapor mass estimates from the model and the impact dynamics that are not explored in this paper.
 A first order estimate comes from assuming that all of the observed species are derived from the same mass of regolith. An estimate can be made using the mass that is excavated from the crater. If a total mass of 3150 kg of regolith completely liberates its volatiles, the relative abundances of Hg, Ca, Mg, CO, and H2 are 0.39%, 0.50%, 0.12%, 1.3% and 3.7% by weight in the regolith. These values are shown in Table 2. However, these species have different volatilities. It is more reasonable for the different species to be derived from different total masses of regolith. Table 2 gives the heats of vaporization and the atmospheric boiling point of each species. From these quantities, the boiling point at any pressure can be calculated. It is outside the scope of this paper to examine the temperature and pressure functions during the early stages of the impact, when vaporization occurs. Yet the boiling point gauges the relative volatility. At any conceivable pressure, the 950 K temperature Diviner measured after impact [Hayne et al., 2010] far exceeds the temperature needed to vaporize Hg, H2 and CO. Therefore, the amount of material that was heated enough to vaporize the more volatile constituents was probably greater than ∼1000 kg of material that was heated to 950 K. In contrast, at 1 atm., 950 K is less than that needed to release Ca or Mg. Mg and Ca are probably derived from a smaller mass of regolith than 1000 kg.
 Abundances of MgO in returned Apollo samples are around 7–11 wt% [Papike et al., 1982 and references therein]. Counting only the mass of Mg, the predicted abundance of Mg in the cold traps is 6 wt. %. The CaO abundance in Apollo samples is ∼10–14 wt. % [Papike et al., 1982]. The mass of Ca predicted to be in the regolith is then about 9 wt. %. However, Cabeus is more consistent with Apollo 16 soils, which are more Ca-rich with 3 wt% Mg and 11 wt% Ca [McKay et al., 1991]. If their release is stoichiometric and complete, that implies that they are released from 110 to 140 kg mass of regolith. These values appear in the last column of Table 2, which provides the mass of regolith needed to have the modeled amount of material released fit the predicted abundance. This is consistent with a smaller mass that might reach vaporization temperature for Mg and Ca. The calculation that the Ca derived from a slightly greater mass of regolith than Mg is counter to expectation based on the relative volatility of those species. Perhaps Ca/Mg is slightly higher in Cabeus than in returned highlands soils.
 The presence of Hg in lunar cold traps is proposed by Hodges . Reed  uses gradients Hg concentrations in Apollo drill cores to estimate the exchange between the surface and the exosphere. Assuming 50% delivery efficiency to the cold traps, Reed  predicts Hg quantities of 0.02 g cm−3 (0.28 wt. %) in lunar cold traps. With a volatility temperature of 140 K [Paige et al., 2010], Hg is likely derived from a mass greater than the 1000 kg that reaches 950 K. The regolith abundance that is suggested by using 3150 kg is 25% higher than the value predicted by Reed, well within the uncertainties in interpreting LAMP observations in terms of regolith abundance and the uncertainties associated with extrapolating Apollo abundances to cold-trapped abundances. For the Hg to have an abundance of 0.28 wt %, the Hg would have to be released from 4400 kg of regolith.
 Neutron spectrometers onboard LRO and previously on Lunar Prospector both detect depressions in epithermal neutron fluxes at Cabeus [Mitrofanov et al., 2010; Feldman et al., 1998]. Neutron data is ambiguous in that it is sensitive to the presence of hydrogen atoms, but cannot determine in what form the hydrogen exists in the regolith. Within Cabeus, the LEND instrument on LRO determined a hydrogen abundance of 0.047 wt. % with a spatial resolution of 10 km [Mitrofanov et al., 2010]. Lunar Prospector neutron measurements were modeled by a pixon deconvolution to be consistent with 0.08 wt.% of hydrogen concentration in Cabeus [Elphic et al., 2007]. Any H2 in the regolith would contribute to the neutron absorption signal detected at the poles if it resides in the top 1 m of regolith. Furthermore, LCROSS detected water ice in the ejecta [Colaprete et al., 2010], further increasing the total amount of hydrogen released by the LCROSS impact. Thus the hydrogen present in the PSRs is likely in multiple forms. Because of the extreme volatility of H2, only a small rise in temperature is needed to mobilize it. Using the LEND-derived H abundance, the mass of affected regolith would have to be ∼250,000 kg to account for merely the H2 released, and more would be needed to also account for the water. Assuming a density of 1.8 g/cm3, 250,000 kg comprises a cube of 5.2 m on a side, which is still smaller than (∼20% of) the expected volume of the crater of 25 m diameter and 3 m depth [Schultz et al., 2010a]. This mechanism is consistent with the lower temperature associated with the H2 observed by LAMP compared to the species in the 180–190 nm plume.
 Alternatively, the low values from neutron spectrometry compared to the H in the LCROSS vapor plume could suggest that hydrogen is concentrated in rich areas smaller than the 10 km footprint of the neutron measurements. Lateral heterogeneity is expected from space weathering modification of a volatile deposit on the Moon [Crider and Vondrak, 2007]. Another possibility is that the H2 excavated by LCROSS might be buried by dry regolith and resides below the ∼1m depth sensitivity of neutron detection of hydrogen. However, Korycansky et al.  show that over half of the ejecta is derived from the top meter of regolith through impact modeling, refuting the possibility that the H2 was derived from greater depth.
 Before the LCROSS impact, it was thought that CO was not stable enough to remain in lunar cold traps. Thus no predictions exist on the amount of CO in lunar PSRs. Gibson and Moore  did detect a signal at mass 28 during thermal gas release experiments on Apollo sample 61221. This sample comes from 30 to 35 cm below the lunar surface and is very immature. They postulate that these gases remain from the cometary impact that formed North Ray crater. The mass 28 signal comprised 2–5 wt% of the gases released between 175°C and 350°C, compared to 5–10 wt% H2. The relative abundance of H2 and CO observed after the LCROSS impact is consistent with the relative abundance derived from sample 61221.
4.4. Source of Volatiles
 CO is a very low temperature volatile [e.g., Zhang and Paige, 2009] that is prevalent in the interstellar medium and in comets. The abundance of CO is about 1/3 that of H2 in the vapor plume. If CO was deposited by a comet impact on the Moon, it would be accompanied by carbon dioxide, methane, methanol, ethane, ethanol, and formaldehyde among other volatiles, and Colaprete et al.  observed many of these associated species from the LCROSS Shepherding Spacecraft. Work has not yet been done to put the abundance of CO in perspective with those reported by Colaprete et al. . LAMP and the SSC have orthogonal fields of view, therefore more data are available to constrain the modeling. Colaprete et al. suggest that the relative abundances of molecules they detected are more commensurate with hot molecular cloud core abundances. Both CO and H2 formation are consistent with this scenario, where cold grain chemistry synthesizes molecules in the lunar cold traps.
 The abundances of Mg and Ca are consistent with highland soils [Papike et al., 1982]. Therefore, they appear to be lunar materials that have no enhancement at the polar cold traps. In contrast, the abundance of Hg is consistent with the migration of Hg from low latitudes through the atmosphere of the Moon for eventual deposition and condensation in the cold traps [Watson et al., 1961; Hodges, 1981; Reed, 1999]. The Hg is also indigenous to the Moon; however, exists in enhanced quantities in the cold trap.
 LAMP's observations of the LCROSS vapor plume detected 5 species in the exosphere of the Moon for the first time: H2, CO, Mg, Hg, and Ca. Through modeling, we find that the vapor observed by LAMP emanating from the LCROSS impact into Cabeus is consistent with an isotropic vapor cloud released with a bulk velocity component of 3.5–4.0 km/s for Hg, Mg, and Ca, with temperature being less constrained. At these velocities, the majority of the vapor escapes the Moon. This is consistent with the fact that LAMP did not observe any emissions on the subsequent pass two hours later. The bulk velocity is necessary to fit the timing of the LAMP light curve. Especially for the Hg, Mg, and Ca light curve, the narrow peak requires a nearly simultaneous, instantaneous release of these species.
 For the H2 and CO light curve, isotropic model runs with a bulk speed of 3.0–3.5 km/s and temperature from 500 to 1000 K provide the best fit to the data. The lower apparent translational kinetic energy associated with the molecular constituents might arise from the additional degrees of freedom that molecules have over elemental species. The longer decay of the light curve after the peak for the H2 and CO light curve comes from the high thermal speed of H2, which provides a wider range of velocities in the vapor plume.
 The total modeled abundance of ejected vapor is about 3.8, 12.4, 16, 41, and 117 kg for Mg, Hg, Ca, CO, and H2, respectively, assuming an isotropic distribution and about 3.5 km/s non-thermal velocity. H2 and CO are highly volatile and are likely released from a larger mass of regolith than the other species observed. Mg and Ca are less volatile and might be released with lower efficiency than for the highly volatile Hg, H2, and CO. In order for the abundances to match expectations, the Mg, Hg, Ca, CO, and H2, would be released from 110 kg, 4400 kg, 140 kg, 180,000 kg, and 250,000 kg of regolith, respectively. This is consistent with the difference in volatility of these species.
 The high abundance of hydrogen compared to neutron measurements may indicate that the hydrogen might be derived from depths greater than the 0.5–1.0 m over which neutron measurements integrate and/or a heterogeneous lateral distribution on the scale size of the neutron spectrometer footprint. The abundance of Hg in the cold traps agrees with the migration of indigenous Hg to the cold traps through the lunar exosphere. The abundances of Mg and Ca are consistent with Apollo 16 type soils. Interestingly, the relative abundance of CO to H2 is similar to the trapped volatiles in a subsurface Apollo 16 sample thought to be associated with the comet impact that formed North Ray crater.
 This work was supported by NASA Lunar Reconnaissance Orbiter and by the NASA Lunar Science Institute through grant NNA09DB31A. We thank the referees and editors for helpful comments.