Dynamic Secondary Illumination in Permanent Shadows within Artemis III Candidate Landing Regions

Investigations that can be conducted at the Artemis III candidate landing regions will benefit from the knowledge of the thermal environment within permanently shadowed regions (PSRs). Within PSRs, secondary illumination controls the surface temperature, varying diurnally and seasonally, affecting the stability and concentration of volatiles cold-trapped within the PSRs. In this case study, we characterize the dynamic nature of secondary illumination at four PSRs that overlap five of the Artemis III candidate landing regions. Our analysis is based on secondary illumination model-generated images paired with PSR images acquired by ShadowCam on board the Korean Pathfinder Lunar Orbiter. We find that illumination and thermal conditions can change rapidly within the PSRs, and knowledge of time-variable secondary illumination can be decisive for the efficient design of investigations and sample collection operations at the PSRs.


Introduction
The unique thermal environment at the lunar poles enables the sequestration of volatile species via cold-trapping within permanently shadowed regions (PSRs; Watson et al. 1961;Arnold 1979;Ingersoll et al. 1992).Volatiles at the polar PSRs may have accumulated over long periods of solar system history (Siegler et al. 2015) and represent high-priority science and exploration targets (e.g., Lemelin et al. 2014;Lawrence 2017;Flahaut et al. 2020).The Artemis III science definition report calls out goals specific to the Artemis III mission (currently planned for 2025; NASA-Press 2023), which will seek to characterize the nature and spatial distribution of surface or subsurface volatiles.The Artemis III science definition report also highlights the connection between a selected landing site and the scientific return toward realizing these goals.Suggested factors for site selection from the Artemis III science definition report include sufficient illumination for long-duration solar power stations; availability of a range of crater sizes, blocks, and locations for radial traverse and comprehensive sampling opportunities; and proximity to PSRs and geologic units that can drive highpriority investigations.The current Artemis III candidate landing regions (A3CLRs) selected in 2022 August (NASA-Press 2022; Petro et al. 2023) are located in the south polar region (within an area 6°from the south pole).These 13 regions were down-selected based on criteria that determine the landing and extravehicular activities (EVA; e.g., terrain slope, communications viability, lighting conditions) possible with the evolving suite of Artemis hardware elements and integrated capabilities of the landing systems under consideration (Lawrence et al. 2023).
Within 6°from the lunar south pole, all candidate regions overlap multiple small PSRs (between 1 and 5 km 2 ), and few of the regions either overlap or are proximal to relatively larger PSRs (>5 km 2 ).Candidate regions have locations of extended solar illumination close to the PSRs, and traverse paths can potentially be selected with direct illumination available more than 50% of the time.The 13 regions are expected to be shortlisted to three to five regions, from which a final landing site will be selected (Lawrence et al. 2023).Characterization of the candidate landing regions that will lead to the eventual shortlisting will be based on factors like the availability of geospatial data, vehicle capability, and favorable communication and illumination conditions (Lawrence et al. 2023).
However, the time-varying nature of the localized thermal behavior within PSRs that can have a decisive impact on EVA planning has yet to be discussed in the context of A3CLR Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
activities.Thermal conditions within PSRs largely depend on indirect illumination (light scattered by local topography; Paige et al. 1992;Kloos et al. 2021;Lucey et al. 2021), and secondary illumination (single reflection) is the largest component of the indirect illumination (Mahanti et al. 2021a).The primary (direct) illumination changes seasonally and diurnally, causing time variability of the secondary illumination and thus the surface temperatures at the PSRs.
While analysis of temperatures within large-sized PSRs (>10 km 2 ) is possible at a 240 m pixel scale from available LRO Diviner measurements, the analysis of illumination within relatively smaller PSRs (<10 km 2 ) is possible at a finer pixel scale based on topography (Bussey et al. 2010;Gläser et al. 2018;Mazarico et al. 2018;Mahanti et al. 2021a;Kloos et al. 2021).Here, we add the perspective of the dynamic local thermal environment within the PSRs overlapping the A3CLR by analyzing secondary illumination images.
The work presented here extends a previous analysis (Mahanti et al. 2023) and involves five of the 13 A3CLRs (Figure 1) showing the dynamic nature of secondary illumination conditions within four PSRs.For these PSRs, we characterize the time-varying nature of the secondary illumination (modeled irradiance estimates at 60 m scale) that can directly affect mission design and EVA.For qualitative validation of model-generated secondary illumination images, we use images acquired by ShadowCam (Robinson et al. 2022) at the four PSRs.ShadowCam is a PSR imaging system on board the Korean Pathfinder Lunar Orbiter (Kim 2022).We perform spatial and temporal analysis of the secondary illumination and discuss dynamic thermal conditions, volatile stability, and illumination in and around the PSRs.The topography-based analysis presented here is general, not mission-or A3CLR-specific.

Scope of Analysis
The five A3CLRs we evaluated wholly or partially overlap four PSRs with areas larger than 5 km 2 (Figure 2, Table 1) that are selected for study.Each A3CLR includes smaller PSRs (see Appendix A for IDs and locations of all PSRs larger than 1 km 2 ), but we consider only the larger PSRs (>5 km 2 ) for this case study.For these PSRs, topography surrounding the PSR has a more significant moderating effect on the secondary illumination compared to the topography inside the PSRs at the scale of analysis performed here (60 m pixels).Larger PSRs (>10 km 2 ), in general, have greater chances of harboring cold traps and may offer better sampling locations.However, large PSRs are not contained within any of the A3CLRs and are only proximal with minor overlap in a few locations, e.g., PSRs at Haworth and Faustini; their areal coverage is much more extensive, and analysis of local topography that significantly affects their overall secondary illumination is outside the scope of this study.
The median elevation for the four PSRs ranges between −1 (PSR 1) and 6 (PSR 3) km.Craters that host PSRs 1 and 2 have identifiable rims and appear less degraded than the craters with muted morphological features that host PSRs 3 and 4 (Figure 3).
PSR 1 near de Gerlache crater is partly overlapped by the de Gerlache Rim 2 region (the previously recognized site 011 of Mazarico et al. 2011 was in a similar location).This nearly circular-shaped PSR is north of the Eratosthenian crater de Gerlache and straddles a Nectarian era massif with more than 3000 m of relief within the area.PSR 1 has the lowest elevation of the four PSRs and the largest area (8.2 km 2 ).PSR 3 on Leibnitz plateau (also identified as the PSR at Mons Mouton) is partly overlapped by two regions, Nobile Rim 1 and the Leibnitz Beta plateau.The average elevation of the PSR is the highest of all the PSRs considered here (+5 km) but has the smallest area (6 km 2 ) PSR 4 is within the "peak near Shackleton" region, located between Shackleton and Slater craters; a small area (−88.79,124.5) receives persistent solar illumination (approximately 80% of the time; Mazarico et al. 2011).The site rests on a pre-Nectarian South Pole Aitken basin massif (Spudis et al. 2008); elevation within the site varies by about 2.7 km (Barker et al. 2016) between the peak (located at approximately the center of the site) and the lowest point within the PSR.
All analyses presented here will correspond to a region-ofinterest (ROI) bounding box around the PSR, where the PSR boundary and the ROI boundary are separated by 3 km.This allows analysis of illumination conditions for any traverse of 2.5 km and shorter from a landing site within an A3CLR and moving toward the PSR.Recent studies indicate that the farthest traverse distance for Artemis 3 is expected to be no more than 2 km from the lunar lander (Coan 2020;Scoville 2022;Pena-Asensio et al. 2024).For the description of directionality within an ROI, we will adopt the o'clock nomenclature.All map rasters presented here are in polar stereographic projection, and horizontal and vertical distances are from the south pole.geometries.Areas with zero illuminated coverage or extremely low signal-to-noise ratio images were identified by comparing image locations with PSRs and average Sun visibility maps (Mazarico et al. 2011).The LROC NAC mosaics are cropped to approximately 3 km outside the PSR boundary in all directions and clearly show the change in local morphology and highlight nearby craters (including secondary crater chains) and boulders that may be sampled during the course of an EVA to the PSRs.The illuminated terrain coverage from LROC NAC also shows the seasonally shadowed regions outside the PSR boundary.The seasonal shadows and the PSR illumination levels are approximately 2-3 orders of magnitude lower than the illuminated terrain and represent a transition zone where the illumination drops when moving toward the center of the PSR (e.g., during a traverse to each PSR from a landing spot outside the PSR but inside the landing region).The LROC NAC mosaics are calibrated in radiance units and help to convert simulated primary illumination irradiance images to radiance units.

Correspondence between Subsolar Latitude and Calendar Dates
The Moonʼs orbital plane does not remain fixed in inertial space but precesses (0°to about 5°inclination with respect to the ecliptic) with an 18.6 yr cycle (2006 and 2024-25 are peak inclination years), and the entirety of this cycle is sampled and used in our simulations of secondary illumination.However, from a lunar mission perspective, we would also like to know the mission time in terms of Earth date.A mapping between the subsolar space and calendar year between 2023 and 2029 enables the reuse of simulation results over the subsolar range, that is, for prospective mission timelines over a multiyear calendar interval (Figure 4).The seasonal sampling interval in our simulation is 0°.02 of subsolar latitude, corresponding to approximately 1 Earth day.The diurnal sampling is affected by sampling the subsolar longitude axis in 15°intervals corresponding to ∼1 day Earth time.This work focuses on the summer season because the best illumination conditions are expected in summer.
We provide the mapping between subsolar latitude intervals and calendar date in Appendix B. The intervals correspond to subsolar latitude limits −1 to −1.3 (early/late summer) and −1.3 to −1.5 (before and after midsummer) and subsolar latitude < −1.5 (midsummer).Note that the peak summer month changes from February in 2023 to September in 2029 (Figure 4).

Secondary Illumination for the PSRs
To accurately calculate secondary illumination, it is important to first outline the map area to include the PSR and nearby topography that can contribute reflected light.This is done on a case-by-case basis by analyzing the topography around the PSR and considering the amount of direct solar illumination, the line of sight from directly illuminated topography, and the PSR and distance of directly illuminated topography from the PSR.For the selected PSRs, a square map area with 8 km sides centered on the PSR was deemed sufficient for robust computation of the secondary illumination.Once the map area is defined, a shapefile for the PSR and topography (Barker et al. 2016; 60 m pixel scale) cropped to the map area is used to obtain viewsheds and view factor maps. Viewsheds are binary maps indicating the presence (or absence) of a line of sight from PSR locations to the rest of the map area.View factor maps contain numerical coefficients (view factors or form factors) that represent the fraction of primary illumination that gets reflected from a source outside the PSR to a receiver inside the PSR (Cohen et al. 1993).
Secondary illumination for each PSR was estimated by first generating primary illumination maps for the map area ( 8 km × 8 km) surrounding the PSR and overlapping the A3CLR for subsolar latitude increments of 0°.1 and subsolar longitude increments of 10°.The incident solar vector is a function of the subsolar latitude (affects the elevation of the solar vector, varies between ±1°.586) and the subsolar longitude (azimuthal direction of the solar vector, varies between 0°and 359°).The solar vector direction defines the angle of incidence for the primary illumination, and map cell values (60 m pixels) are proportional to q ( ) cos i , where θ i is the incidence angle.The primary illumination is computed over the map area but uses a topography extending out to 80°S.The primary illumination map and the view factor maps are used to compute the secondary illumination for the topographic facets within the boundary of PSRs.For simplicity, we assumed a Lambertian photometric function and uniform albedo (for primary illumination scattering).The secondary illumination modeling methods used here can be found in Mahanti et al. (2021b).The pixel scale of topography used for simulation is fixed at 60 m, since a slightly coarser pixel scale leads to faster processing of the complete seasonal behavior yet effectively simulates the spatial illumination conditions for this case study.Note that the pixel scale of the simulation is limited only by the effective pixel scale of the available topography.

ShadowCam Secondary Illumination Images at the PSRs
The modeled secondary illumination inside the PSRs was calibrated with ShadowCam images by first obtaining a pixelto-pixel ratio within the PSR (between ShadowCam and modelgenerated images at 60 m pixel −1 ) and then computing the median ratio to convert from model irradiance to radiance values.ShadowCam images for each PSR (Figure 6; 60 m pixel −1 ) represent the maximum radiance mosaic; i.e., for each PSR, the pixel shows the maximum radiance that was observed by ShadowCam from observations acquired between 2023 January and 2023 October.Average radiance in the ShadowCam maximum value mosaics was much higher for PSRs 1 and 2 (0.28 and 0.35) compared to PSRs 3 and 4 (0.09 and 0.08).
Simulated secondary illumination images (calibrated to radiance units) generated for the entire summer are used to generate the maximum secondary illumination mosaic, similar to the ShadowCam maximum radiance mosaic (Figure 6).For each PSR, the maximum value is computed for a pixel across all images for summer.This process is repeated for all pixels (60 m) to get the maximum illumination mosaic.Note that the simulated maximum illumination maps cover the entire synodic period, so the time period over which the maximum statistic is derived for ShadowCam images is small in comparison and may not sample the true maximum lighting at any given location.However, ShadowCam and modeled mosaics exhibit similar spatial contrast (Figures 5 and 6).

Temporal Variation of Primary and Secondary Illumination
Primary illuminated topography around a PSR contributes to the secondary illumination within the PSR.Due to local topographic variations, not all directly illuminated pixels can contribute to secondary illumination at each PSR pixel.Viewsheds and view factor maps of PSR pixels encode the visibility and energy exchange from the primary illuminated pixels.At each subsolar point, the primary illumination also changes, so over summer, there is a series of primary and secondary illumination maps.The time-varying primary average source illumination and the time-varying secondary average illumination are obtained for each PSR by the following steps.For generating the time series of the primary illumination signal, the simulated primary illumination irradiance images are calibrated to radiance units using the LROC NAC mosaics (at 60 m pixel −1 ).

Illumination across the PSR Boundary
Illumination levels will drop significantly (factors of >10; Wagner et al. 2023) in traverses from primary illuminated terrain into a PSR.For each of the PSRs, we track the maximum magnitude of available illumination (primary illumination outside and secondary illumination inside) within an ROI square ( 8 km × 8 km) centered at the PSR and include all points 2 km distant from each point on the PSR boundary.First, a combined map (primary and secondary) is obtained for each ROI, including the PSR.Then the combined map is averaged radially from the PSR center to a distance larger than 2 km outside the PSR boundary.Statistics are obtained from the 60 m simulations and normalized by the area of the sampling region.

Volatile Sublimation Rate Maps
The potential for cold-trapping water is assessed using the sublimation rates for the PSRs derived by Schorghofer & Williams (2020).The retention of water and other volatiles is extremely sensitive to the surface and near-subsurface temperatures (Watson et al. 1961) ) and partitioned in subsolar (diurnal) and ecliptic (seasonal) longitude bins.Bins with no observations were interpolated, and sublimation rates for each map pixel were determined using the vapor pressure expression from Murphy & Koop (2005).Water ice can accumulate when sublimation rates are less than 10 2 -10 3 kg m −2 Gyr −1 , corresponding to temperatures of 109-114 K.

Secondary Illumination and Volatile Resource Potential within PSRs
Each of our four study areas has regions with direct sunlight (primary illumination) for long periods during the lunar summer and relatively stable temperatures outside the PSR boundaries.Within the PSRs, the secondary illumination controls the thermal conditions.The surface temperatures in PSRs result from a thermal balance between self-heating from nearby terrain, loss to space, and subsurface conduction.The secondary illumination is a dominant component (Buhl et al. 1968;Lucey et al. 2021), and characterizing the spatially variable and time-variable secondary illumination reveals the dynamic nature of the thermal environment within the PSRs.Any seasonal character of primary illumination is transferred to secondary illumination.Local topography around and within a PSR further affects the secondary illumination and corresponding thermal behavior (Hodges 1980;Ingersoll et al. 1992;Vasavada et al. 1999).Temperatures within PSRs are expected to change as secondary illumination levels vary diurnally or with the season.Sublimation rates of volatiles and the cold-trap nature of a PSR depend on temperature and directly affect the resource potential of a PSR.The dynamic nature of the temperature within PSRs can affect the schedule of field studies attempting to study and conduct sampling activities at and within that PSR.

Spatial Variability of Secondary Illumination
The spatial distribution of PSR secondary illumination depends on both large-scale regional morphologies, e.g., preimpact planes, and small-scale topography, e.g., central peaks, domes, and mounds.For PSRs within craters with a distinct asymmetry in the preimpact plane, the elevated crater wall direction receives higher levels of primary illumination, and the opposite wall and floor will then receive higher levels of secondary illumination.Also as a consequence, the areas near the floor on the same side that has an elevated rim will have lower secondary illumination levels.The symmetry of sunlit topography around the PSR influences the symmetry of the spatial statistics of secondary illumination.Since PSRs usually lie on the equator side, on the pole-facing slopes of craters or topographic depressions, secondary illumination typically has a radially asymmetric nature.The area of sunlit topography around the PSR is another factor affecting secondary illumination magnitude.The fractional radiative energy transferred from a sunlit topographic facet to a PSR facet is inversely proportional to the square of the distance between them.Accordingly, large craters often have less secondary illumination reaching the PSR at the crater floor.Planes facing each other and close together have larger radiative interaction.Low amounts of secondary light are expected on flat PSR floors, since the topographic facets at the floor and the illuminated portions of the wall are far apart and the angular orientation is large.In contrast, increased secondary illumination is possible on the steeper inner wall slopes of the crater close to the floor due to the orientation with respect to the directly illuminated topography.In the discussion below, the secondary illumination details are same as in Figure 5; i.e., the maximum secondary illumination maps for each PSR are overlaid on top of the maximum primary illumination map (see Section 2.4 for details), both at 60 m pixel scale.
PSR 3 on the Leibnitz Beta plateau and PSR 4 at the peak near Shackleton crater are located in relatively symmetric regional settings (Figure 7) when compared to PSR 1 near de Gerlache crater (the 4 o'clock direction is higher than 10 o'clock) and PSR 2 in Marvin crater (the 8 o'clock direction is higher than 2 o'clock).PSRs 1 and 2 are both located on the floors of craters formed on a tilt whose elevated wall causes an asymmetry in the secondary illumination.PSR 4 is located at a local depression within an area with an elevation of about 800 m that is higher than the nearby topography.Consequently, no topography near PSR 4 contributes strongly to secondary illumination, and PSR 4 has the least illumination of all the PSRs.PSR 3 also has low levels of secondary illumination compared to PSR 1 (highest average) and PSR 2. From the ShadowCam maximum value mosaics, maximum and average radiance values (Wm −2 sr −1 μm −1 ) for PSRs 1, 2, 3 and 4 are approximately 0.53 (average = 0.28), 0.6 (average = 0.35), 0.42 (average = 0.09), and 0.2 (average = 0.08), respectively, and confirm the analysis based on simulated images.
Within PSRs, the spatial distribution of secondary illumination controls temperature and volatile stability zones.Relatively low illumination values indicate zones of lower temperature and thus higher stability.However, zones of higher volatile stability may not be located in regions that are easy to approach with conventional mobility systems.For purposes of analysis, here we assume that the landing site within an A3CLR is 1 km from the PSR boundary.Actual measurements of distance and time for a traverse are outside the scope of this analysis, but we provide general discussions below for the four PSRs.
Within PSR 1, the low-illumination zone (green marker, Figure 8(A

Seasonal and Diurnal Variations of Secondary Illumination
Spatially averaged primary illumination (over the entire PSR) levels (P(t); see Section 2.5), remain nonzero for PSRs 2, 3, and 4 varying between 8 and 14 Wm −2 sr −1 μm −1 for the summer (Figure 9).The magnitude of average primary illumination P(t) does not change substantially across the summer as the subsolar latitude varies from early to late summer.The seasonality in primary illumination controls secondary illumination (i.e., the averaged secondary illumination signal follows the primary illumination changes, S(t); see Section 2.5), but the diurnal signal may approach a pulselike behavior (high for some subsolar longitudes and low for others) due to the location of the PSR and the associated morphology.For PSR 1, the secondary illumination follows the primary illumination, going to zero before the primary illumination signal becomes zero (PSR completely in shadow around sslon = 100°) and reappears after the primary illumination signal is restored (around sslon = 220°).PSR 1 has a tilted topography, with the southeast wall (4 o'clock) contributing most of the secondary illumination.For sslon between 100°a nd 220°, no secondary illumination reaches PSR 1 for each diurnal cycle.
Unlike PSR 1, the secondary illumination signal does not completely become zero for PSRs 2 and 4 but reduces to about 2 orders of magnitude, although the primary illumination signal does not change by more than 5% across the summer.For PSR 2, the southwest (8 o'clock) crater wall contributes the most to secondary illumination, as it is well lit when the Sun illuminates from the opposite direction.Between sslon 100°a nd 240°, there is barely any primary illumination for the southwest wall; the contribution from the distal topography on the west is small, and accordingly, the magnitude of the secondary illumination signal is low (10 −4 ).Note that for PSRs 1 and 2, the primary illumination of the opposite wall dictates the secondary illumination (Figure 7).
PSR 4 has the lowest levels of secondary illumination for the entire summer, compared to the other PSRs.The peak secondary illumination level for PSR 4 is approximately 0.05 and occurs for sslon between 0°to 30°and 270°to 360°, when the direction of the Sun is approximately 9 o'clock.Proximal topography to the south and east of PSR 4 contributes most of the secondary illumination, and when the Sun direction is approximately 3 o'clock, the secondary illumination signal levels are lowest (10 −5 ).Unlike the other PSRs, PSR 4 is located on peaked topography such that reflections from elevations outside the crater and above the crater rim are too far to contribute effectively.PSR 3 is the only PSR of the four considered here that is not located close to a crater rim that can occlude the primary illumination.Accordingly, for PSR 3, the secondary illumination signal follows the primary signal but does not change significantly diurnally.
For each PSR, the high parts of the secondary illumination signal do not change across the summer, but for the subsolar longitudes where the secondary illumination signal is <0.001, there are small changes, and the signals are even lower during the weak summer.For practical purposes, however, and from the point of view of volatile stability, we hypothesize that signal levels below 0.001 correspond to very low temperatures (<50 K) and may not significantly affect the sublimation rate.

Sublimation Rates
The time-averaged sublimation rates within the PSRs based on the observed Diviner temperatures are consistent with the secondary illumination conditions with the lowest sublimation rates occurring where the lowest irradiance levels are observed (Figure 10).The PSR with the highest levels of secondary illumination (Figure 8(A); PSR 1 near de Gerlache) has sublimation rates of >100 kg m −2 Gyr −1 throughout its interior, making it a weak candidate for coldtrapping water except for possible double-shadowed areas at length scales smaller than the Diviner surface footprint (∼200-300 m; Figure 11).The remaining PSRs contain areas with surface temperatures cold enough to be considered cold traps for water ice.The cold-trapping area within PSR 2 in Marvin (Figure 10(B)) is confined to the poleward-facing side of the PSR near the most equatorial edge and comprises 24% of the total PSR surface area.The two other PSRs have larger fractions of their interiors at temperatures low enough to cold-trap water, with PSR 3 on Leibnitz Beta (Figure 10(C)) having 78% of its interior favorable for cold-trapping water, with the coldest temperatures occurring near its eastern edge, and PSR 4 at peak near Shackleton having nearly its entire interior (97%) cold enough to coldtrap water (Figure 10(D)).The area with the lowest sublimation rate within this PSR experiences temperatures between 37 and 68 K during the summer season, when the subsolar latitude is below the equator, and reaches a minimum temperature of 27 K in winter (Williams et al. 2019).The maximum temperatures remain below 100 K throughout the interior, making it a strong candidate for coldtrapping water, even within close proximity to the PSR boundary.
Figure 9.Diurnal variation of average secondary and primary illumination for the four PSRs for summer.The average primary illumination is 2-3 orders of magnitude higher than the secondary illumination at every point on the subsolar longitude axis.Blue arrows indicate the temporal location of the lowest secondary illumination value.Subsolar latitude classes for summer (midsummer, before/after midsummer, and early/late summer) are the same as in Figure 4.

Volatile Sampling and EVA Considerations
The investigations outlined in the Artemis III Science Definition Report will directly benefit from the knowledge of the PSR environment, and analyses similar to that conducted in this case study at more refined scales for the finally selected site can contribute to this endeavor.Investigations 2c-1 (distribution of water/OH within a PSR) and 2a-3 (temporal variability of frost) outlined in the Artemis III Science Definition Report directly relate to this work.The requirement assessment of both these investigations in the Artemis III Science Definition Report calls out the average and diurnal temperature of the surface as key.Temperatures affect the stability and concentration of volatiles and are expected to vary over diurnal and seasonal timescales.The Artemis III Science Definition Report also asserts that the timing of measurements and sample collection is also critical to document, since the local thermal environment, even in PSRs, is subject to diurnal and seasonal temperature changes that can affect the mobility of volatiles on those timescales.Analyzing both the spatial and temporal nature of the local thermal environment is the target for the seasonal secondary illumination analysis presented here.The diurnal nature of the thermal environment will also constrain the timing of the sample collection.Considering a specific case for PSR 2 inside Marvin crater and a hypothetical EVA scheduled on 2024 January 18, we can show that in less than 24 hr, the secondary illumination increases by about 5 times in some locations of the PSR (Figure 12).Further, considering the primary and secondary illumination together, we can see that consistent direct illumination may be available for a timed approach to the PSR from the north (slopes range between 10 and 15).An optimized EVA design can then include temporal information about the PSR secondary illumination as described here and sunlit pathways up to the PSR rim catering to mission-specific survival capabilities (Mazarico et al. 2023).
Understanding the secondary illumination dynamics will also aid with preparedness for the volatile monitoring (tracking the evolution of volatiles during the sampling process) and containment (techniques and instrumentation in place to mitigate science loss) critical for the safe sampling, transportation, storage, and analysis of volatile-rich samples (Mitchell et al. 2021).For example, rapid changes in available illumination over short periods can indicate a greater need for monitoring, while relatively stable illumination is expected to indicate lower initial concerns over sublimation and volatile loss during collection.Considering a specific case for PSR 2 inside Marvin crater and a hypothetical EVA scheduled around 2024 January 16-18 (Figure 13), we can see that on January 16, the secondary illumination levels increase by approximately 2 orders of magnitude within 8 hr, then decrease until the middle of January 17, and then increase again constantly until January 18.As indicated earlier, secondary illumination changes are expected to have similar effects on volatility/sublimation rates, and based on the knowledge of secondary and primary illumination, details of an EVA that would be suitable for sample collection can be decided.Note that a similar seasonal/ diurnal secondary illumination cycle is expected for a more realistic Artemis mission timeline (e.g., in 2024 and 2025), as we elaborate in Section 2.3, with a possible shift in the day of the year to match the subsolar latitude and longitude variation.
For possible frost surveys, the Artemis III Science Definition Report notes, monitoring the temporal variation of surface frost will require longer-term measurements than the Artemis III EVA durations.Frost surveys conducted by the astronauts would benefit from landing in the early morning to assess the time-of-day changes in frost deposition and location.Such initial measurements can be made in situ by astronauts and through targeted sample collection.The deployment of longerterm instrument packages is required for time-dependent measurements over a minimum of one lunar day/night cycle.Analysis of the seasonal behavior of secondary illumination will directly benefit the scheduling/mission timeline design.

Traverse into a PSR: Illumination Variation across the PSR Boundary
For human operations purposes, it is useful to know what these radiance values mean in terms of lighting conditions that a human would observe.As the model results are calibrated to the radiance values reported by ShadowCam (in Wm −2 sr −1 μm −1 ), we can use methods derived for ShadowCam to convert them into luminance units (Wagner et al. 2023).The spectrum of the incident light (sunlight * lunarhighlandspectrum) is convolved with the response curve of ShadowCam's sensor and the CIE l ¯( ) y function for the responsivity of the human eye (International Organization for Standardization 2023).The resulting curve is then integrated and multiplied by the constant for converting from W to lumens (683 lm W -1 ), resulting in a conversion factor of 70.5 cd (W sr −1 μm −1 ) -1 to convert radiance units into cd m −2 , a measure of surface brightness as visible to humans.This conversion factor was used to convert radiance-calibrated simulated images of the four PSR ROIs for the summer season.The average illuminance image over the summer was computed from all the summer images.Azimuthal averaging was then performed to compute the radial variation of the illuminance (cd m −2 ) for a traverse starting about 2 km from the PSR boundary and progressing toward the PSR center.
The time-averaged surface brightness inside the modeled PSRs is 0.8-6 cd m −2 (Figure 14), which corresponds roughly  to nighttime street lighting at the low end to residential room lighting at the high end.Maximum surface brightnesses are 4× brighter, with the high end reaching normal lighting levels inside an office building.Outside of the dimmest areas, the only vision difficulty astronauts would likely encounter would be the glaringly bright illuminated crater wall on the horizon (3000-6000 cd m −2 , typical daylit ground brightness) being in their field of view, disturbing their "indoor" vision.In most cases, astronauts would benefit from handheld or helmetmounted lights for inspecting geologic features or samples in detail.However, as our case study shows, they may not need artificial light to navigate or identify objects of interest, provided the field activities are planned considering the existing secondary illumination.

Conclusion
We characterized the dynamic nature of secondary illumination at four PSRs >5 km 2 that overlap five of the 13 A3CLRs.Secondary illumination within the PSRs controls surface temperatures, affecting the stability and concentration of volatiles cold-trapped within the PSRs.During summer, the peak illumination within these PSRs causes the highest surface temperatures, corresponding to the conditions when volatiles would be least stable at the surface.Our analysis shows how the illumination within these four PSRs varies spatially and temporally, and we conclude that not all of the four PSRs would be ideal for EVA and sample collection.PSR 4, located in the peak region near Shackleton, received the least summer illumination of the four PSRs and is expected to be the coldest and most efficient cold trap.On the other hand, PSR 1, located near de Gerlache crater in the de Gerlache Rim 2 region, received the highest levels of illumination during summer, making it much warmer and a less efficient cold trap.Average sublimation rates at the four PSRs vary spatially within each PSR and correspond to the spatial variation of secondary illumination.
Diurnal illumination can rapidly change within PSRs.Three of the four PSRs considered here had illumination drop by at least 2 orders of magnitude for approximately 30% of a diurnal cycle.For some PSRs (for example, PSR 1), there is no secondary illumination for a large portion of the diurnal cycle.During those times, the surface temperatures can drop substantially, even during peak summer.Sharp changes are also possible; for example, within 8 hr, the secondary illumination magnitude in the Marvin PSR 2 decreased by 2 orders of magnitude.A proportional behavior is expected for volatility and sublimation rates within the same period and could affect EVA planning within the PSR.
The availability of illumination within the PSRs depends largely on their topographic setting.PSR 4 receives the least amount of illumination despite being located near a region of high Sun visibility.PSR 3 at the Leibnitz Beta plateau (Mons Mouton) is situated atop a relatively high plateau with limited local topography available to scatter light, ensuring the secondary illumination does not have significant diurnal changes.Available illumination drops sharply at the boundary of the PSR and varies by over 3 orders of magnitude.In a hypothetical radial traverse that starts outside a PSR and proceeds inward, the lighting would vary from daylit ground brightness to nighttime street lighting.
Artemis science objectives will require visiting PSRs and extracting samples, with transportation and curation at cryogenic temperatures (−200°C or lower; Cohen et al. 2023).The geologic context, illumination, and thermal conditions are critical information for efficiently planned surface activities and addressing real-time variations.The local thermal environment changes with the seasonal and diurnal variation of secondary illumination and can affect the appropriate timing for measurements and sample collection within PSRs.

Figure 1 .
Figure 1.The 13 A3CLRs with the five regions considered in this work (pink).PSR 3 is overlapped by edges of two regions in the Leibnitz Beta plateau.PSRs 1, 2, and 4 are also near the edges of the de Gerlache Rim 2, Connecting Ridge Extension, and peak near Shackleton regions, respectively.

Figure 2 .
Figure 2. The four PSRs (PSR shape outlined in yellow) at the five A3CLRs.Color-coded topographic elevation proximal to each PSR within an ROI (black square) box for each of the PSRs, the A3CLR regions are delimited with yellow square boxes.Secondary illumination analysis for each PSR is conducted for the ROI box map area.
PSR 2 is in Marvin crater (D = 4.6 km) within the "Connecting Ridge Extension."The floor of Marvin crater has an elevation of −30 m, and the PSR straddles the crater wall adjacent to the Spudis crater.PSR 2 in Marvin is the closest to the south pole of the four PSRs.
Henriksen et al. (2023) constructed 1 m pixel scale LROC NAC-controlled mosaics covering the A3CLR sites, which are useful for supporting mission planning.These mosaics are composed of images selected to optimize illuminated terrain coverage.Subsolar longitudes guided image selection and ordering to ensure local areas had consistent lighting

Figure 3 .
Figure 3. Outlines of the four PSRs in red overlaid on the LROC NAC-controlled mosaics at 20 m pixel scale.(A) PSR 1 is near de Gerlache crater, (B) PSR 2 is in Marvin crater, (C) PSR 3 is on Leibnitz plateau (Mons Mouton), and (D) PSR 4 is within the peak near Shackleton region.

Figure 4 .
Figure 4. Summer subsolar latitude variation for 2023-2029.The red dot indicates the position where the Sun is highest at the south pole.The ranges for midsummer, before and after midsummer, and early/late summer are indicated by red, orange, and yellow, respectively.
. Schorghofer & Williams (2020) calculated the time-integrated sublimation rates from bolometric temperatures observed by the Diviner instrument (Paige et al. 2010b).Individual brightness temperature observations from 2009 July 5 to 2020 March 15 for each of the Diviner infrared channels were map-projected onto a polar stereographic grid at 240 m pixel −1 resolution down to 80°S latitude and converted to bolometric temperatures (Paige et al. 2010a

Figure 5 .
Figure 5. Simulated secondary illumination within PSRs (radiance units) overlaid on simulated primary illumination, cropped to 3 km distance from the PSR perimeter in all directions.The color bar indicates radiance values for the PSR.The maps show maximum secondary illumination over the peak summer period; pixel values can have different time stamps.PSRs 1 and 2 show a larger spatial variability in secondary illumination magnitude over the peak summer compared to the other two PSRs.Note (A) PSR 1 near de Gerlache crater, (B) PSR 2 in Marvin crater, (C) PSR 3 on Leibnitz plateau (Mons Mouton), and (D) PSR 4 in peak near Shackleton.

Figure 6 .
Figure 6.ShadowCam measurements of maximum illumination at the four PSRs overlaid on LROC NAC mosaics, cropped to 3 km distance from the PSR perimeter in all directions.Gray color scale is for the ShadowCam radiance within the PSR, and LROC NAC mosaic radiance is typically 10 times higher.Note (A) PSR 1 near de Gerlache crater, (B) PSR 2 in Marvin crater, (C) PSR 3 on Leibnitz plateau (Mons Mouton), and (D) PSR 4 in peak near Shackleton.
)) inside the PSR is at 4 o'clock with respect to the PSR center at the crater floor.For a hypothetical landing site at 6 o'clock and more than 1 km away from the PSR, a longer path is required to access this low-illumination zone, and easier access (lower slopes) is possible from the 12 o'clock direction.The low-illumination zone in PSR 2 inside Marvin is at 8 o'clock and easier to approach from the south pole side or 3 o'clock.For PSR 3, the low-illumination zones occur at 12 o'clock and 4 o'clock with respect to the PSR center and are approachable by a traverse from the 12 o'clock direction.PSR 4, which has the least illumination among the four PSRs, has the lowest-illuminated zone at 4 o'clock, is reachable by traverses from nearly all directions (except 3 o'clock), and requires traverses at slopes of ∼10°and below.

Figure 7 .
Figure 7. Role of local topography outside the PSR boundary in moderating the maximum secondary illumination within the four PSRs (A: PSR 1, B: PSR 2, C: PSR 3, and D: PSR 4).Note the "perched" nature of the location of PSRs 3 and 4 visible in the average elevation profiles (vertical: 12 o'clock to 6 o'clock in red; horizontal: 9 o'clock to 3 o'clock in blue) with respect to the topographic grid.Note that the average elevation profile represents the whole map area.The yellow arrow shows the direction of the south pole.Spatial X-and Y-axes are in kilometers, and elevations are in meters.The color scale indicates normalized primary illumination -darker shades indicate low illumination, and brighter shades indicate higher levels of primary illumination for the summer season.Inside PSRs, darker shades indicate lower levels of secondary illumination, and brighter shades indicate higher levels of secondary illumination (see Figure 5).

Figure 8 .
Figure 8. Slope and ease of approachability to the least illuminated zones of the PSRs (A: PSR 1, B: PSR 2, C: PSR 3, and D: PSR 4).The yellow arrow shows the direction of the south pole.Spatial X-and Y-axes are in kilometer distance from the south pole.The filled contour plot indicates the slope computed over a 180 m × 180 m box.The slope color scale is in degrees; brighter colors indicate higher slopes, and darker shades indicate lower slopes.Green markers indicate the locations with the lowest levels of secondary illumination during summer (see Figure 5).

Figure 11 .
Figure 11.Histograms of the mean sublimation rates for water from the PSRs in Figure 10 (A: PSR 1, B: PSR 2, C: PSR 3, and D: PSR 4).The vertical dashed lines show the sublimation rate for 100 kg m −2 Gyr −1 , the approximate threshold for long-term ice stability.

Figure 12 .
Figure 12.Change in secondary illumination magnitude for PSR 2 inside Marvin crater on 2024 January 18.

Figure 13 .
Figure 13.Change in secondary illumination (Wm −2 sr −1 μm −1 ) at a specific location (blue) and the PSR average between 2024 January 16 and 2024 January 18 for the PSR within Marvin.

Table 1
PSRs at the Artemis III Candidate Landing Regions Considered for This Work 1. Define the map area for the PSR and obtain the corresponding DEM and PSR shapefiles.2. Compute viewshed and view factor maps for all PSR pixels from the DEM and PSR shapefiles.3. Compute primary illumination irradiance map P o (x, y, t) from the DEM for subsolar time intervals.4. Compute secondary illumination radiance into the PSR over time S(x, y, t) from P o (x, y, t) view factor maps.For simplification, a fixed albedo and Lambertian photometry are assumed.5. Compute the primary illumination source over time P(x, y, t), irradiance from the primary illumination map P o (x, y, t), and the viewsheds of PSR pixels.6. Compute secondary average illumination as a function of time S(t) radiance from S(x, y, t) by averaging spatially for each of the subsolar time instances.S(t) shows the time dependence of average secondary illumination over the summer.7. Compute primary average source illumination as a function of time P(t) irradiance from P(x, y, t) for each of the subsolar time instants.P(t) shows the time dependence of average primary illumination over the summer.