Lunar exospheric argon modeling

Icarus 255 (2015) 135–147

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Lunar exospheric argon modeling Cesare Grava a,⇑, J.-Y. Chaufray b, K.D. Retherford a, G.R. Gladstone a, T.K. Greathouse a, D.M. Hurley c, R.R. Hodges d, A.J. Bayless a, J.C. Cook e, S.A. Stern e a

Southwest Research Institute, 6220 Culebra Rd., San Antonio, TX 78238, USA LATMOS/IPSL, CNRS, Paris, France c Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Rd., Laurel, MD 20723, USA d LASP, University of Colorado, PO Box 4384, 130 W. Main St., Frisco, CO 80443, USA e Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302, USA b

a r t i c l e

i n f o

Article history: Received 3 January 2014 Revised 8 September 2014 Accepted 16 September 2014 Available online 17 October 2014 Keywords: Moon Atmospheres, dynamics Moon, surface

a b s t r a c t Argon is one of the few known constituents of the lunar exosphere. The surface-based mass spectrometer Lunar Atmosphere Composition Experiment (LACE) deployed during the Apollo 17 mission first detected argon, and its study is among the subjects of the Lunar Reconnaissance Orbiter (LRO) Lyman Alpha Mapping Project (LAMP) and Lunar Atmospheric and Dust Environment Explorer (LADEE) mission investigations. We performed a detailed Monte Carlo simulation of neutral atomic argon that we use to better understand its transport and storage across the lunar surface. We took into account several loss processes: ionization by solar photons, charge-exchange with solar protons, and cold trapping as computed by recent LRO/Lunar Orbiter Laser Altimeter (LOLA) mapping of Permanently Shaded Regions (PSRs). Recycling of photo-ions and solar radiation acceleration are also considered. We report that (i) contrary to previous assumptions, charge exchange is a loss process as efficient as photo-ionization, (ii) the PSR cold-trapping flux is comparable to the ionization flux (photo-ionization and chargeexchange), and (iii) solar radiation pressure has negligible effect on the argon density, as expected. We determine that the release of 2.6  1028 atoms on top of a pre-existing argon exosphere is required to explain the maximum amount of argon measured by LACE. The total number of atoms (1.0  1029) corresponds to 6700 kg of argon, 30% of which (1900 kg) may be stored in the cold traps after 120 days in the absence of space weathering processes. The required population is consistent with the amount of argon that can be released during a High Frequency Teleseismic (HFT) Event, i.e. a big, rare and localized moonquake, although we show that LACE could not distinguish between a localized and a global event. The density of argon measured at the time of LACE appears to have originated from no less than four such episodic events. Finally, we show that the extent of the PSRs that trap argon, 0.007% of the total lunar surface, is consistent with the presence of adsorbed water in such PSRs. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction The lunar atmosphere was first detected by Apollo 12, 14 and 15 with the Cold Cathode Gauge Experiments (CCGE) deployed on the lunar surface. These CCGE measurements determined a density of 107 cm3 and 2  105 cm3 in daytime and nighttime, respectively (Johnson et al., 1972). CCGE showed a large day/night density ratio, opposite to what is expected for non-condensable gases. Therefore, it was clear that the dominant gases in lunar atmosphere were adsorbed at night and released on the dayside.

⇑ Corresponding author. E-mail address: [email protected] (C. Grava). http://dx.doi.org/10.1016/j.icarus.2014.09.029 0019-1035/Ó 2014 Elsevier Inc. All rights reserved.

1.1. Past observations with Lunar Atmosphere Composition Experiment (LACE) The Lunar Atmosphere Composition Experiment (LACE) was a mass spectrometer deployed on the lunar surface in December 1972 during the Apollo 17 mission as part of the Apollo Lunar Surface Experiments Package (ALSEP). LACE was the first and, until very recently (Benna et al., 2014a), the only instrument to convincingly detect argon in the lunar exosphere. The argon density at the Apollo 17 site was seen to vary cyclically and also to show an overall decrease in density during 9 lunations. Fig. 1 of Hodges and Hoffman (1974) is the only published measurement of lunar argon during all 9 lunations, although efforts to restore the ALSEP data stream are ongoing (Williams et al., 2013). It was soon clear that

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argon showed the typical behavior of a condensable gas given the cold nighttime surface temperature of the Moon. The density decreased soon after sunset because of the increasing adsorption, and increased before sunrise due to atoms coming from the already illuminated portion of the dayside surface. This pre-sunrise increase of argon occurred 50 km before the terminator (Hodges, 1973) because LACE was located in the floor of Taurus–Littrow valley and the mountains to the East delayed the illumination of the site by 8 h (Hoffman et al., 1973). There is also a smaller peak at sunset, resulting from a contribution of atoms migrating from the hot dayside. The fact that the peaks are not symmetric, as one might expect from the T5/2 dependence of the density in the horizontal transport assumption (Hodges and Johnson, 1968), is due to sequestration at nightside, which increases with decreasing temperature, and, to a lesser extent, at dayside microscale coldtraps (Henderson and Jakosky, 1997; Paige et al., 2010). 1.2. Origin of argon On the Moon, argon is released from the interior by radioactive decay of 40K. Therefore, its production depends on the quantity of potassium present in the crust. With a concentration of K within the crust of 100 ppm (Taylor and Jakes, 1974), the argon production within the Moon was inferred to be 2.4  1022 atoms s1 (Hodges, 1975). From simulations it was initially determined that effusion of argon from the interior to the atmosphere was 2  1021 atoms s1, meaning that 8% of the argon production rate for the entire Moon escapes to the exosphere while the majority of argon atoms is retained within the crust. This effusion rate was later revised to be 1.4  1021 atoms s1 (Hodges, 1977), corresponding to 3 ton/year. However, the mechanism for release for such a large amount of argon remained uncertain. Hodges (1977) initially excluded diffusion among the sources, on the basis that (a) it is too slow and (b) the returned lunar rock samples would show a paucity of 40Ar instead of the excess reported by Heymann and Yaniv (1970). Hodges (1977) further concluded that argon must be released from small, warm regions at greater depth than the crust, in the molten asthenosphere, 1000 km in depth, where Latham et al. (1973) identified a highly attenuating zone for seismic shear waves. This depth has been recently revised to be 1250 km by Weber et al. (2011). The deep source origin for argon was first questioned by Hodges (1981) and, 25 years later, by Killen (2002). Applying a sophisticated multipath diffusion code, Killen (2002) showed that diffusion from the crust (i.e., a source much closer to the surface, 25 km) could account for the effusive flux of argon into the lunar atmosphere. The proposed mechanism was the release of argon from opening of micropores and cracks, i.e. natural diffusion out of grains to pore spaces in the rocks with subsequent spilling into the exosphere after shallow moonquakes. A deep source was no longer necessary. We discuss moonquakes in more detail in Section 4.1 in light of our model’s assumed population being consistent with the amount of argon that can be released during a moonquake. 1.3. Fate of argon Fig. 1 in Hodges (1975) shows two diurnal profiles of the densities of argon measured by LACE just above the surface during lunations separated by 120 days, starting with the maximum argon density measured during the month of April 1973. We report it in Fig. 1.1 The argon density is seen to decrease by a factor of 2 1 Hereafter, we use LACE’s convention for the ‘‘local time’’: 0° (from the subsolar point) means noon, 90° means sunset, 180° means midnight, and 270° means sunrise.

Fig. 1. The argon density measured by LACE over two different lunations, separated by 120 days. The y axis has a logarithmic scale; the x axis is the local time, measured in degrees from subsolar point. Digitized from Hodges (1975). The data from the more recent lunation start slightly later, at 110° longitude.

in 120 days, with minor short-term variations in the intervening lunations. Our modeling work aims to identify what caused this decrease. As the past works based on these measurements, we assume that there was no degradation in the instrument, and that all calibration errors were taken into account (for a detailed description of the calibration of LACE, see Hoffman et al., 1973). Loss of argon through ionization by solar UV photons is far more efficient than gravitational escape, and has previously been determined to be the primary loss mechanism (Hodges, 1977; Killen, 2002). Once argon atoms are ionized, the photo-ions are instantly entrained by the convective electric field Esw = vsw  BIMF (vsw is the velocity of the solar wind, and BIMF is the interplanetary magnetic field). Roughly half of these photo-ions are thought to impact the surface and to be neutralized because of their large gyroradius (Manka and Michel, 1970) combined with the low scale height of neutral Ar (in fact, the pickup ion velocity distribution is dependent upon the velocity of the ion and the gyroradius/scale height ratio, which in turn varies as the mass squared (Hartle and Killen, 2006; Hartle et al., 2011). This process is termed ‘‘recycling’’ since these particles may again be released from the surface as neutrals. The short-term variations from lunation to lunation were first (Hodges, 1977) attributed to High-Frequency Teleseismic (HFT) events measured by other Apollo stations (Nakamura et al., 1974) but Hodges (1980) proposed that seasonal (i.e., 1–10 years) storage of argon in Permanently Shaded Regions (PSR) could explain, at least partially, the time variations measured by LACE. The trapped argon would then be occasionally released from PSRs following shallow moonquakes, meteor impact, or seasonal warming of polar caps (Hodges, 1982). The argon PSR cold-trapping hypothesis followed the analogy for water retention in PSRs, which was proposed well before the beginning of the Apollo program itself (Watson et al., 1961; Arnold, 1979). Hodges (1980) demonstrated that argon retention on water contaminated rocks for a year or more is mainly in doubly shielded regions of large, flatfloored craters located at latitudes greater than 75°. The area affected by this argon retention is 0.5% of the area of the lunar surface at latitude greater than 75°, or about 0.05% of the total lunar surface. The reason for this double-shielded argument is that the heat reradiated by nearby orographic features (such as rims exposed to sunlight) would liberate argon from the surface. More recent observations with LRO/LOLA and modeling (Mazarico et al., 2011) suggest PSRs cover an area of 13,000 and

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16,000 km2 at the North and South Poles, respectively, or 2% and 2.5% of the area of the cap within 15° from each pole. The newly defined PSRs areas translate into 0.03% and 0.04% (for the N and S Poles respectively) of the total lunar surface, which we refer to here. In comparison, Watson et al. (1961) previously estimated an area 10 times too high, i.e. 0.5% of the total lunar surface, when analyzing photographs taken from the Earth. 1.4. Current and past campaigns to detect lunar exospheric argon The LAMP (Lyman Alpha Mapping Project) UV spectrograph onboard the Lunar Reconnaissance Orbiter (LRO) is studying the far-UV reflectivity of the PSRs using illumination by starlight and interplanetary Lyman-a skyglow to investigate their volatile content and distribution (Gladstone et al., 2012). Argon is thought to be among the stored volatiles and its temporary storage could in theory account for the variation in density observed by LACE (Hodges, 1975). Therefore, a transport and storage model is required in order to study the behavior of argon, whose lateral migration likely resembles other important volatiles, like water, which have been modeled in recent years (e.g. Hodges, 2002; Crider and Vondrak, 2002; Schorghofer and Taylor, 2007; Hurley, 2010; Farrell et al., 2013). Further detections of lunar argon from space-based experiments have, until recently, proven elusive. The mass spectrometers flown during Apollo 15 and 16 had no success in determining upper limits for specific neutrals (Hodges et al., 1972; Stern, 1999). Detection of argon from the UV spectrograph onboard the ORFEUS – SPAS II satellite was claimed by Flynn (1998), but was subsequently rebutted by Parker et al. (1998). Recently, LRO/LAMP has placed only an upper limit of 2.4  104 cm3 for argon near the poles (Cook et al., 2013). The LAMP argon limits are 5% and 38% lower than LACE measurements two-hours before and after the dawn and dusk terminators, respectively, in the comparable local time regions measured by LAMP in LRO’s polar orbit. Sridharan et al. (2013) published a study on the 40Ar/36Ar ratio obtained by Chandrayaan-1, but they do not report the 40Ar density. Finally, preliminary results from the LADEE spacecraft confirmed the detection of argon near the sunrise terminator (Benna et al., 2014a) for the first time after four decades. We address here the expected density of argon to aid ongoing interpretation of LRO/LAMP and LADEE measurements. Consideration of radiative transfer effects is needed to provide expected argon brightness and is left for future LRO/LAMP argon observation papers. 1.5. Current approach In Section 2 we describe the exosphere model, which is built upon the temporal Monte Carlo method described in Chaufray et al. (2009). Section 2.2 describes the incorporation of a LRO/Diviner surface temperature map while Sections 2.3 and 2.4 explain our ad hoc method for representing the residence time of argon atoms as a function of this temperature using the LACE determined diurnal behavior itself. Argon loss and source processes are described in Sections 2.5 and 2.6 respectively. In Section 3 we organize our model runs with increasing complexity, starting with loss by solar photo-ionization and solar wind proton charge exchange alone and then including additional loss by PSR sequestration. Our discussion in Section 4 is organized with a continued discussion of the initial production of argon by moonquakes, the implications of argon trapped in PSRs, and the study of a localized release of argon. We list four main findings in Section 5 together with recommendations for future LRO/LAMP and LADEE measurement comparisons.

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2. Lunar argon exosphere model 2.1. General description and physical assumptions We developed a Monte Carlo code to study the ejection, transport, loss and storage of argon in the lunar surface-exosphere environment. In the first simulation, which we describe here, production of argon is assumed to be once, i.e. a single event, with no prior knowledge of the source, and globally distributed across the entire lunar surface. Later on (Section 4.2) we simulate both a global and a local release of argon on top of a pre-existing, global, steady-state argon exosphere, in order to test the hypothesis that a sudden release of argon close to the mass spectrometer might best describe the LACE argon dataset. We start with a given population which is constrained by the density as a function of latitude and longitude. We assume that diffusion from the crust is slow compared to loss processes, therefore no more production occurs after the initial release. We begin by describing argon globally distributed across the surface. Our Monte Carlo simulation method (Chaufray et al., 2009) follows the fate of argon atoms from their injection into the exosphere, to annihilation (e.g., by solar photo-ionization or chargeexchange with solar wind protons) or implantation at the surface. Particles are randomly emitted across the lunar surface or from a localized point (see Section 4.2) with a Maxwell–Boltzmann Flux distribution (f(v)dv / v3 exp (v2)dv, Brinkmann, 1970), in order to have particles with a Maxwell–Boltzmann velocity distribution in the exosphere (Smith et al., 1978). We first generate 2 random numbers r1, r2 between 0 and 1, and we find the starting location coordinates as h = arccos(1  2r1); / = 2pr2. Based on the temperature T of this cell, we calculate the most likely thermal velocity as vth = sqrt(2  kB  T/mAr), where mAr is the mass of the argon atom. Initial directions are also determined from a flux distribution: hvel = arccos(sqrt(r4)) and /vel = 2pr5, where r4 and r5 are, again, random numbers between 0 and 1. To find the magnitude of the velocity of the emitted particle we use the acceptance-rejection method, using a function g(x) = exp(x/2) which is everywhere greater than the Maxwellian Boltzman Flux function f(x) = x  exp(x). We generate a random variable x distributed as g, that is x = 2 ⁄ ln(r6), where r6 is a random number between 0 and 1. This value of x = (v/vth)2 is accepted only if a second random number r7 between 0 and 1 is lower than f(x)/g(x) = x  exp(x/2). If this is the case, the particle is emitted with velocity vth  sqrt(x). If this is not the case, we start again by generating another r7. The trajectories of the test particles are computed using a 2nd order Runge–Kutta algorithm. This rejection method has been validated for uniform conditions at the surface by comparing the results from the Monte Carlo model with the Chamberlain’s solution (Chamberlain, 1963). This description differs from the models developed by e.g. Butler (1997) and Crider and Vondrak (2002), who determine the position of the impact without describing the movement along the full trajectory. The main drawback of our approach is an increase of the CPU time required for the simulation, but the advantage is the ability to derive the density and other moments of the velocity function distribution at any point in the exosphere. This distinction is crucial for direct model comparisons with measurements of exospheric distributions either in situ with LACE and LADEE’s Neutral Mass Spectrometer, or remotely along line-of-sight integrations as for LRO/LAMP. We used a constant value of lunar gravity, given the short scale height of argon: Hmax = kBTmax/mg = 50 km, if Tmax = 388 K, the maximum surface temperature as inferred from our Diviner temperature map; m is the mass of the argon atom, and kB the Boltzmann constant. Our results include both the fraction of particles delivered to the poles, as studied by Butler (1997), and timescales,

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as investigated by Crider and Vondrak (2000). Once a particle impacts the regolith, it resides for a certain sticking (or residence) time, which depends on the surface temperature. Each time a particle hits the surface, we compute its residence time, defined as (Hodges, 1982):

t res ¼

C T2

exp

  4:19Q ; RT

ð1Þ

where Q is the heat of adsorption (expressed in calories mole1), C is a constant (expressed in s K2), 4.19 is the conversion between calories and Joules, and R is the gas constant (see Section 2.3 for a thorough discussion of the residence time). We then generate a random number r and we compare the residence time to the time step of the simulation dt (typically 5 s); if:



dt exp  t res



>r

ð2Þ

the particle is kept in the surface cell; otherwise, the particle is released, with a velocity determined from the local surface temperature. We assume that the particle accommodates to the surface temperature. In other words, the energy of the particle is independent of the energy the particle had before encountering the surface. One usually refers to this assumption as a = 1, with the accommodation factor a defined as

a¼

Eafter  Ebefore ; ET  Ebefore

ð3Þ

where Ebefore and Eafter are the energies of the particle before and after the impact, respectively; ET is the mean energy per atom in thermal equilibrium with the surface (Shemansky and Broadfoot, 1977):

ET ¼

1 mv 2L ; 2

ð4Þ

and thus Eafter = ET; vL is the velocity with which the particle is liberated. For every particle temporarily trapped in the regolith, because our surface grid is fixed in local time and not in longitude, we update the residence time to account for changes in surface temperature when the location where the atom resides is exposed to sunlight at dawn. For this reason, at each time step a new residence time tnew res is computed (for particles stuck at the surface). We then generate a random number r; if:

  dt exp  new < r t res

We performed two modifications to the temperature map. First, we shifted it along the longitude in order to have noon (or subsolar point) at 0° longitude, sunset at 90°, and midnight at 180° (at that day the subsolar point was at 303.7°; from Horizons’ website). Second, we degraded the map temperature resolution to bins of 5° in latitude and 7.5° in longitude, in order to speed up the simulation (Fig. 2). It is true that the degradation in the resolution of the temperature map has the effect of smoothing the PSRs, but it does not affect the way we compute the cold-trapping, which is a probabilistic approach (Section 2.5.4) The temperature map is the key in defining the local variations in residence time (see following section). 2.3. The residence time We take into account the residence time an argon atom spends adsorbed at the lunar surface. The residence time tres depends on the surface temperature T via Eq. (1). That equation is slightly different from the formula used in other works, in that the factor which multiplies the exponential depends upon the inverse of the squared temperature. For example, Frisillo et al. (1974) proposed tres = 1.6  1013  exp(Q  4.19/RT) with Q = 104 cal mole1, while Hodges (1980) found a good agreement with the data with Q = 6000 cal mole1 (and Frisillo’s formula). Bernatowicz and Podosek (1991) used tres = h/kBTexp(Q  4.19/RT) with Q = 5800 cal mole1, and h is the Planck’s constant. Note that the pre-exponential factors of Frisillo et al. (1974) and Bernatowicz and Podosek (1991) are the same for T = 300 K. The physical meaning of the pre-exponential factor, sometimes referred to as s0, is the vibration (or oscillation) period (for the van der Waals potential) of the adsorbed atom (Hunten et al., 1988). It is a property of the adsorbing material, not of the gas, and it is determined from statistical mechanics. However, it can vary by several orders of magnitude for different adsorbers (Frisillo et al., 1974), likely explaining why different authors used different values. The exponential factor represents the number of oscillations an adsorbed atom experiences with the solid, and the physical meaning of the heat of adsorption Q is the energy an atom must have to escape the barrier that binds it to the lattice structure (Hunten et al., 1988). One of the limitations of the study of the interaction of exospheric atoms with the lunar surface is the lack of measurement of the heat of adsorption Q on realistic samples. Therefore,

ð5Þ

the particle is released; otherwise, the particle is kept in the surface cell. We did not take into account the roughness of the surface, but ejected all particles with an angle within ±90° from the normal to the surface. Another important assumption, discussed in Section 2.3, is that a particle can only make one collision with the surface. 2.2. Surface temperature Unlike previous models (e.g. Hodges, 1973; Butler, 1997; Leblanc and Chaufray, 2011), which use an analytical formula for the surface temperature, we used a global temperature map constrained by measurements from the Diviner instrument onboard LRO. The way the map is generated is the following: first, data from one orbit of LRO is collected (Diviner is only sampling a narrow stripe along the nadir); then, a model fit is applied (Vasavada et al., 2012). This is the map that was provided to us from the Diviner team, and refers to data from October 8th 2009, corresponding to summer in the lunar Southern Pole.

Fig. 2. Lunar surface temperature map from a thermal model fit to one orbit of Diviner data (courtesy from Matt Siegler and the LRO/Diviner team) degraded to a coarse resolution (bins of 7.5° in longitude and 5° in latitude). The day of the map was October 8th, 2009, one day prior to the Lunar Crater Observation and Sensing Satellite (LCROSS) impact. Temperature is expressed in K.

C. Grava et al. / Icarus 255 (2015) 135–147

we performed sensitivity studies on these different definitions of residence times and we found that the formulation of Hodges (1982) is the one that best describes the behavior of argon observed by LACE. In particular, we reproduced the LACE dataset by means of a chi-squared fit to the actual night side data above a threshold of 400 cm3, which is a conservative estimate of the sensitivity of LACE (100 cm3, from Hoffman et al., 1973). When the chi-squared statistic is minimized, our model best reproduces LACE’s observations and we have a good estimate for Q, C, and the initial population. In Fig. 3 we compare the residence times as a function of surface temperature for the different definitions presented above. This ad hoc approach is not intended to truly determine the residence time for an argon atom on the lunar surface, which in reality undergoes multiple collisions within the porous regolith before leaving the surface rather than the assumed single direct release. Instead, the residence time reproduces accurately the behavior of argon atoms observed by LACE within the context of our model approach. Our best model fit to the night side slope (black points in Fig. 4) has pre-exponential factor C = 4  106 s K2 and heat of adsorption Q = 6500 cal mole1. Our best value for the heat of adsorption Q (6500 cal mole1) is very similar to the value published by Hodges (1982), 6485.1 cal mole1, which is high compared to the 3800 cal mole1 measured for argon on glass (Clausing, 1930; DeBoer, 1968). This high value of Q was attributed by Hodges (1980) to the high cleanliness of lunar soil, due to exposure to solar wind cleansing and meteorite bombardment, which is not attainable in the laboratory. Hodges (1991, 2002) pointed out that this high value is consistent with water adsorbed in the lunar regolith in the scant quantity of 30 lmoles per gram of regolith, suggesting that the lunar surface is an exceptionally dry environment. However, Bernatowicz and Podosek (1991) found that a distribution of Q, instead of a single value, is more reasonable. They explained that the presence of a small fraction of highly adsorptive sites, even if the rest of the lunar surface is slowly adsorptive, would render the lunar soil as a whole highly adsorptive. If this is the case, then it is not required that the overall lunar surface is exceptionally dry in water. We will discuss the consistency of our result with the presence of adsorbed water later, in Section 4.3. Our best-fit value for the constant C (4  106 s K2) is 4 orders of magnitude higher than the constant used by Hodges (1982). This discrepancy is likely attributed to our assumption of a single collision with the surface. In Hodges (1982), the particle was assumed

139

Fig. 4. Lunar exospheric argon densities measured by LACE (digitized from Hodges and Hoffman, 1974) for the March 24th–April 7th 1973 lunation with measured densities shown as the black asterisks. The black points are the result of our simulation after 70 days of initialization to steady-state (it is an average of argon density over days 60–69), and well fit the night side data, especially between sunset and midnight. The red dashed line is the threshold above which we fitted LACE data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to make n collisions with the soil grains, with n given by the inverse of formula (1) in that paper:

n¼



1:28 1P

2

 1;

ð6Þ

where P is the probability of the atom to emerge from the surface after n collisions with the soil grains. The actual residence time must be multiplied by n, which, depending on P, can be enormous (with tres potentially larger than the Solar System age). Therefore our higher constant C essentially takes into account this higher number of collisions. This treatment by Hodges (1982) and more recently Hodges et al. (2012) is more physically realistic than our present approach, but has little influence on our results. Other minor contributions to the discrepancy between our tres and Hodges’ include the different temperature map: we used Diviner’s global temperature, while Hodges (and other workers) used an analytical formula. The use of an analytical formula mainly affects the terminators, owing to orographic effects (Hurley et al., 2015). In Fig. 4 we also show that the maximum peak in atmospheric density predicted by the model was not recorded by LACE. In fact, the dayside argon density profile is not constrained by observations owing to the exospheric signal being completely swamped by degassing from the hot instrument itself (Hoffman et al., 1973). Nonetheless, our model, which is built matching the night side measured profile, gives an indication of the amount of argon that can be expected on the dayside, for comparison to LADEE orbital measurements. 2.4. Model – data comparison

Fig. 3. The desorption time (in s) for argon on different materials. The curve ‘‘de Boer’’ has been drawn using our formulation for the residence time with the value of Q derived for argon on glass (DeBoer, 1968).

We first reproduce the diurnal curve of the highest concentration detected by LACE, from 24th March to 7th April 1973 (Fig. 4, black points). In particular, we aim to reproduce the characteristic nightside profile (the slope) of the density, and the relative intensities of sunrise and sunset peaks. We initialize the code with no losses so that the simulation reaches the steady state, assuming that such non-zero, steady state population originally exists for simplicity. That is, there is equilibrium between particles that stick to the surface and particles that are released from the surface to

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the exosphere. This steady state is reached at approximately 70 days (i.e. 2.5 lunations) from the beginning of the initial global release of argon. In Fig. 5, we plot the global latitude-local time distribution of argon density. The decrease of argon density during the night is shown from sunset to sunrise. A pre-sunrise increase appears. The structure in latitude at the dawn terminator shows the influence of using a more realistic Diviner surface temperature basemap. Fig. 6 displays the global coverage of argon at different altitudes, namely 20 and 45 km. The dayside information provided by our model is an important result that will help guide future observations from LRO or LADEE. In particular, the density after dusk and before dawn is in agreement with the upper limit (2.4  103 cm3) derived by Cook et al. (2013) using LRO/LAMP ‘‘twilight observations’’ (from 2009 to 2013), i.e. when the spacecraft was in shadow but the atmosphere beneath it was illuminated. Thus our model, which was tuned to meet LACE density measurements, is also in good agreement with LRO polar observations. While a more direct comparison is not possible with Cook et al. (2013) dataset (the density is obtained adding observations taken at different times at night), a comparison with LAMP dawn/dusk observations is ongoing (Cook et al., 2014). Finally, preliminary results from LADEE’s Neutral Mass Spectrometer reported by Benna et al. (2014b) show a concentration of 40Ar in the dayside of K 2  104 cm3 , which is only a factor of 2 higher than our model’s dayside values. For comparison, the only previous model of 40 Ar (Hodges and Hoffman, 1974) shows dayside values of K 103 cm3 . 2.5. Argon loss processes After determining the proper residence time formalism in the context of our direct ejection model, we adjusted the initial population of atoms to match the initial density measured by LACE. The population is 1.0  1029 atoms, corresponding to 6.7  103 kg assumed to be pre-existing at the beginning. The implications of this finding are discussed in Section 4.1. 2.5.1. Photo-ionization and charge-exchange with solar protons Photo-ionization was determined to be the main source of loss for argon atoms in the lunar exosphere (Hodges, 1977; Killen, 2002). In our simulation, we consider also charge exchange of neutral argon atoms with solar wind protons as an additional loss process. The cross section for charge-exchange (CEX) peaks at 2  1015 cm2 for 1 keV protons (Graph I in Nakai et al., 1987). We multiplied this value for the solar wind proton flux, obtained by multiplying solar wind speed by proton density from the GSFC/SPDF OMNIWeb database interface at http://omniweb.gsfc.nasa.gov. We used the median of these values during the period of interest, i.e. from March 24th 1973 to August 8th 1973. The assumption of a constant cross section neglects the

Fig. 5. The global latitude-local time map of argon density, in logarithmic color scale, at the steady state time (average of argon density over 10 days, from day 60 to day 69). In this particular plot, solar local time is expressed in degrees from midnight at 0°: sunset is at 90°, while sunrise is at +90°.

energy distribution of protons, but this is acceptable at the Moon because the solar wind proton energy distribution is strongly peaked at 1 keV. The resulting loss rate for CEX, 4.9  107 atoms s1, is comparable to the photo-ionization rate of Huebner et al. (1992) relative to quiet Sun,2 i.e. 3.05  107 atoms s1, and indicates that charge exchange is not a negligible loss process for argon. We did not include proton impact ionization in our simulation, because its cross section is 1 order of magnitude smaller than that for charge-exchange of protons (Fig. 16 in Abignoli et al., 1972). Electrons are 3 orders of magnitude less energetic than protons, below the threshold for argon impact ionization (Straub et al., 1995) and likewise negligible, and electron impact ionization is not discussed further. Table 1 summarizes the relative importance of these loss processes. The ‘‘rate’’ for PSR cold-trapping is calculated from our simulations, which indicate that the loss rate for PSR coldtrapping is comparable to that of ionization alone (Section 3.2). Hereafter, ‘‘ionization’’ refers to both photo-ionization and chargeexchange with solar protons combined. At the beginning of the simulation, we compute the lifetime of each particle for ionization in this way:

sioniz ¼ s0ioniz ln r;

ð7Þ

where s0ioniz is the lifetime for ionization. It is computed as the inverse of the sum of the photo-ionization and charge-exchange loss rates (Table 1). At every time step spent in the dayside, we remove the time step dt from the lifetime of each particle and we then check whether the particle is ionized (sioniz < 0). If so, it is removed from the simulation and the number of ionized/chargeexchanged particles is updated. In this way, we can distinguish between time spent in daylight and time spent at night, and decrease the lifetime only in the first case. One word of caution on the way we implement the sinks of the lunar exosphere. Our approach, i.e. a pre-computed lifetime which decreases at each time step, is slightly different from the more orthodox method of computing the probability of loss at each time step. In fact, our method should lead to a slight overestimate of the loss by solar processes, because in this case the particle which survives a time step is more likely to be lost in the next time step. Conversely, this would yield a slight higher trapping in the Permanently Shaded Regions. We tested both approaches, and found only slight discrepancy between the two methods. The differences are a measure of the uncertainty we introduce by taking the conservative approach of a pre-computed lifetime. The photo-ionization rate decreased by 6%, while the trapping rate increased by 2%. 2.5.2. Recycling of photo-ions Once formed, the exospheric argon ions begin to gyrate around the direction of the solar wind magnetic field in the plane that contains the convective electric field Esw and the solar wind velocity. Manka and Michel (1971) demonstrated that, for heavy ions like argon, the radius of the cycloid is much larger than the lunar radius. Argon ion trajectories are therefore nearly parallel to Esw, and for certain initial latitudes (i.e. where the ion is formed) the ions will re-impact the lunar surface, where they can be neutralized and later released as neutrals. The fraction of such recycled photo-ions was initially estimated to be 40% (Manka and Michel, 1970), but was later revised by Hodges and Hoffman (1975) to be 10%, in order to be consistent with the observed lifetime of exospheric argon (100 days) on the Moon (including time spent adsorbed on the surface). The most recent estimate, which takes into account the self-sputtering of the lunar atmosphere (i.e. exospheric ions that return to the surface triggering sputtering of neu2 We chose this condition as LACE observations (1973) were close to Solar Cycle 20 minimum (which occurred in April 1976: http://www.solen.info/solar/cycl20.html).

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Fig. 6. The argon density (in cm3) at 20 (left) and 45 (right) km altitude. The sub-observer longitude is at 30° longitude West of subsolar point, i.e. shortly before noon. Argon appears to be concentrated at the sunrise terminator (on the left in both globes).

Table 1 Summary of loss processes for argon in the lunar exosphere, and their relative importance. ‘‘n/a’’ is listed for ‘‘not applicable’’ details such as cross sections for PSR cold-trapping and for solar radiation pressure. Process

Cross section (cm2)

Flux (cm2 s1) of impacting particle

Rate (atoms s1)

Lifetime (s)

References

PSR cold-trapping Photo-ionization Charge-exchange with solar protons Solar radiation pressure

n/a 1.9  1015 2  1015 (d)

n/a 1.57  108 (b) 2.3  108 (c)

3.0  107 (a) 3.0  107 (b) 4.9  107

3.3  106 3.3  106 3  106

n/a

1.57  108 (b)

9  108 (e)

1.1  109

(a) This work (b) Huebner et al. (1992) (c) King and Papitashvili (2005); (d) Nakai et al. (1987) (e) Parker et al. (1999)

trals), is 50% (Poppe et al., 2013). We use this latter value in our simulation. 2.5.3. Solar radiation pressure Solar radiation pressure (Chamberlain and Hunten, 1987) is an important loss process for the exospheric alkalis such as sodium and potassium, because their g-value, or the quantity of solar photons available for scattering, is high. The high g-value leads to a tail of neutral sodium atoms in the anti-sunward direction many planetary radii long both at the Moon (Mendillo et al., 1991; Matta et al., 2009; Line et al., 2012) and at Mercury (Potter et al., 2002; McClintock et al., 2008; Schmidt et al., 2012). As an example, the g-value for the combined D2 + D1 lines of Na (5900 Å) at 1 AU was 0.8 s1 for the observations of Mendillo et al. (1991). For neutral argon, which resonantly scatters at 1048 Å, the g-value is e.g. 8.9  108 s1 (Parker et al., 1999). We briefly confirmed with a test simulation that the influence of SRP is indeed negligible and undetectable when introduced in our models (the difference is well below the statistical noise). 2.5.4. Argon loss by thermal adsorption and trapping in Permanently Shaded Regions To include in our simulation the loss of argon by cold-trapping in the PSRs, we applied a stochastic approach that both tracks the location of particle trajectory landings and tests for proximity to the polar region. This stochastic approach, while not directly tied to the physics of the temperature dependent surface-ejection processes in the simulation, works well within the Monte Carlo model method. We took the most recent estimate for the area of PSR regions around each Pole, from the LRO/LOLA topography: according to Mazarico et al. (2011), the PSR areas are 12,866 km2 and 16,055 km2 for the North and the South Pole, respectively, i.e. 1.99% and 2.48% of the area of the cap within 15° from each pole (6.6  105 km2, assuming the Moon’s radius to be 1737 km). Therefore, if a particle impinges on a point in the surface com-

prised within 15° of the North (South) Pole, we compute a random number. If this random number is less than 0.0199 (0.0248) then the particle is considered cold-trapped in the North (South) polar cap and is removed from the simulation. As we will discuss in Section 4.3, using the full area of PSRs resulted in too much loss. A reduction in the value of the PSR areas at both poles down to 10% of the total PSR area (Fig. 8), corresponding to only the coldest (<42 K) PSR regions, provides the best match to the LACE data. It bears mentioning that the size of the cold traps is different for different species, with the most volatile ones being frozen only in the coldest places. The Diviner temperature map inputs to residence time calculations at the poles were not relied on, in favor of the stochastic approach, for the following reasons: (1) the degraded resolution of the global temperature map removed all of the cells where the <40 K temperature threshold is met, (2) only one example lunar rotation is used for the temperature map and propagated in local time rather than a full year-long cycle of true temperatures, (3) the long term storage of volatiles in PSRs is better represented by daily Diviner products while the shorter-timescale exosphere transport processes are best represented with the daily global maps used here, and (4) any higher fidelity representation requires longer CPU run times and/or optimization of the code. Future work will build upon the model framework developed here to include the Diviner surface temperature maps in more direct physical modeling of the PSR cold-trapping process. Note that loss by photo-ionization and charge-exchange was continued during the simulation of losses to PSR sequestration. These processes compete to remove atoms from the simulation. 2.6. Argon source processes The ultimate source for lunar exospheric argon is the lunar crust. As discussed in Section 4.1, argon can be released during moonquakes, which provokes slumping of material on buried argon frost and/or outgassing from cracks in the crust. A more

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localized surface-release of argon could come from impacts (meteoritic or man-made, like the LCROSS impact), and has been investigated (Section 4.2). Other sources for argon include surface sputtering, but Wurz et al. (2007) demonstrated that it is a negligible process, at least for argon (Sarantos et al. (2012) showed that it is not so for refractories and metals). While an important source for the lunar helium exosphere, the solar wind delivers very little 40Ar compared to 36 Ar, as demonstrated by Yaniv and Heymann (1972). We therefore considered first a single ejection of 40Ar, consistent with what could be released during a moonquake. The starting population of 1.0  1029 atoms is sufficient to test whether the maximum density observed by LACE is best described by a moonquake, as previously suggested (Hodges, 1977). We also performed a second simulation with a release of argon on top of a pre-existing atmosphere (see Section 4.2).

3. Results 3.1. Loss by photo-ionization and solar wind charge-exchange alone We ran the model first taking into account only photo-ionization and charge-exchange with solar protons. The simulation time included a 70 day initialization period to reach steady state and then covered an additional 120 days, for a total of 190 days. In Fig. 4 we showed the situation after the first 70 days of initialization (average of argon density over the days 60–69), where no loss occurs, and the model profile (blue diamonds) well represents the LACE data (black) for the lunation with maximum densities (24th March–7th April 1973). In Fig. 7 we show the situation after the additional 120 days with only ionization turned on, and compare the model results (purple diamonds) with LACE data from both the starting lunation (black) and the lunation of July 1973 (gray), which we want to reproduce. The model densities are not sufficiently depleted to reach the lower density recorded after 120 days. An exception occurs two hours before sunrise, when both the modeled and measured densities approach the 100 cm3 sensitivity limit of LACE (Hoffman et al., 1973). We conclude that neither photo-ionization, nor charge-exchange is

Fig. 8. Same as Fig. 7, i.e. argon density after 120 days from steady state (average over days 180–189), but including loss by photo-ionization, charge exchange, and PSR cold trap adsorption. The model (purple) agrees well with the final LACE measured value on the July 20th–August 3rd 1973 lunation (gray), and provides a good description of the decrease in density relative to the initial March 24th–April 7th 1973 lunation (black). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

efficient enough to completely explain the observed decrease by LACE over the 120 day period between lunations. The ionization rate is 1.7  1021 atoms s1, similar to the value (1.2  1021 atoms s1) inferred by Hodges and Hoffman (1974) when considering only photo-ionization.

3.2. Loss by photo-ionization, solar wind charge-exchange, and cold trapping We repeated the simulation with the addition of the loss by cold trapping in PSRs (Section 2.5.4). In Fig. 8, we report the density of argon after 120 days from the steady state. The agreement between the model and the LACE measurement is much better with the inclusion of losses to PSR sequestration. In this case the ionization rate is 1.5  1021 atoms s1 (slightly lower because now we also have particles trapped), while the rate of argon cold-trapped at both poles is 1.7  1021 atoms s1, which is 1.2 times higher than the loss rate for photo-ionization and charge exchange (1.5  1021 atoms s1). This result demonstrates that a non-negligible amount of PSR cold-trapping is needed to help explain the decrease of argon observed by LACE, beyond the previously considered photoionization and the charge-exchange with solar wind protons. While a relatively simplistic stochastic modeling approach for the PSRs is used in the present simulation, future improvements are warranted. Note the discrepancy just before sunrise, which is easily explained by our model having density lower than the reported sensitivity of LACE (102 atoms/cm3).

4. Discussion 4.1. Initial production by sudden release moonquakes Fig. 7. Argon density after 120 days from steady state (average over days 180–189) including loss by only photoionization and charge exchange. The model (purple line) is compared to the final LACE measured nightside value on the July 20th– August 3rd 1973 lunation (gray). Without additional losses, the density of argon does not reach the observed value after 120 days (gray). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The four seismometers deployed on the lunar surface during the Apollo 12, 14, 15, and 16 missions, as part of the ALSEP’s Passive Seismic Experiment (PSE), detected averages of 600–3000 moonquakes per year (Latham et al., 1973), depending upon the station. There are four different types of moonquakes:

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– Thermal moonquakes: feeble quakes that arise abruptly two days after lunar sunrise, and continue until sunset. Thermal moonquakes are generated by (1) cracking or movement of rocks along zones of weakness; or (2) (the preferred hypothesis) slumping of soil on lunar slopes triggered by thermal stresses (Duennebier and Sutton, 1974). – Deep moonquakes: generated when the strain energy accumulated at the base of the lithosphere is released at 800–1000 km depth. Deep moonquakes comprise the vast majority of the quakes recorded by the Apollo seismometers. They are fully controlled by tidal stress variations (Lammlein et al. 1974). – Meteoritic moonquakes: Among the most energetic quakes, and generated by meteoroids in the mass range 100 g to 1 ton with peak rates in April through July, when large objects intersect the lunar orbit (Latham et al., 1973). – High Frequency Teleseismic (HFT) events: rare, big, and isolated quakes (each of those was recorded by no more than 1 station) (Nakamura et al., 1974). Because of their isolation, it is difficult to establish the depth of the HFT events, but they are generally thought to be generated within 200 km from the surface (Nakamura, 1977), below the aseismic 50-km thick crust. Of particular interest for the present work is the last category, or HFT events, because the highest density peak of argon (black asterisks in Fig. 4) was preceded by one of these events recorded by one seismometer (Hodges, 1977, Fig. 3) on March 13th 1973. The energy released by this 3.2-magnitude moonquake, the biggest of three such HFTs recorded during the operational time of LACE, was 2  1017 ergs (Goins et al., 1981a). A second, much smaller HFT event (magnitude 0.8) was recorded on February 8th 1973 (Nakamura et al., 1979, Table 1). Binder (1980) used four methods (two empirical and two theoretical) to estimate the amount of argon released during a moonquake, founding a range of 1.5  1025 to 2.0  1028 atoms, with possible extension to 1030 atoms of argon in the unrealistic case that the larger scarps (or faults) were formed during only one moonquake. In our simulation, we find that we need an initial population of 1.0  1029 argon atoms in order to describe the maximum density recorded by LACE (black asterisks in Fig. 4). However, LACE was recording argon even before this HFT event. In Fig. 5 of Hodges (1975) the photoionization rate is seen to vary from 2.4  1021 atoms s1 in February 9th 1973 to 2.8  1021 atoms s1 in March 26th 1973, the time of maximum argon density; i.e., an increase of 16% in 45 days. The photoionization rate is linearly related to the sunrise number density of argon atoms (Eq. (1) in Hodges and Hoffman, 1974), therefore if we apply the same ratio to our modeled population of 1029 atoms (relative to April 1973), the pre-existing exosphere consisted of 8.6  1028 atoms (i.e., 1.0  1029/1.16), and the difference between February (with density similar to January) and April accounts for 1.4  1028 argon atoms, which have survived the first 45 days (1.5 lunations) of ionization and cold trapping. Using our inferred loss rate of 1.7  1021 atoms s1 for cold-trapping and 1.5  1021 atoms s1 for ionization (previous Section), the initial population released by the moonquake was then 1.4  1028 + (1.7  1021 + 1.5  1021) ⁄ 45 ⁄ 86,400 = 2.6  1028 atoms. Based on our simulation, this is the amount of argon that must have been released to bring the already existing exosphere to the densities measured in March/ April (black points in Fig. 4). This value is not too far from that calculated by Binder (1980) for the same HFT event (8  1027 atoms) and close to the upper end of the theoretical amount of argon that could be released during a moonquake (2.0  1028 atoms). The agreement is even closer if we consider that there were two HFT events, although the smaller magnitude of the first HFT event likely released fewer argon atoms. Our initial population is therefore

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consistent with the amount of argon that can be released during a HFT event. In addition to this, it bears noting that, given our inferred loss rates and the amount of argon released during one single moonquake, the argon population at the time of LACE measurements appears to have originated from multiple surface ejections (at least four). As a matter of fact, between the deployment of the first seismometer on the Moon and the deployment of LACE, seven HFT events were recorded (Nakamura et al., 1979). 4.2. Local versus global release of argon To test the importance of the location of the initial release, we performed another simulation releasing argon at one point on the surface, close to LACE. In fact, Nakamura et al. (1979) pointed out that HFT events, concentrated mostly in the northeast and southwest quadrants (e.g. Fig. 12 of Lammlein, 1977), are possibly correlated with impact basins, even if too few events were detected, to be of statistical relevance. Similarly, Runcorn (1974) reported that deep moonquakes seem to be generated along circular fault systems around impact basins. Middlehurst and Moore (1967) discovered that Lunar Transient Phenomena, potentially explained by sporadic outgassing from the Moon (e.g. Stern, 1999; Crotts, 2009), are also distributed around circular maria. If argon is released locally along circular fault systems, then one can ask whether LACE, which was deployed at the border between two of them (Mare Serenitatis and Mare Tranquillitatis), could have observed a localized event rather than a global one. In our additional model, we initially simulate the global release of 8.6  1028 atoms. Then, when the steady state is reached, we simulate an additional release of 1.4  1028 atoms localized close to LACE’s latitude (30°N) and close to midnight. We chose this time because (a) we wanted to study the behavior of this additional pocket of gas while it was in the night side; and (b) this is a good approximation, since the location of the HFT event that triggered the argon emission (Longitude 139.0° ± 21.1°W, from Table 2a in Goins et al., 1981b) was effectively at night (as determined from the Horizons’ ephemeris). For comparison, we also simulated the same 2-step process but with the second release being global instead of local. Fig. 9 depicts the evolution of a local/global release of argon from the surface on top of a steady-state argon exosphere. In the local release, the gas remained localized near the source during the nighttime, to reach the sunrise terminator after 4 days (not shown). After 6 days the local pocket of gas is already highly dispersed, and after 21 days, the local release is indistinguishable from the global release. Therefore it is not possible to determine whether LACE observed a localized event or not. Fig. 10 shows the argon density averaged over days 180–189, i.e. the equivalent of Fig. 8 for these updated simulations, and clearly shows that global and local releases of argon on top of a pre-existing atmosphere are almost indistinguishable. 4.3. The amount of argon permanently trapped To put the number of argon atoms emitted and trapped into perspective, at the beginning we have 1.0  1029 argon atoms, corresponding to 6700 kg, and after 120 days 2.9  1028 atoms have been trapped, corresponding to 1900 kg of argon. This ending value is 30% of the initial population. The total mass trapped at each pole is very similar: 900 kg in the North Pole, and 1000 kg in the South Pole. Given the extent of the PSRs, in our simulation argon is only adsorbed in the very first surficial layer. Also, the statistical nature of our Monte Carlo model does not presently allow us to infer physically meaningful details on the location of the PSRs. As mentioned previously, the efficiency of the PSR cold-trapping loss process was found to be too efficient,

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Fig. 9. Argon density (in cm3) for a local (left) and a global (right) surface-ejection after 10 min of the first day (top), 1 day (second row), 6 days (third row) and 21 days (bottom). Local ejection occurs at 30° from midnight, towards dawn, roughly located in latitude where the LACE Apollo 17 measurements occurred.

and required only 10% of the total PSR area to match the additional loss of argon in the LACE measurements. To roughly estimate what is the temperature corresponding to the 10% PSRs area (0.007% of the total lunar surface area), we divided the original full resolution Diviner surface temperature map (not degraded) into a histogram with bins of 2 K each (the exact range is 27–398 K). We then found the cumulative number of points which have a temperature below each bin, and we show this cumulative distribution (normalized to 1) for the range 20–100 K in Fig. 11. At this point we determine the temperature bin that 10% of the total PSR area corresponds to, and the result is 40–42 K. This first-order guess has important consequences on the presence of water adsorbed at the PSRs. As pointed out by Hodges (1980),

the maximum possible temperature for argon trapping is 40 K on surfaces contaminated by water, and nearly 70 K on clean rocks. Our result is therefore consistent with water being adsorbed in at least 10% of the PSRs. For comparison, the area covered by points in the Diviner surface temperature map with temperature below 70 K is 90,500 km2, according to the same cumulative distribution, which is 0.24% of the total lunar surface. Such an area is three times larger than the total PSR area. Cold-trapping of argon at 70 K is therefore inconsistent with the loss rates constrained by the LACE dataset, and suggests that surficial water plays an important role in argon transport and storage near the poles. Finally, we produce a rough estimate of the amount of argon trapped in the Cabeus crater, and therefore of the quantity of argon

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search for emission from the Ar-1048 Å resonant line. While a lack of confidence in the early calibration of LAMP’s sensitivity at this wavelength prevented inclusion of argon in the list of species presented in Gladstone et al. (2010), we report an upper limit brightness of 1 Rayleigh, which, in the optically thin case, suggests a column density of 1.2  1013 cm2 (2-r upper limit) and a soil mass abundance of 5.8% (upper limit) in Cabeus crater. With these upper limits to the argon detected in the LCROSS impact plume by LRO/LAMP (corresponding to 580 kg), 106 such HFT events would need to have occurred since the time Cabeus became a PSR (>1 Gya, Paige et al., 2010) assuming no subsequent loss or scavenging of trapped argon. The frequency of these HFT events averaged to 5 per year, according to Nakamura et al. (1979), which is more than sufficient to deposit more argon than constrained by LCROSS upper limits. Further modeling which includes the loss of argon trapped in the PSRs due to space weathering and its burial due to nearby impacts (Crider and Vondrak, 2003; Hurley et al., 2012) is needed to resolve this discrepancy. Fig. 10. Same as Fig. 8 but with a local (blue diamonds) and global (red triangles) release of argon on top of a steady-state atmosphere. The global release is indistinguishable from a local one. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

5. Conclusions and future projects We performed a Monte Carlo simulation to study the origin and transport of lunar exospheric argon, and to compare the relative importance of its loss by photo-ionization and charge-exchange (CEX) with solar wind protons versus storage in PSR cold-traps. Our reference data were those from the surface-based LACE mass spectrometer, deployed during the Apollo 17 mission. The model results are summarized in Table 2 and the main findings are listed here:

Fig. 11. Cumulative distribution of points in the Diviner map lower than a certain temperature (x axis). Vertical axis has been normalized to 1. The horizontal dashed line corresponds to the total PSR area that we have introduced in our simulation, normalized to the total lunar surface.

expected to be released during the LCROSS impact. The crater excavated by LCROSS has a diameter of 30 m (Schultz et al., 2010) and thus an area of 700 m2. Using our value for the amount of argon trapped at the South Pole following a single moonquake-sized release a mere half gram of argon is expected to be present in the crater. An initial analysis of LAMP spectra of the LCROSS impact plume was performed by Gladstone et al. (2010), including a

1. To reproduce the maximum argon density observed by LACE, 1029 atoms of argon must be injected in the exosphere, the first 8.6  1028 atoms being released to form the steady-state atmosphere, and the additional 1.4  1028 atoms released later. From our inferred loss rate (due to photoionization and charge exchange with solar protons), 2.6  1028 atoms were released during an energetic, localized, High-Frequency Teleseismic (HFT) moonquake, in agreement with theoretical calculations, although we showed that LACE measurement cannot be used to distinguish between a global and a local emission of argon. 2. Charge-exchange with solar wind protons is a non-negligible loss process for argon, with loss rate comparable to the one of photo-ionization, previously considered the dominant sink for argon. Nonetheless, these two processes are not enough to reproduce the entirety of the observed decrease of argon density that LACE measured during 4 lunations (120 days). 3. Cold-trapping of argon in the PSRs can explain the additional decrease in density observed with LACE over a 120-day period beyond the losses attributable to photo-ionization and charge exchange with solar wind protons. Our simulations show that trapping within just 10% of the fractional area of polar PSRs determined by LRO/LOLA is efficient enough to explain the

Table 2 The different processes investigated in our simulations. Model

Purpose

Processes included

Key results

Loss by photo-ionization and charge exchange alone

Study the influence of photo-ionization and charge exchange in explaining the observed decrease Test the importance of Solar Radiation Pressure (SRP) Test the importance of PSRs as a sink for exospheric argon

Photo-ionization, solar wind proton charge-exchange Photo-ionization, charge-exchange, SRP Photo-ionization, charge-exchange, PSR cold-trapping Photo-ionization, charge-exchange, PSR cold-trapping

These two processes are insufficient to fully explain the observed decrease in LACE measured densities SRP can indeed be neglected

Loss by photo-ionization and charge-exchange + SRP Loss by photo-ionization and charge-exchange + PSR cold-trapping Loss by photo-ionization and charge-exchange + PSR cold-trapping, global/local release on top of a steady-state argon exosphere

Test the hypothesis of a sudden release of argon very close to LACE

Loss by <42 K PSR cold-trapping accounts for the additional decrease in argon observed by LACE LACE data cannot be used to distinguish between a localized and a global release of argon

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observed decrease of argon density. The corresponding quantity of argon trapped is 1900 kg, or 30% of the surface-ejected quantity, and the loss rate from PSR cold-trapping is 20% higher than the loss rate from photoionization and charge-exchange. 4. A rough estimate of the temperature of the PSR area actively trapping argon is consistent with the presence of adsorbed water in these PSRs and the polar regions. 5. Our initial argon density is in agreement with the upper limits reported by Cook et al. (2013) to argon densities determined from LRO/LAMP ‘‘twilight’’ data, which are now better understood to be consistent with a latitude and local time selection effect in the context of our global model. Our model also reproduces preliminary dayside argon densities measured by LADEE’s Neutral Mass Spectrometer better (factor of 2 discrepancy) than any previous model (factor of 10 discrepancy). 6. Based on the inferred loss rates and the amount of argon released during one single moonquake, the argon population present at the time of LACE measurements appears to have originated from no less than four surface ejections. Future implementations of the code will include a more accurate treatment of the gas-surface interaction, of the solar wind interaction, and of the lunar topography, by means of the exospheric code LExS (Hodges, 2011). A radiative transfer model will also be included, to estimate the brightness of the argon column density expected for LRO/LAMP remote sensing observations. Finally, we plan to study the contribution of fresh ions in desorbing additional neutrals from the surface, or self-sputtering (Poppe et al. 2013). A revised analysis of LAMP spectra of the LCROSS impact plume is being performed to better constrain emission from the Ar-1048 Å resonant line, and the inclusion of higher spatial resolution temperature maps and diurnal trending could lead to new insights into the argon content of Cabeus crater. This work sets the basis for analyzing new data from atmospheric campaigns of the LAMP UV spectrograph simultaneous with LADEE Neutral Mass and UV–Vis Spectrometers measurements of argon and other species (Mahaffy et al., 2012; Elphic et al., 2013, 2014). In particular, Fig. 6 guided observations of argon performed by LRO/LAMP towards the region in the sunrise terminator, looking towards the nightside to remove the bright dayside lunar reflectance (Grava et al., 2014). Acknowledgments This work was supported by NASA ROSES/LASER Grant NNX09AM59G and NASA LRO/LAMP contract NNG05EC87C. We thank the entire LRO/LAMP team, and Matt Siegler and the LRO/ Diviner team for providing us with the temperature map of the lunar surface. The authors wish also to thank the reviewers for their insightful suggestions. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.icarus.2014.09. 029. References Abignoli, M., Barat, M., Baudon, J., Fayeton, J., Houver, J.C., 1972. Differential measurements on ion-atom collisions in the energy range 500–3000 eV. IV. H+-noble gas atom collisions. J. Phys. B: Atomic and Molecular Physics 5 (8), 1533–1553. Arnold, J.R., 1979. Ice in the lunar polar regions. J. Geophys. Res.: Solid Earth (1978–2012) 84 (B10), 5659–5668. Benna, M., Mahaffy, P.R., Hodges, R.R., 2014a. Early results from exospheric observations by the Neutral Mass Spectrometer (NMS). In: 45th Lunar and

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