Modeling of the vapor release from the LCROSS impact: Parametric dependencies

Authors


Abstract

[1] The Lunar Crater Observation and Sensing Satellite (LCROSS) mission included an intentional impact into the Cabeus crater, a permanently shadowed region near the Moon's south pole. The impact produced a vapor plume of volatile species liberated from the impact site. Using a Monte Carlo model to simulate the vapor plume expansion, this paper investigates the expansion as a function of the physical properties of the gas. For a thermal release scenario, the cloud expands with the highest density at the center, with the density dropping within the cloud in time as the cloud expands. When a significant non-thermal component to the velocity (a bulk speed) exists, the vapor expands as a hemispheric shell outward from the impact site. For heavier species, the high bulk velocity produces a hemisphere of higher density of gas that appears as a ring from above. For lighter gases like H2, the thermal velocity is on the same order as the bulk velocity. If the source is prolonged, the source rate is dominant in determining the local density, however. Gases produced by photodissociation have a prolonged source close to the impact site compared to promptly produced vapors.

1. Introduction

[2] On 9 October 2009, the Lunar Crater Observation and Sensing Satellite (LCROSS) experiment succeeded in crashing two projectiles into a permanently shadowed region (PSR) on the Moon [Colaprete et al., 2010]. The first projectile was the empty Centaur stage of the Atlas V lift vehicle. The Centaur, weighing approximately 2300 kg, was a cylindrical, hollow, metal projectile that possibly was tumbling on impact. It was hardly an “ideal” impactor [Davis, 2009; Schultz et al., 2010]. The second projectile was the shepherding spacecraft (SSC), which was instrumented to measure and transmit data from the Centaur impact. The SSC impacted the Moon 4 min after the Centaur.

[3] The Centaur hit the Moon at a velocity of 2.5 km/s, slightly higher than lunar escape speed. This is not energetic enough to vaporize either the projectile or the target rock [e.g., Melosh, 1989]. However, the thermal wave would release some of the highly volatile species that are trapped in the extreme cold of Cabeus crater. Thus it was a clever technique to explore the volatile components stored within the crater.

[4] The target was Cabeus crater, which contains a permanently shadowed region on the Moon that is a potential reservoir for ice. The fact that it is in permanent shadow precludes mapping of the impact location in visible light. The Lunar Reconnaissance Orbiter (LRO) began to characterize the southern polar region of the Moon in its commissioning phase. These preliminary data were used to help pick the impact site [Mitrofanov et al., 2010; Paige et al., 2010]. As the Lunar Reconnaissance Orbiter mission continues, altimetry, radar, neutron, thermal, scattered light, and UV mapping will look into the region [Vondrak et al., 2010]. However, prior to impact, the target was not fully characterized in terms of composition, porosity, and topography.

[5] With non-ideal projectiles, poorly quantified targets, and borderline energy regimes, the parameter space for characterizing the impact is broad [e.g., Davis, 2009; Korycansky et al., 2009; Summy et al., 2010; Killen et al., 2010]. The instrumentation on the SSC observed the impact flash, curtain and plume, and crater over a broad spectrum [Colaprete et al., 2010]. Lunar Reconnaissance Orbiter (LRO) passed by the impact site between the times of the Centaur and SSC impacts [Gladstone et al., 2010]. Ground based observatories watched the event [e.g., Killen et al., 2010; Hong et al., 2011; Miller et al., 2009; Heldmann et al., 2011]. Thus, data were taken from multiple perspectives to determine the composition and quantities of materials in the ejecta.

[6] A good way to constrain a broad parameter space and to compare an array of data is to model the event under a range of conditions and find the parameterization that best explains the data. A Monte Carlo model of the Moon's exosphere [Crider and Vondrak, 2000, 2002] is run for the conditions of the LCROSS experiment in a few select physical regimes. This paper provides an in-depth explanation of the model. It analyzes the propagation through the model of various choices regarding the physical assumptions to demonstrate how observations at later times can distinguish between physical scenarios. These results may guide mission planning and selecting viewing geometries for future, similar experiments that might be flown. Additionally, the results presented here may serve as a guide for interpreting existing data of the LCROSS plume. In this paper, the model output is presented as a “big picture” framing the observer field of view. The breadth of potential initial conditions is explored.

[7] However, detailed comparisons of the model output to far-ultraviolet data of the LCROSS impact plume are discussed in an accompanying paper (D. M. Hurley et al., Modeling of the vapor release from the LCROSS impact: 2. Observations from LAMP, submitted to Journal of Geophysical Research, 2011); and comparisons to other data are left for future work. The evolution of the plume appears different depending on the species being examined [Colaprete et al., 2010; Killen et al., 2010; Schultz et al., 2010; Gladstone et al., 2010]. The complete presentation of the parametric dependences of the model in this paper serves as a standard reference for those investigations. By discussing the data sets in separate papers, it enables a detailed analysis of the specific issues elucidated by the data analyses without dilution with discussion of details irrelevant to that particular observation.

2. Monte Carlo Model Description

[8] The simulation is a Monte Carlo model that follows the trajectory of particles through the Moon's atmosphere under gravity [Crider and Vondrak, 2000, 2002]. The model is based on earlier work by Arnold [1979] and Butler [1997]. The model takes an input of spatial and velocity distribution of particles and follows them through time accounting for interactions with the surface, photolysis, and escape. This version of the model has been used on both Mercury and the Moon to simulate a variety of atmospheric components, including H2O and all of its fragments. The application to the LCROSS vapor plume involved little modification to the existing model.

[9] Particles are released in the simulations from a specified location, i.e., the impact site. The actual topography of the Moon is not explicitly included in the simulation because the scale size of the particle motion is much larger than the lunar topography. However, it will be worthwhile to do one or two scenarios with actual lunar topography once an accurate map of the impact site and local topography becomes available.

[10] A velocity is assigned to the particle when it is released, and several velocity distributions were tested. Most of the work presented here bases the initial velocity on a Maxwellian velocity distribution based on an assumed temperature [Smith et al., 1978]. Details of the assumed velocity distribution follow in the next section, as variations are introduced to demonstrate the effects that various assumptions about the release mechanisms make on the evolution of the plume. The “release temperature” used in a collisionless simulation is equivalent to the Maxwellian distribution at the point the gas becomes collisionless.

[11] Once initialized with a position and velocity, each particle then follows a ballistic trajectory under lunar gravity. The Monte Carlo model assumes that the particles comprise a collisionless vapor. If the density is high enough that collisions occur, this model is not the appropriate choice. However, for an expanding vapor plume, as is expected in the LCROSS aftermath, the vapor reaches a collisionless state very quickly. The point where the vapor plume becomes collisionless depends on the actual mass of material released and the energy associated with the material. Model results indicate that this occurs within the first half-second of expansion and at a radius on the order and just below 1 km. Applications presented in this paper are for times much longer than 1 s and for distances much greater then 1 km.

[12] Although the model can be used with radiation pressure, it is expected to be a small modification to the acceleration, and is thus, neglected. Therefore the model uses the equation of motion including only gravity to compute the trajectories of the particles after release. While the particles are in flight, the model determines whether each particle is illuminated and calculates the probability of photolysis [Huebner et al., 1992]. It records any photodissociating or photoionizing reaction and stops tracking those particles. The photodissociation products can then be used as input to a subsequent model run that tracks those species from their creation onward. If the particles reach the edge of the simulation space, they are recorded as escaped particles and tracking stops. The size of the bounding box used did not affect the results because any particles that escape the bounding box in the simulation time would not return to the simulation box if tracking were to continue with them.

[13] If a particle survives to reencounter the surface, the model has a package that handles the surface interaction. In the simulations presented here, between 0.1% and 2% of particles reencounter the surface in the simulated time period. Thus the exact sticking function and reemission function used has little effect on the outcome of the simulations. The sticking module approximates adsorption by allowing the user to choose a sticking function. For inert gases and gases with low activation energies, the material does not stick to the surface. If adsorption is a possibility, the model can handle it by setting a sticking temperature, below which particles stick until the temperature increases. Particles that do not stick are reemitted from the surface with an energy assigned from a linear combination of an energy chosen from the local thermal distribution and the rebound energy, approximating any degree of partial thermal accommodation. The combinations selected for these simulations are either purely rebounding, purely thermalized, or comprised of the sum of half of the rebound energy and half from the local thermal distribution.

[14] Because the LCROSS impact was a singular, instantaneous event, the simulations proceed in time from the impact time in 1-s increments until the gas is lost from the system or until the time of interest passes, depending on the run. Loss processes that are included are photolysis, escape, and sticking to the surface. Very little loss occurs during the period of interest, i.e., the first ten minutes when there are observations for comparison. Runs simulating the prompt vapor release do consider the entire vapor cloud to be released instantaneously. In contrast, there might be a sustained production of vapor sublimating off of illuminated crater ejecta, mobilization from warm ejecta emplacement, or fragments created by photodissociation of other vapor. Some simulations for sustained production are presented here as well.

[15] The Sun is the most important factor in the atmosphere dynamics. Therefore, the simulations are done in a Sun-State (SS) coordinate system, where +x points from the center of the Moon to the Sun, +y is opposite to the direction of the motion of the Earth-Moon system in its revolution around the Sun, and +z points north from the ecliptic plane. For simulations of the LCROSS impact, the model releases particles at the impact site in Cabeus (314.5°E. Long., 84.74°S. Lat.). On 9 October 2009 at 1131 UTC, the subsolar point on the Moon was 1.51°S. Lat, 291.9°E. Long. In SS coordinates, the impact location was 83.4°S. Lat., 17°E. Long. Thus, the plume was near 1 P.M. local time and a solar zenith angle near 83°.

[16] The advantage of a Monte Carlo treatment of the lunar exosphere is that individual species can be treated separately. Likewise, if multiple mechanisms are involved for a given species, the distributions resulting from each mechanism can be treated separately. Then, to find the expected values, one can simply add the different distributions in proportion to their expected source rate. For example, Schultz et al. [2010] found that the plume consisted of a low angle and a high angle component. Artem'eva et al. [2001] and Korycansky et al. [2009] show that an anisotropy exists in the distribution of velocity such that the material traveling nearly vertical is moving faster than material traveling closer to the horizontal. This Monte Carlo model can be run separately for several release angles, the output compiled and compared to the data. Similarly, the model can approximate a prolonged source by adding the vapor distribution from several time steps, if done carefully. The disadvantage of this treatment is that collisions are neglected.

[17] Collisions occur in the very early times of the vapor plume expansion. During the collisional phase, a gasdynamic approach is appropriate. Davis [2009] applies analytic solutions to vapor plume expansion into a vacuum for the LCROSS impact to predict the impact flash in the initial milliseconds. The parameters of the impact put a limit on the maximum bulk velocity of 5.5 km/s, which is achieved in 10–20 ms. By that time, the size of the plume is 0.110 km in radius with an average temperature of 3500 K. Korycansky et al. [2009] use an array of modeling techniques to simulate the LCROSS impact. The RAGE code handles the vapor plume evolution from impact to 70 ms and 0.5 km height. The RAGE simulations demonstrate that the plume expands hemispherically during the initial phase and comprises 1e5 kg of mass in the vapor plume at 70 ms. The calculations predict greater speeds close to the vertical than close to the horizontal with a maximum speed of 7 km/s and a temperature <1230 K. The gasdynamic output should be the input to the Monte Carlo simulations. A Monte Carlo code begins at the point where collisions become unlikely, which is at such early times and small distances that they are not far from the origin on the scales of interest in the Monte Carlo model. Thus the most important parameter for initializing the Monte Carlo code is the velocity.

[18] Summy et al. [2010] perform simulations that cover both the collisional and the collisionless phases of the LCROSS impact. They simulate the evolution of the dust plume. Then they simulate water subliming off of illuminated dust. The prolonged source calculations shown in section 3.3 of this paper are similar to those simulations [Colaprete et al., 2010].

3. Parametric Study

[19] Before directly comparing the simulations to the observations, it is instructive to first investigate the parametric dependence of the evolution of the vapor cloud on the physical assumptions used in the model. The model is run through a range of possible values of initial temperature, bulk velocity, and release rate. These parameters are varied one at a time and the effects are studied from various perspectives in this paper.

3.1. Initial Temperature

[20] One of the parameters used in the model is the initial temperature of the gas release. The temperature of the release of gas might be determined by the thermal wave resulting from the impact [Hayne et al., 2010], from sublimation off of grains lofted into sunlight [Schultz et al., 2010], or from excess energy in photon stimulated desorption or photodissociation reactions [Huebner et al., 1992]. In the model, the velocity assigned to each particle upon release is taken from the velocity distribution function for the assumed temperature [Smith et al., 1978]. Because the molecules move on ballistic trajectories without interacting, the initial velocity governs the dispersal of the plume.

[21] Figure 1 shows the column density looking across the cloud at a time of 45 s after impact for four different assumed initial temperatures: 200 K (first panel); 500 K (second panel); 1000 K (third panel); and 1500 K (fourth panel). Each panel uses the same scale for the column density (right). This example shows the evolution of calcium, although it is representative of a typical vapor. Calcium is chosen because it is one of the species observed by LAMP [Gladstone et al., 2010]. The column density is normalized to a 1 kg release of Ca, so the expected column could be multiplied by the actual amount of Ca released to get the resulting column density of Ca. Immediately obvious are two properties with increasing temperature. The hotter initial temperature produces a larger cloud with lower peak density. In general, lower temperature means lower velocity. Thus, lower temperature gases expand more slowly than higher temperature gases. For a cold initial temperature, the cloud remains compact and dense for a longer time than for a higher initial temperature. Thus, the highest densities are expected for a low temperature release.

Figure 1.

A snapshot at 45 s after impact of the modeled column density of the initial vapor cloud is shown from the side view. The four panels show the calcium abundance from top to bottom for T = 200 K, 500 K, 1000 K, and 1500 K.

[22] Taking a closer look at the expansion of the clouds, one can examine the effective size of the cloud as a function of temperature. For each of H2 and CO (which were both observed by LAMP), the cloud radius at 90 s after impact as a function of temperature is plotted in Figure 2. The cloud size is quantified by taking the full width at half of the maximum (FWHM) of the column density in the horizontal cut that includes the peak column density and is parallel to the tangent to the surface at the impact point. For H2, a light molecule, the FWHM at 90 s for a 200 K expansion is 168 km ± 22 km. This implies a bulk velocity of 1.9 km/s. For 500 K, the FWMH is 267 km ± 36 km. For the 1000 K H2 cloud, FWHM is 379 K ± 51 K. And for 1500 K, FWHM is 464 km ± 62 km, implying a bulk speed of 5 km/s. The escape speed is 2.38 km/s. In Figure 2, the effective cloud size is fit very well by a function that is proportional to the thermal velocity, i.e., to the square root of the temperature over the square root of the mass.

Figure 2.

The relationship between the size of the vapor cloud and the release temperature at 90 s after impact. Model results from H2 are shown with squares and from CO with diamonds. The dotted lines show a function proportional to the square root of temperature over mass. The error bars are the ±1 σ error bars propagating the model error into the Gaussian fit algorithm.

[23] Figure 2 also displays the size of the cloud at 90 s after impact for simulations of carbon monoxide. Those results are fit by the same function of thermal velocity with the same proportionality constant. Again, the width of the cloud increases with the square root of the assumed initial temperature. The width of the cloud is smaller than that of H2 by the inverse square root of the molecular weight because CO is heavier. For a 200 K release, the FWHM of the CO cloud is 43 km ± 5 km. At 1500 K, the CO cloud size is 120 km ± 15 km. These correspond to a velocity, including projection effects of 0.5 and 1.3 km/s, respectively. The CO cloud is expanding slower than the escape speeds for these simulations.

[24] The other major effect of different initial temperature is the peak column density observed. In Figure 1, the peak column density of calcium for the 1500 K run is a factor of 6.3 lower than for the 200 K run at 45 s after impact. Figure 3 shows the column density calculated in the model runs as it would be observed from LRO for the release of 1 kg of H2. For the same amount of H2 released, the highest column density is observed for the lowest temperature model run. From this perspective, the timing of the light curve is a large function of temperature as well. This is because the higher temperature gas expands more quickly to reach the field of view of the observer sooner than the lower temperature gas.

Figure 3.

The time series of the simulated column density shown as it would be observed from LRO for the release of 1 kg of H2 for 200 K (solid line), 500 K (dotted line), 1000 K (dashed line), and 1500 K (dash-dotted line) thermal releases.

[25] In interpreting data from observations of the impact, one takes the observed column density and uses the model to convert it into a total mass of material released. The initial temperature affects the results when applying this process. For a constant column density at a certain time, more total gas would have to be released if the initial temperature were low than if it were high. Killen et al. [2010] demonstrated that the total inferred mass released based on ground-based observations of sodium column density increases as a function of assumed release temperature. Part of the sodium results displayed there are reproduced here in Figure 4. The scatter in the plot is due to the small number of particles used in the Monte Carlo runs, however the trend is evident. For a 200 K sodium release, 0.3 kg of sodium would have to be released to produce the observed column density. If the initial temperature were 2500 K, the initial amount of sodium would have to be closer to 10 kg to produce the same observed column. Thus being able to constrain the temperature through secondary observations would provide the information needed to constrain the total mass of material released from a peak column density observation.

Figure 4.

The inferred total mass of sodium released from the LCROSS impact by converting the peak column density observed to the mass release that would reproduce that column abundance as a function of the temperature used in the simulation (modified from Killen et al. [2010]).

3.2. Bulk Velocity

[26] One of the prompt effects of a high-velocity impact is the propagation of a shock out from the impact site. Vapors released by the impact have a velocity component from the shock that excavates material out of the crater. This produces the bulk expansion radially outward in the upward hemisphere from the impact site into the vacuum. A thermal component to the velocity exists in addition. This effect is modeled by the superposition of a bulk velocity in the radial outward direction and the thermal velocity in a random direction. Figure 5 shows the modeled magnesium column density at 90 s after impact from LAMP's perspective for 4 different runs: bulk velocity of 2, 3, 4, and 5 km/s. Magnesium was observed by LAMP. Using a low temperature (200 K) in this example accentuates the effects originating from the bulk velocity. Typical prompt vapor expansion occurs at about 3 times the thermal velocity [Zel'dovich and Raizer, 1966] and rarely much exceeds the impactor velocity. The expectation in the LCROSS impact is for an expansion between 1.5 km/s (3 times thermal velocity) to the impactor velocity of 2.5 km/s; thus some of the bulk velocities shown here are much higher than dynamically expected. The 2 km/s runs are more realistic than those with higher values. Furthermore, a spread in bulk velocity is more realistic than a single value.

Figure 5.

The column density of magnesium shown at t = 90 s after impact from LAMP's perspective for four different modeled bulk velocities: (top left) 2 km/s, (top right) 3 km/s, (bottom left) 4 km/s, and (bottom right) 5 km/s.

[27] From the side view in Figure 5, it is clear that the morphology of the cloud is a hemispheric shell. Notice that the distance to the edge of the cloud in the horizontal direction is a little less than 90 s times the bulk velocity. When a bulk velocity is not used (see Figure 1), the peak density remains in the center of the plume regardless of the initial temperature throughout the expansion of the cloud. In contrast, there is a shell of higher column density that forms when a bulk velocity component is included. The peak density in this projection moves slower than the bulk speed. For the 2 km/s bulk, the ring that forms is thick and has high peak density. For higher bulk velocity, the peak column density is lower and occurs at greater distance from the impact for the same amount of material released and the same time.

[28] From the top view, the hemispheric shell instead appears as a ring of enhanced density. Figure 6 shows the time evolution of 1000 K Ca in a 3 km/s simulations every 30 s for the first two minutes after impact from the overhead perspective. The outer edge of the cloud is at the distance equal to the bulk velocity multiplied by the time. As time proceeds, the integrated line of sight density for the expanding shell appears as a ring. The ring marches outward with time while the density everywhere decreases. The ring has not moved far away from the blast site in the 90 s in this perspective because it is the integrated column along the line of sight perpendicular to the plane shown. Thus, the intense ring appears at the place where the line of sight is longest through the expanding shell. The time dependence of the diameter of the density enhancement for water simulations for 2, 3, 4, and 5 km/s bulk velocities is given in Figure 7. The slopes of the lines indicate that the radius of the shell appears to be moving at a velocity lower than the bulk velocity used in the simulation.

Figure 6.

The instantaneous modeled column density of Ca with a bulk velocity of 3 km/s and a temperature of 1000 K is shown as would be viewed from above at 30 s intervals from (top) 30 s after impact to (bottom) 120 s after impact.

Figure 7.

The diameter of the highest density ring from the overhead perspective over time for water modeled with 4 different assumed bulk velocities: 5 km/s (solid line); 4 km/s (dashed line); 3 km/s (dotted line); and 2 km/s (dash-double-dotted line).

[29] The simulations shown in Figures 57 use an initial bulk velocity that has a constant magnitude for every particle. The thermal velocity is used to impose deviations to the bulk velocity. However, in addition, the bulk velocity is expected to vary within the vapor cloud [Zel'dovich and Raizer, 1966; Melosh, 1989; Korycansky et al., 2009]. This distribution forms during the collisional phase of the plume evolution. Gasdynamic models have been used to describe the collisional phase of the plume. Korycansky et al. [2009] simulate with the RAGE code the vapor plume from an aluminum impactor. The velocity is a function that increases with distance from the impact. However, there is an anisotropic distribution in which there are higher velocities in more vertical directions than in more horizontal directions. Further, the density is highest close to the impact site and decreases with distance. This is implemented into the model by setting the bulk velocity to a random value between 0 and a maximum value. That maximum velocity is a linear function of angle from the horizontal, where the value is double at the vertical the value at the horizontal. The maximum velocity at the vertical is set to 5 km/s.

[30] Using a similar distribution to the gasdynamic simulations as an input to the Monte Carlo model, we present the evolution of a water vapor in Figure 8. The distributions of velocity magnitude for the gasdynamic bulk velocity, the thermal velocity, and the vector combination of the two are shown on the right side of Figure 8. The simulation shown on the left side of Figure 8 uses a low temperature to accentuate the non-thermal component. The vapor plume is morphologically similar to the thermal case presented in section 3.1 (Figure 1). The peak density remains in the central plume. Without a thermal velocity adding to the bulk velocity, the plume is strongly peaked in the center on any horizontal cut through the plume. The anisotropy is evident in the greater vertical extent of the plume with the gasdynamic starting velocity than the purely thermal case. The gasdynamic simulations suggest that the temperature of the plume would be ∼1200 K [Korycansky et al., 2009]. The distribution of the combined bulk and thermal velocities is shown in the gray-shaded bars of the histogram in Figure 8. The combination appears similar to a thermal distribution, although the anisotropy in angle persists (not shown).

Figure 8.

(left) The line of sight column density from Earth's perspective of water vapor at 90 s after release shown for an initial velocity profile that is a function approximating the gasdynamic results. (right) Comparison of the distribution in velocity magnitude for the gasdynamic (red-dotted histogram), purely thermal (black-dashed histogram), and the combined (gray filled histogram). Figure 8 (left) uses the red-dotted histogram.

3.3. Release Rate

[31] All of the examples shown so far have assumed that the gas is released simultaneously and instantaneously. The prompt source is material that is in the initial vapor plume. Shuvalov and Trubetskaya [2008] estimate that 1% of water ice in the target gets vaporized on impact. However, the next examples show the structure of a gas cloud that has a prolonged source. A prolonged source matches the physical situation of a gas sublimating off of grains lofted into sunlight. Likewise, a prolonged source is appropriate for a gas produced by photodissociation of a parent gas. In addition, a prolonged source could include a slow diffusion out of the surface.

[32] Figure 9 demonstrates how the light curve observed by the descending SSC for water vapor would be for three different prolonged release rate scenarios for comparison with the instantaneous release (thin gray line). In all the scenarios, the same total mass of water is released. The constant release rate (solid black line) assumes the release of 1 kg s−1 H2O release rate for the first 120 s after impact. After an initial ramp up in the observed column density, by t = 20 s, the source rate balances the expansion rate to produce a relatively flat light curve until the source is artificially turned off at t = 120 s. Figure 9 also shows in the dashed line the column density that would be observed by the SSC if the source rate were linearly decreasing with time from 2 kg s−1 at impact to 0 at t = 120 s. In this case, the same amount of H2O is released over the first two minutes as in the constant release case. However, the front-loading of the release in time produces a decreasing nadir column visible to the SSC over time. In contrast, when assuming a linearly increasing release rate from 0 kg s−1 at impact to 2 kg s−1 at t = 120 s, the nadir column increases (dotted line) as the spacecraft descends through the vapor plume until the source is artificially cut off at 120 s. Comparing to Colaprete et al. [2010] observations of water vapor, this modeling suggests that a prolonged release mechanism is most consistent with the observations, although detailed comparisons have not yet been done with this model. Colaprete et al. [2010] use simulations of water vapor subliming off of illuminated ejecta particles to interpret the measurements.

Figure 9.

The water column abundance from the perspective of the field of view of the LCROSS SSC as it descends toward the Moon for 4 time profiles of the release of 120 kg of water: instantaneous release (gray); constant for 120 s (solid black); linearly increasing release rate over 120 s (dotted); and linearly decreasing source rate over 120 s (dashed). The FOV is assumed to be 1° looking nadir at 600 km at t = 0 and descending immediately over the impact site at 2.5 km/s.

[33] From Figure 9, the release rate is more important than the total amount of gas released in determining the column of material immediately above the impact site. Materials disperse from the central plume with only ∼10% remaining in 1° of vertical within 20 s after release. This is the natural tendency for material to spread out from a point source. The crater remains approximately a point source for material that sublimes off of lofted grains or that steams out of the warm crater or from the warm emplaced ejecta over top of volatiles that were previously at 40 K.

[34] For OH and other daughters of water vapor, photoproduction represents a prolonged source even if the water is released instantaneously. If the water has a prolonged source, then there are two prolonged sources contributing to the production of OH, O, H, and H2. The photodissociation products of an instantaneous water release are shown in Figure 10. The absolute production rate is already figured into the calculations using the water dissociation branching ratios of Huebner et al. [1992] for quiet Sun conditions. The primary branch of the photodissociation of water is the OH + H reaction. When considering all of the reactions the relative amount of H, H2, O, an OH produced from photodissociation is 0.98, 0.05, 0.11, and 0.86, respectively, for each water molecule dissociated. Thus, the densities are higher for H and OH than for H2 and O, because of their greater production rates.

Figure 10.

Photodissociated daughters from instantaneous H2O source 45 s after the release. The plots give the number of particles in the horizontal column of (top to bottom) H, H2, O, and OH. Each is displayed in proportion to the amount of water released.

[35] In Figure 10 (top) H has the largest spatial extent owing to its high velocity in the dissociation reaction. OH and O have a relatively small spatial extent, remaining close to the production site with a size similar to the H2O cloud from which they originated.

[36] Photoproduction is a prolonged source for an instantaneous water release. Because the photodissociation rate is so small, the daughters are produced at a near constant rate over the short time considered here. In Figure 11, the time evolution of the spatial extent of the photoproduced OH and the column density in the side view are shown. The OH cloud grows in diameter (radius) with time at 1.7 km/s (0.9 km/s) from a linear fit to the FWHM function in Figure 11. The peak column density increases rapidly for the first 20 s, showing the production rate of new OH molecules. However, then the peak density begins to increase more slowly. Secondary species, e.g., those produced by photodissociation, are not produced by a point source. As the water vapor cloud disperses, the spatial volume over which the daughter species is produced increases. Furthermore, those daughters then travel on in a random direction from the production site. Those daughters repopulate the central plume area, but slowly. Thus, the modest growth of the central peak at times greater than 40 s is the combination of the growing size of the production volume from the expansion of the water vapor cloud and from the dispersal rate of the newly produced OH approximately balancing the increasing total number of OH molecules.

Figure 11.

The full width at half maximum and one sigma error bars shown for OH photodissociated from a water cloud as a function of time. The peak value of the density is provided by the dashed line in units of 108 particles.

[37] However, there can be two simultaneous prolonged sources for water's daughters. The water itself may be produced over a sustained time period from sublimation or seepage. That water is then photodissociated, producing daughters in proportion to the parent's abundance. Figure 12 shows parameters describing the evolution of the OH vapor cloud under 6 different water release scenarios. The water release rates over the first 120 s are shown in the top panel. In each scenario, a total of 120 kg of water vapor is released, however the timing of the source is different for each scenario. The water is subject to photodissociation in sunlight to produce the OH that is also tracked after production. The production scenarios considered include the ones described above for Figure 9: instantaneous water release; constant (flat) water release rate; linearly increasing water release rate; and linearly decreasing water release rate. Two additional scenarios are also shown here. One is a step function where the water is released at a constant rate over the first 20 s, after which no more water is released. It is interesting to compare this scenario with the flat scenario to examine the differences once the source is turned off in the step function. The second is a triangle function where the release rate ramps up for the first 60 s, then ramps back down. This is interesting to compare with the linearly increasing scenario because for the same amount of water to be released over the 2 min, the release rate for the triangle function is exactly double that of the increasing function over the first minute.

Figure 12.

The evolution of the OH cloud that forms from photodissociation of a water cloud that has a prolonged source. (a) Source rates. (b) The size of the cloud measured by the full width at half of the maximum. (c) The peak column density observed from the side view, plotted as a function of time. (d) Same as Figure 12c except that the values are normalized to account for the varying amounts of OH in each scenario.

[38] Figure 12b shows the diameter of the cloud as observed from the side perspective for OH. The thin solid gray line shows the rate for the instantaneous water release, as also appears in Figure 11. Note that this scenario produces the broadest cloud of OH. This is because the other scenarios with a prolonged water vapor production keep resupplying water in the central plume, whereas the water in the instantaneous release can only keep expanding. For the flat water-production scenario, the cloud diameter (radius) grows at 1.1 km/s (0.5 km/s). Unsurprisingly, the step function tracks the cloud size of the flat function exactly until the source is turned off in the step function. By 13 s after the end of the step, the cloud diameter of the step is 10% larger than of the flat function. The increasing function and the triangle function track each other in cloud width while the triangle function is in the increasing phase. When the water production is weighted more heavily to later times in the “increasing” case, the cloud diameter (FWHM) grows at 0.7 km/s. The decreasing case has a cloud size that is smaller than the step function and larger than the flat function. However, the decreasing case is very close to the flat function and does not grow larger than 10% bigger than the flat function until 79 s into the event.

[39] Figure 12c shows the peak column density as a function of time for the side view. From Figure 10, the peak column is just over the impact site. The highest peak column density for all times is from the instantaneous release case. Although the cloud disperses, there are simply more OH molecules existing at all times from this scenario because all of the water vapor is subject to photodissociation for the entire time period. But compared to the density from the step function, the peak density nearly catches up to the instantaneous function about 40 s after the source shuts off demonstrating that the dispersal of material in the instantaneous case is offsetting the lower total number of OH in step function case. Comparing the step function and the flat function demonstrates that the release rate being higher at the beginning is important in determining the peak column density. The cloud shape (Figure 12b) is the same but the peak density is different. Similarly, the triangle function has a greater release rate than the increasing function at early times, thus the peak column for the triangle is larger than for the increasing function. Thus the most important factor in determining the column density of a daughter like OH is the integrated amount of water vapor exposed to sunlight over time, i.e., the time integral of the water release rate. Comparing this panel to the OH feature observed by Colaprete et al. [2010] suggests that two sources of OH might contribute to the observations. One promptly released population could provide the broad peak in the first 50 s. The secondary peak could be from photodissociation of a prolonged water vapor source. Detailed comparisons have yet to be done.

[40] Accounting for the total amount of OH in existence by dividing the peak column density by the total number of OH (Figure 12d), the normalized central column density shows much less dependence on the release scenario. The curves are inverted from Figure 12c. The increasing function is on top and the instantaneous function on the bottom. This occurs because of the higher source at the center at late times for the increasing function. The exponential fall off of all the curves shows the effect of expansion on the central plume. The varied source timing is at most a factor of 2 in the peak density. However, the cloud expansion has an effect of an order of magnitude. For the nadir look direction, the parameters evolve in a similar manner, but are not shown.

3.4. Species Mass

[41] The observed gas species have a range of masses, from H2 at 2 AMU to Hg at 201 AMU. Models are also run for species H (1 AMU), O (16 AMU), OH (17 AMU), H2O (18 AMU), Na (23 AMU), Mg (24 AMU), CO (28 AMU), and Ca (40 AMU). As discussed in section 3.1, the particle mass is important in the thermal velocity, which in turn drives the expansion rate.

[42] In addition, the plots in this section are normalized to particles per kilogram of that species of gas. Thus there are fewer particles in the plots for the heavier particles. This offsets the increase in density for the slower speed particles.

[43] The solid ejecta emanating from an impact has a distribution resembling an upside-down lampshade [e.g., Melosh, 1989]. Solid ejecta are sufficiently heavy that any superimposed thermal velocity would be small compared to the bulk velocity. In contrast, the gas is not confined to a limited range of angles like the solid ejecta. In the case of H2 gas, the mass is low enough that the thermal velocity is on the same order as the typical bulk velocity of a few km/s. Because the escape speed of the Moon is 2.4 km/s, many of the gaseous particles are escaping the Moon.

[44] In photodissociation, the species mass is important in the distribution of excess energy from the dissociation reaction. In order to conserve momentum for the daughter products, the low mass species must be released with a higher velocity than the high mass species. For dissociation of water, the H or H2 released has higher velocity. Thus those clouds have a much wider extent in Figure 10 than the OH and O clouds.

[45] In these reactions, the excess energy of around 4eV is distributed into the kinetic, rotational, and vibrational energy of the daughters. Conservation of momentum requires that most of the energy go to the lighter species of the products. Thus, the H and H2 are extremely hot as a result of photoproduction. The OH and O are hotter than the original H2O, but only slightly.

4. Conclusions

[46] The physical parameters of the gas upon release control the expansion and dissipation of the gas plume. The mass of the species, the temperature, the bulk velocity, and the source rate each has an effect. Modeling these dependencies enables the physical interpretation of observations of vapor from the LCROSS impact. Using a Monte Carlo model neglects the extremely early expansion of the plume. The initial conditions for the Monte Carlo model represent the conditions when the isentropic expansion of the gasdynamic plume into a vacuum becomes rarefied enough to be collisionless.

[47] There are thermal and non-thermal properties included in the simulations. A species' mass is a key factor in determining the relative importance of the thermal component. The temperature of the gas is more important for light gases than for heavy gases because the thermal velocity is proportional to the inverse square root of the mass. If temperature dominates the dynamics, the gas appears as a hemisphere with the highest column density in the central region of the plume, decreasing in column density toward the edges of the hemisphere. In general, increasing temperature increases the growth rate of the cloud. The cloud has a greater size at any given time for a higher initial temperature. When the thermal velocity dominates, the cloud diameter is proportional to the thermal velocity. For releases of the same amount of gas, a lower initial temperature results in a large peak column density because the cloud does not occupy as big of a volume and does not disperse rapidly. Temperature is important if the gas diffuses out of the impact crater after the immediate explosion.

[48] A second scenario demonstrated is a regime with a large, uniform bulk velocity. The excavation stage of an impact results in a pulse of material at the bulk velocity with velocity decreasing toward the interior of the cloud. This scenario produces a hemispheric shell of high density material that expands outward in time. As viewed from the side, the shell appears as a semi-circle of high column density. As viewed from above, the shell appears as a ring of higher column density material. In this scenario, the highest density does not occur near the impact site owing to the velocity profile. Thus it would have a light curve that is quite different than thermally dominated release or the gasdynamic scenario.

[49] The beginning of the expansion can be described by the gasdynamic flow into a vacuum. In reality, the parameters from the gasdynamic phase are the starting point for the collisionless flow. The Monte Carlo model also demonstrated the expansion of the plume using initial parameters like from the end of the gasdynamic phase. The plume morphology is similar to the purely thermal, with the exceptions that 1) the initial velocity is not mass-dependent and 2) the plume expands faster vertically than horizontally. For light species, the thermal velocity should dominate. For heavier species in which the thermal velocity is low, there is a minimum velocity profile that is set in by the initial collisional expansion.

[50] The source rate has a profound effect on the distribution of material. For some species, the release may be from a prolonged source like sublimation off of lofted grains or from photodissociation of molecules. In some cases, there are multiple sources or a multistep process involved in the production. In that case, the dispersion of species from the production site is rapid. Observations may only have a small field of view and not provide the global picture. Thus knowing the source rate is essential in converting observed densities to total releases.

[51] This paper shows how the modeled vapor plume evolution responds to various physical conditions. It is left to subsequent papers (Hurley et al., submitted manuscript, 2011) to apply the model to observations of the LCROSS impact and use what is learned here to interpret those data.

Acknowledgments

[52] This work was supported by the NASA Lunar Science Institute under grant NNA09DB31A and the NASA Planetary Atmospheres Program under grant NNX09AH15G.

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