Volume 124, Issue 7 p. 1935-1944
Research Article
Free Access

The Temporal and Geographic Extent of Seasonal Cold Trapping on the Moon

Jacob L. Kloos

Corresponding Author

Jacob L. Kloos

Centre for Research in Earth and Space Sciences, York University, Toronto, Ontario, Canada

Correspondence to: J. L. Kloos,

[email protected]

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John E. Moores

John E. Moores

Centre for Research in Earth and Space Sciences, York University, Toronto, Ontario, Canada

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Jasmeer Sangha

Jasmeer Sangha

Centre for Research in Earth and Space Sciences, York University, Toronto, Ontario, Canada

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Tue Giang Nguyen

Tue Giang Nguyen

Centre for Research in Earth and Space Sciences, York University, Toronto, Ontario, Canada

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Norbert Schorghofer

Norbert Schorghofer

Planetary Science Institute, Tucson, AZ, USA

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First published: 04 July 2019
Citations: 21

Abstract

We assess the geographic distribution and temporal variability of seasonal shadow at the lunar polar regions and explore its influence on surface water migration and deposition within known permanently shadowed regions (PSRs) in the modern era. At its largest expanse near the winter solstice, seasonally shadowed area more than doubles the permanently shadowed area at both poles. The growth and decay of polar shadow throughout the year enforce distinct seasonal patterns in the poleward migration of water as well as a cyclical variation in the polar surface hydration throughout the year if a continual source of water is assumed. The polar surface water abundance peaks near the hemispheric vernal equinox—significantly offset from the solstice where the seasonal trapping area is most expansive—due to the retention of seasonally trapped water. Owing to their low areal density, lower-latitude PSRs do not significantly hamper the poleward migration of water, enabling water to reach the high polar latitudes where cold trapping area is densest. We find that northern hemisphere PSRs accumulate more water per unit area than southern hemisphere PSRs and that this disparity is especially prominent beyond 85°. The north/south asymmetry is attributed to differences in the hemispheric PSR size-frequency distributions; such differences enable unique north/south migration diffusivities, which favor more water reaching the high northern latitudes.

Key Points

  • Seasonally shadowed regions have more than twice the area of PSRs at the winter solstice in both hemispheres
  • A seasonal variation in the polar H2O concentration is modeled due to the growth and decay of seasonal shadow
  • The peak concentration occurs near the hemispheric vernal equinox due to polar retention of seasonally trapped water

Plain Language Summary

The research presented in this work describes modeling efforts to identify the locations and temporal variability of seasonally shadowed regions (SSRs) near the lunar poles. SSRs are temporarily shadowed regions of the surface that form due to the slight tilt (1.5°) of the Moon's spin axis with respect to the ecliptic normal and are significant given that their temperatures are expected to be low enough to temporarily trap water molecules and other volatiles that are migratory on the surface. Using a Monte Carlo simulation, we model how SSRs influence the migration of water across the surface and estimate the seasonal variation in the polar surface concentration of water. We find that if water molecules are continually produced at the surface via solar wind interactions with the surface regolith, as has been suggested based on the results of orbital remote sensing data, the polar concentration of water varies significantly throughout the year. In addition, we use our model to constrain patterns in the delivery of water to permanently shadowed regions (PSRs) at the north and south poles and find that northern hemisphere PSRs accumulate more water per unit area than southern hemisphere PSRs.

1 Introduction

After decades of exploration, the preponderance of data from a host of remote sensing and in situ investigations point toward an enrichment of volatiles at polar latitudes of Earth's moon (Lawrence, 2017, and references therein). Attempts to map the abundance and geographic distribution of volatiles, in particular H2O water ice and its derivatives, have been made using orbital neutron spectroscopy as well as ultraviolet and infrared (IR) reflectance measurements. From these data, several key findings have emerged: (1) surficial ice deposits are locally concentrated within permanently shadowed regions (PSRs), where temperatures may be low enough for ice to remain thermodynamically stable across geologic timescales (Gladstone et al., 2012; Hayne et al., 2015; Li et al., 2018; Lucey et al., 2014); (2) epithermal neutron deficits poleward of ±70°, signifying the presence of hydrogen-bearing material in the upper meter of regolith, are positively correlated with proximity to the pole (Feldman et al., 2000; Mitrofanov et al., 2010)—a trend which is also observed in surficial water ice deposits (Fisher et al., 2017; Hayne et al., 2015; Li & Milliken, 2017); and (3) IR spectroscopic measurements show enhanced concentrations of H2O/OH near the terminators, suggestive of a diurnal variation at the surface and a potential steady source of water, likely of solar wind origin (Clark, 2009; Pieters et al., 2009; Sunshine et al., 2009), although this finding is controversial (Bandfield et al., 2018).

Theoretical study of volatile transport from a variety of endogenic and exogenic sources may aid in the interpretation of orbital data by clarifying geotemporal trends in volatile dispersion and cold trapping. To this end, numerous Monte Carlo simulations of surface transport have been performed which have emphasized different aspects of migration such as the influence of surface roughness (Prem et al., 2018), fractionation during transport (Butler, 1997; Moores, 2016; Schorghofer, 2014), diurnal variability (Schorghofer et al., 2017), and infall within PSRs (Moores, 2016). A parameter generally ignored thus far, however, is the influence of the lunar obliquity with respect to the ecliptic plane (<1.59°) and the associated seasonal patterns in migration. Although small, the obliquity implies a semiannual variation in polar cold trapping area, which may have two important implications for lunar volatile studies: (1) seasonal cold traps constitute localized reservoirs where volatiles may be temporarily stored and exchanged with the exosphere and (2) for a continual supply of water such as production at the surface via solar wind implantation and subsequent oxygenation, the polar concentration of H2O will oscillate throughout the year as the trapping area expands and recedes.

In this work, we develop an illumination model using polar topographic data to assess the temporal variation and geographic extent of shadowed surfaces at the north and south pole of the Moon (poleward of ±80°). These data are used in conjunction with Monte Carlo simulations of water transport in order to explore the influence of seasonal shadow on surface migration as well as patterns in deposition within known PSRs in the modern era.

2 Model and Data

2.1 Illumination Model

The small obliquity of the Moon gives rise to a seasonal variation in solar insolation that oscillates with a period of 346.6 days, or one draconic year (Paige et al., 2010). Shadowed area near the rotational poles may vary significantly across this time interval. Seasonally shadowed regions (SSRs), defined here to be a region of the surface that remains continuously in shadow for at least one lunation, are significant due to their expected low temperatures and may offer temporary shelter for water and other exospheric constituents such as argon (Hodges Jr, 2018). The extent and distribution of SSRs will depend on the local topography and time of year: Polar regions of topographic high such as the rim of Shackleton crater (89.6°S, 122.0°E) remain near continuously exposed to sunlight (Gläser et al., 2014, 2018; Speyerer & Robinson, 2013); however, the regional expanse of SSRs should reach a maximum near the winter solstice when the solar elevation is reduced.

To identify the location of SSRs, as well as their variation in extent and distribution throughout the lunar year, an illumination model is developed that is similar to those previously described by Mazarico et al. (2011) and Gläser et al. (2014). Publicly available gridded digital elevation models from the Lunar Reconnaissance Orbiter Lunar Orbiter Laser Altimeter (Smith et al., 2010) are used to model the sky visibility for individual surface elements (defined here as one pixel or a 240 × 240-m surface region) poleward of 80°N and 80°S. The horizon method (Mazarico et al., 2011) is employed to ascertain the elevation of the local horizon for 360° of azimuth using a 1° step size. Horizon profiles are derived using vector geometry and therefore account for the curvature of the Moon. Although computationally demanding, this step is only performed once and the horizon profiles are stored in a database.

Following the horizon mapping, the Sun is located from a lunar-fixed reference frame using the DE421 lunar ephemeris (Williams et al., 2008). We begin our illumination survey at the northern vernal equinox on 29 July 2018 and carry it through 12 lunations using a 1-hr time step, thereby encompassing 1.02 draconic years. At each time step and for each surface element, the subsolar point is cross referenced with the local horizon profile to determine the visible fraction of the solar disk. In total, 12 maps are output for each hemisphere that record the geographic locations of PSRs and SSRs poleward of 80°N and 80°S during the lunation modeled; each map therefore typifies the dispersion of potential cold trapping area at a specific period of the lunar year. All SSRs have an associated “release time,” which represents the lunation at which that point of the surface is no longer in shadow—so named because a water molecule trapped at that location would thereby be released.

2.2 Monte Carlo Model

Each Monte Carlo simulation begins with the production of individual H2O molecules, hereby referred to as particles, onto the lunar surface. The generation of a particle initiates the simulation wherein the particle is tracked in space and time until becoming trapped within a PSR or lost to the system through photolysis or escape. Particles are given random initial positions based on a uniform probability distribution as has been implemented in other lunar exospheric models (e.g., Prem et al., 2018). The randomized production scheme was not intended to model a particular source of water; however, it was intended to remove any bias in north/south trapping as a result of the particle's origin latitude, as was shown to occur in the work of Crider and Vondrak (2000) and Schorghofer (2014). Furthermore, implementing a randomized production scheme enables study of the behavior of discrete populations of particles according to their provenance.

Once a particle appears on the surface, it is assumed to instantaneously reach thermal equilibrium with the regolith below and take on the local surface temperature. Here, surface temperatures are determined using topographically resolved bolometric temperature maps derived from the Diviner Lunar Radiometer instrument onboard the Lunar Reconnaissance Orbiter (Williams et al., 2017). Diviner temperature maps were created using nadir observations (emission angles <10°) and are globally resolved at a spatial resolution of 0.5° per pixel. In total, Williams et al. (2017) produced 24 global temperature maps, each of which displays the bolometric brightness temperatures for a particular subsolar longitude using the binned values of all seven of the Diviner IR spectral channels. These maps combine data across a nearly 6-year period between 5 July 2009 and 1 April 2015, and thus, each temperature map represents an annual average of the 24 time steps through a lunation.

The surface temperature controls the surface residence time τ, defined by Langmuir (1916) to be
urn:x-wiley:jgre:media:jgre21182:jgre21182-math-0001(1)
where v0=2.0×1012 s−1 is the vibrational frequency for water, Ea=0.456 eV is the activation energy, kB is the Boltzmann constant, and Tsurf is the surface temperature. The residence time is updated using a 1-hr time step (Δ t = 1 hr), which is achieved by interpolating the Diviner temperature map. For particles where τ > Δt, the model is advanced in time to the first point at which τ < Δ t and the particle is released. For a small fraction of Diviner temperature profiles (0.7%, all of which occur at the polar regions), the temperature remains low enough to effectively permanently trap water despite not being a PSR or SSR; particles that land in these regions are released at the morning terminator.

Particles emitted from the surface inherit a velocity vector in three-dimensional cartesian coordinates where the particle's speed is drawn from the Maxwell-Boltzmann distribution and the vector direction is randomized over 2π steradians. Particle trajectories are simulated in three dimensions using a fourth-order Runge-Kutta scheme, where the lunar atmospheric density is assumed low enough so as to be noncollisional, and therefore, particle flight paths are described by ballistic trajectories. Even the highest temperatures at the lunar surface do not permit a significant number of particles to achieve escape velocity; as such, the dominant way in which water can be lost to the system is through photodissociation. Following Moores (2016), the probability of photodissociation is estimated using a rate of 1.26×10−5 molecules/s, appropriate for normal sun activity (Crovisier, 1989). This method ensures that particles with longer flight times are more likely to dissociate while still retaining the random nature of this process.

In total, 12 Monte Carlo simulations were performed, where each simulation was conducted using 2 million particles and was intended to model spatial trends in the polar deposition of water at a particular period of the lunar year. Each Monte Carlo run was executed with PSR and SSR maps (described in section 2) emplaced at the north and south poles, which record the trapping area out to ±80° latitude at the temporal period being analyzed. To model the delivery of water to low-latitude PSRs and to understand their influence on the poleward migration of water, we additionally place the altimetrically derived PSR maps produced by Mazarico et al. (2011) at the poles, which chart the location of PSRs out to ±65° latitude at 240-m per pixel resolution. When a particle lands within a PSR, the simulation is ended and particle's location and flight time are recorded. For particles landing in an SSR, the model is advanced to the first lunation at which the surface is directly illuminated by the Sun (i.e., the release time); new SSR maps are uploaded, and the particle is liberated and continues its journey until photodissociating, escaping, or becoming PSRtrapped.

3 Results

3.1 Spatial and Temporal Extent of Polar Shadow

Figure 1 displays the locations of SSRs poleward of 80°N and 80°S, where the color denotes the length of time, in Earth days and over a time span of 12 lunations, that the surface spends in shadow. Surface elements that lie in shadow across all 12 lunations (PSRs) are shown in white. As shown here, SSRs tend to emanate from PSRs and expand toward the pole. Regions near the perimeter of PSRs are the longest seasonally shadowed surfaces; with increasing distance from PSR boundaries, SSRs become progressively diminished in temporal extent.

Details are in the caption following the image
Locations of SSRs poleward of ±80° within the northern (a) and southern (b) hemispheres. Color denotes the number of Earth days spent in shadow over the course of 12 lunations (354 days), while PSRs are shown in white. Lines of latitude are shown every 2.5°. (c) Variation in shadowed area throughout the year. Solid lines represent SSR area, while dashed lines show PSR area measured in this work. Green vertical bars show the summer/winter solstices. (d) Geographic distribution of total shadowed area (PSRs + SSRs, solid lines) and PSRs (dashed lines) at its maximal extent. Data are binned using a 0.5° latitude bin spacing. PSR = permanently shadowed region; SSR = seasonally shadowed region.

Cumulatively, the north and south permanently shadowed area determined from this work is 15,772 and 18,909 km2, respectively, which is 23% and 18% larger than previous estimates from Mazarico et al. (2011) whose modeling technique was similar to ours. At least two explanations can be invoked to explain the disparity in PSR size. First, the temporal domain of our survey was shorter than that of Mazarico et al. (2011), whose analysis was performed across multiple lunar precessional cycles (18.6 years). Second, our estimate includes PSRs down to a single pixel, while Mazarico et al. (2011) removes PSRs fewer than 9 contiguous pixels due to uncertainties in the modeling. When the same treatment is performed on our data, our PSR estimates are larger by 13% and 14% for the north and south, respectively, with good geographic alignment. Using a ray tracing method and including single-pixel PSRs, McGovern et al. (2013) obtained PSR estimates of 12,090 and 16,800 km2 poleward of 80° for the north and south; these authors, however, argued that their smoothing operation of the digital elevation model may have resulted in underestimations of PSRs. In the Monte Carlo simulations described below we include all PSRs down to a single pixel while acknowledging the same uncertainties considered by Mazarico et al. (2011). This decision was made in order to provide an upper limit on PSR accretion as well as to account for the influence of smaller-scale PSRs on volatile transport.

Throughout the lunar year, the shadowed area varies significantly (Figure 1c). At its largest expanse near the solstices (green vertical bars), the total SSR area (solid lines) more than doubles the PSR area (dashed lines) in both hemispheres, totalling 43,160 and 41,640 km2 for the north and south, respectively. As expected, the majority of this area is concentrated at high latitudes (Figure 1d). Poleward of 87° lie the densest trapping regions, reaching a peak density near 89° in the north and 88.5° in the south at which point 85% and 72% of the area lie in shadow, respectively. Based on Diviner surface temperature measurements, Williams et al. (2019) have determined a variation in cold trap area of more than a factor of two between summer and winter. These authors define cold traps by Tmax<110 K, and the sizes depend on the choice of this threshold.

3.2 Geotemporal Trends in PSR Water Deposition

Figure 2 shows the resulting spatial and temporal trends in water accretion within northern (panel a) and southern (panel b) hemisphere PSRs. Here, the color axis corresponds to the PSR particle concentration, σp, which is given by the PSR particle count per unit permanently shadowed area (km2) within a 0.5° latitude bin; data are normalized by the production rate, γ, which is defined as the quotient of the total number of particles simulated per lunation and the surface area of the Moon. In the following discussion, we restrict the start location of particles to latitudes equatorward of ±65° to avoid bias in the latitudinal trends of PSR water capture.

Details are in the caption following the image
Geotemporal variations in volatile cold trapping within northern (a) and southern (b) hemisphere permanently shadowed regions (PSRs) spanning 12 lunar days. The color axis corresponds to the PSR particle concentration σp normalized by the production rate γ. (c) Accumulated latitudinal distribution of PSR water after one lunar year. (d) Latitudinal dependence of the infall rate. σs is given by the particle count divided by the area within each 0.5° latitude band.

Variance in PSR water delivery is observed throughout the year, manifesting most strongly near the pole owing to the growth and decay of seasonal shadow. Near the equinox (time = 0–29.5 days), southern hemisphere PSRs exhibit a flat latitudinal distribution, whose mean concentration σp is ∼102 times larger than the production rate γ. As time progresses and the trapping area broadens in the south, water en route to the pole is more likely to become trapped, resulting in a buildup of water within seasonally shadowed terrain and an associated reduction in water reaching high-latitude PSRs. When trapping area is at its largest expanse in the south (time = 59–118 days), 8.5% of particles simulated were seasonally trapped—a 49% increase from the amount seasonally trapped near the equinox (time = 0–29.5 days). Examining the region poleward of 80°S for which seasonal trapping area is modeled, σp decreases steadily moving toward the pole between time = 59–118 days, reaching a minimum of 47γ.

While the high-latitude PSRs accrete less water during the winter months, the surrounding SSRs are temporarily enriched in adsorbed water. Assuming a steady supply, water gradually builds up within seasonally shadowed terrain, where the quantity of water accumulated is proportional to the length of time spent in shadow; SSRs at the periphery of PSRs thereby have the highest seasonal concentrations given their prolonged collection span. As SSRs deteriorate and the sunlight returns to the surface, seasonally trapped particles are eventually released into the exosphere and continue their migration. The reduced polar temperatures produce relatively short hop distances (on the order of 100–150 km poleward of ±80° compared to ∼200 km at the equator), which has two implications for liberated water: (1) The short flight time decreases the probability of loss per hop, as only ∼42% of all seasonally trapped particles were eventually photolyzed or escaped (compared to the 75% of nonseasonally trapped particles which were lost or destroyed); and (2) the decreased hop distance serves to increase the amount of time and the number of jumps that a particle will make at the pole. Given that this is the highest density region of PSRs at both poles (see Figure 1), the majority of liberated water quickly become trapped within a high-latitude PSR, while a minority migrate equatorward and become captured by a lower-latitude PSR. As shown in Figure 2, water is liberated sequentially as the seasonal trapping area contracts; in the south, this can be observed as a gradual increase in σp between time = 118–236 days after the equinox, reaching a peak near the summer solstice (σp = 301γ at time = 206.5–236 days) when the majority of seasonally trapped water is extricated.

The overall temporal trend in PSR accretion is the same in the north as it is in the south; however, there are notable differences in magnitude. Northern hemisphere PSRs, particularly those nearest the pole, accumulate more water per unit area than those in the south. Despite less permanently shadowed area, a similar percentage of the total number of particles simulated were captured in the north as in the south. In total, northern and southern hemisphere PSRs collected 10.7% and 11.0% of the particles simulated, respectively—consistent with previous exospheric models (Moores, 2016; Schorghofer, 2014, 2017). The greatest PSR influx in the north occurs shortly after the vernal equinox (time = 29.5–59 days), where σp = 404γ—about 34% larger than the peak observed in the south. The north/south asymmetry will be discussed in more detail in section 8.

4 Discussion

4.1 Implications for North and South Polar Frost Distribution

When PSR water deposition is totaled across the lunar year, clear latitudinal trends are observed (Figure 2c). In both hemispheres, the PSR water concentration σp increases moving from ±65° toward the pole; however, as discussed below, the latitudinal trends in deposition are markedly different in the north and south. The increased polar concentrations indicate that lower-latitude traps, given their relatively low fractional coverage, do not pose significant barriers to the poleward migration of water. As such, the ability of water to reach high latitudes where flight paths are diminished enables PSRs nearest the pole to efficiently capture water.

While modeling the behavior of water within PSRs is beyond the scope of this work, it is important to note the ways in which water may reach the subsurface. Once arriving within cold traps, molecules may vertically migrate to the subsurface through a diffusive process (Schorghofer & Taylor, 2007). Additionally, water beneath an ice cover may be pumped down into the regolith through diurnal temperature cycles (Schorghofer & Taylor, 2007; Schorghofer & Aharonson, 2014). Burial through impact gardening provides an additional means for water to reach the subsurface, although if thermal conditions allow for ice mobility, water may migrate to a stable depth and thereby counteract burial through impact gardening (Siegler et al., 2015). Water buried at depth may be largely protected from loss mechanisms such as sublimation and may remain stable across longer timescales compared to water at the surface.

The broad-scale trends in delivery and accretion shown in Figure 2c are qualitatively consistent with latitudinal trends in surface ice concentration detected from orbit (Fisher et al., 2017; Hayne et al., 2015; Li & Milliken, 2017) as well as hydrogen abundance (and perhaps water ice abundance) within the upper 1–2 m of the surface as seen from neutron data (Feldman et al., 2000; Mitrofanov et al., 2010). With the exception of two south polar craters and one north polar crater, however, hydrogen enhancements are not coincident with areas of permanent shadow where the surface water ice is confined (Sanin et al., 2012). One possible explanation for the misalignment between subsurface water and present-day PSRs is the theory of Lunar True Polar Wander, which postulates that the spin axis of the Moon has reoriented from a past position and that the current distribution of hydrogen is a record from an ancient palaeopole (Siegler et al., 2016). This theory is based on data from the Lunar Prospector Neutron Spectrometer showing antipodal hydrogen maxima that is offset ∼5.5° from the current spin axis and assumes that water will preferentially accrete near the instantaneous pole and is capable of migrating beneath the surface to a stable depth. While the extent and distribution of cold traps would be different for a palaeopole than for the modern era, the depositional trends shown in Figure 2c support the notion that volatiles may preferentially be delivered to, and accumulate within, cold traps near the rotational poles.

The PSR depositional patterns can be better understood by examining the latitudinal dependence of the infall rate of water at the surface without PSRs present. This is shown in Figure 2d, where σs is obtained by counting the number of particles that fall within a 0.5° latitude band, which is then divided by the latitudinal area; as before, data are normalized by the global production rate γ. As shown here, σs varies by a factor of ∼2.25 from 65° to the pole, reaching a maximum of ∼450γ at 88–89°N and 88–89°S. The increased flux of water at high latitudes is a result of its temperature dependent migration pattern; the diminished surface temperatures at high polar latitudes yield shorter and more numerous hops, resulting in a higher infall rate. The inclusion of subpixel temperature variations introduced by unresolved topography may preferentially reduce the infall rate at lower latitudes (65–70°), as Prem et al. (2018) found higher rates of escape at low latitudes when transport was modeled with a rough surface compared to a smooth surface. These authors also found that, in comparison to a smooth surface, introducing a stochastic rough surface temperature model slightly increased the number of molecules that were cold trapped and correspondingly decreased the number of molecules that were photolyzed. Thus, with surface roughness effects accounted for in our model, the percentage of molecules cold trapped is expected to be larger than the 10.7% and 11.0% figures reported in section 6.

At all latitudes, northern hemisphere PSRs accumulate more water per unit area than those in the south; however, the north/south difference becomes especially prominent nearest the pole. Analyzing the region poleward of 85°, the mean PSR water concentration σp is ∼19% larger in the north than in the south. To understand the cause of this disparity, we examined the influence of SSRs on north/south PSR accretion by performing an additional Monte Carlo simulation without SSRs present (using 2 million particles and identical model parameters as before). The results of this simulation, however, revealed no statistically significant difference in the total number of particles trapped in either hemisphere without SSRs present. As well, the north and south broad-scale latitudinal trends in PSR accretion without SSRs were unchanged from those with SSRs. The north/south asymmetry is therefore attributed to differences in the migration diffusivities owing to dissimilarities in the hemispheric PSR size-frequency distributions; such differences enforce distinct patterns in poleward migration of water, which favor higher surface concentrations at northern high latitudes.

4.2 Implications for Polar Frost Variability

Numerous orbital data sets have provided evidence for a diurnally varying surface concentration of H2O/OH, implying that H2O/OH is produced at the surface via solar wind implantation and subsequent oxygenation and, furthermore, undergoes a temperature-dependent migration over the course of a lunar day (Clark, 2009; Hendrix et al., 2012, 2019; Li & Milliken, 2017; Pieters et al., 2009; Sunshine et al., 2009). If a continual source of mobile water is assumed, the expansion and contraction of seasonal shadow at the poles should give way to a seasonal variation in the surface hydration in addition to a diurnal one. While the magnitude of the seasonal variation would be largest at the polar regions where SSRs are concentrated, variation should also be present to a lesser degree at low latitudes as seasonal water released from the pole migrates toward the equator. The seasonal variation in exospheric argon observed by the Lunar Atmosphere and Dust Environment Explorer spacecraft was attributed to the presence of seasonal cold traps, in which maxima and minima occur at the solstices and equinoxes, respectively (Hodges Jr, 2018).

In Figure 3a we present a model of how the polar concentration of water varies throughout the year assuming a continual source of constant magnitude. Here, σs represents the surface concentration, which is given by the bulk particle density poleward of ±80°. As shown here, σs varies throughout the year, where the peak occurs at time = 340 and 162 days for the north and south, respectively—significantly offset from the solstices where the seasonal trapping area is greatest—due to the retention of seasonal water. The peaks represent a turning point where the loss rate, regulated by the release of seasonally captured water, begins to outpace the rate of water deposition. The overall temporal variation is identical in the north and south, where the maximum concentration reached is ∼45γ in both hemispheres. Figure 3b displays the latitudinal distribution when the polar concentration of water is largest; as can be seen here, a rapid increase in σs occurs at 87° in both hemispheres where the seasonal trapping area is densest.

Details are in the caption following the image
(a) Seasonal variation in the bulk surface concentration σs poleward of ±80° assuming a steady supply of water. Data are normalized by the production rate γ. Green vertical lines represent the summer/winter solstices. (b) Geographic distribution in water for the north and south pole at their respective peak abundances. Data include water captured within seasonally shadowed regions and permanently shadowed regions.

5 Conclusions

In this work, we assess the geographic extent and temporal variability of SSRs poleward of 80°N and 80°S in order to gauge their influence on polar water migration, deposition and infall within PSRs. In both hemispheres, PSR concentration increases moving from low latitudes (±65°) toward the pole, a pattern that is consistent with broad-scale trends of the putative water ice deposits observed from orbit (Feldman et al., 2000; Hayne et al., 2015; Li & Milliken, 2017). While temperature is likely the dominant parameter controlling the overall stability (and therefore distribution) of water ice on the surface (Fisher et al., 2017; Hayne et al., 2015; Vasavada et al., 1999), the ability of water to reach high latitudes where stability is enhanced may have important implications for the long-term evolution of polar volatile abundance and distribution.

In addition, we find that the northern hemisphere PSRs accumulate more water per unit area than those in the south, a disparity which is especially prominent beyond 85°. The north/south asymmetry arises from differences in the poleward migration of water between the two hemispheres, which in turn is a consequence of their unique PSR size-frequency distributions. While it has been shown that a hemispheric asymmetry can be caused by shifting the source of water to either side of the equator (Crider & Vondrak, 2000; Moores, 2016; Schorghofer, 2014), the model results shown here suggest that, even for a uniformly distributed source of lunar water, asymmetries in concentration between northern and southern hemisphere PSRs are found due to underlying differences in their ability to capture water.

Finally, our Monte Carlo simulations reveal that for a continual source of water, the growth and decay of shadow at the polar regions give rise to a variation in the polar surface concentration of H2O. A seasonal lag is observed due to polar retention of seasonally trapped water; the concentration of cold-trapped water peaks near the hemispheric vernal equinox, significantly offset from the solstice where the seasonal trapping area is most expansive. Seasonal variation should occur on other airless bodies in the solar system with nonzero axial tilt such as Ceres, where the variation may be even more pronounced given its current ∼4° obliquity (Schorghofer et al., 2017).

Acknowledgments

We would like to thank Igor Mitrofanov and an anonymous reviewer for their thoughtful and constructive comments to our manuscript. This work was funded in part by a grant from the Canadian Space Agency's Flights and Fieldwork for the Advancement of Science and Technology (FAST) program. J. L. K. acknowledges additional funding through the Technology for Exo-Planetary Science (TEPS) CREATE program supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. The LOLA data products and PSR maps from Mazarico et al. (2011) used in this work are archived on the Planetary Data System (PDS). As well, the Diviner GCP (Global Cumulative Products) data, from which the global temperature maps of Williams et al. (2017) were derived, are available on the PDS, and the rasters are made available at the diviner.ucla.edu website. The SSR maps described in section 2 and the Monte Carlo model described in section 3 have been included in the supporting information.