RESEARCH ARTICLE
10.1029/2019JE006219
Key Points:• Solar wind standoff can explain
the correlation between the Reiner
Gamma swirl and the colocatedmagnetic anomaly• The outer bright lobes emerge inthe simulated weathering pattern
only when integrating over the entire
lunar orbit• Both the proton and helium energy
flux to the surface need to be taken
into account to best reproduce theswirl pattern

Correspondence to:
J. Deca,jandeca@gmail.com

Citation:
Deca, J., Hemingway, D. J.,
Divin, A., Lue, C., Poppe, A. R.,
Garrick-Bethell, I., et al. (2020).
Simulating the Reiner Gamma swirl:
The long-term effect of solar wind
standoff. Journal of GeophysicalResearch: Planets, 125, e2019JE006219.
https://doi.org/10.1029/2019JE006219

Received 26 SEP 2019
Accepted 3 FEB 2020
Accepted article online 21 FEB 2020

Simulating the Reiner Gamma Swirl: The Long-Term
Effect of Solar Wind Standoff
J. Deca1,2,3 , D. J. Hemingway4 , A. Divin5 , C. Lue6 , A. R. Poppe7
I. Garrick-Bethell8,9 , B. Lembège3 , and M. Horányi1,2,10,

1 Laboratory for Atmospheric and Space Physics (LASP), University of Colorado Boulder, Boulder, CO, USA, 2 Institutefor Modeling Plasma, Atmospheres and Cosmic Dust, NASA/SSERVI, Moffett Field, CA, USA, 3 Laboratoire
Atmosphères, Milieux, Observations Spatiales (LATMOS), Université de Versailles à Saint Quentin, Guyancourt,
France, 4 Department of Terrestrial Magnetism, Carnegie Institution for Science, Washington, DC, USA, 5 Physics
Department, St. Petersburg State University, St. Petersburg, Russia, 6 Swedish Institute of Space Physics, Kiruna,
Sweden, 7 Space Sciences Laboratory, University of California at Berkeley, Berkeley, CA, USA, 8 Earth and Planetary
Sciences, University of California, Santa Cruz, CA, USA, 9 School of Space Research, Kyung Hee University, Seoul,
South Korea, 10 Department of Physics, University of Colorado Boulder, Boulder, CO, USA

Abstract The Reiner Gamma swirl is a prime location to investigate the lunar albedo patterns andtheir colocation with magnetic anomalies. The precise relationship between impinging plasma and theswirl, and, in particular, how these interactions vary over the course of a lunar day, remains an open issue.
Here we use a fully kinetic particle-in-cell code, coupled with a magnetic field model based onorbital-altitude observations, and simulate the interaction with the Reiner Gamma anomaly for all plasma
regimes the region is exposed to along a typical orbit, including different solar wind incidence angles andthe Moon's crossing through the terrestrial magnetosphere. Consistent with the hypothesis that swirls
form as a result of plasma interactions with near-surface magnetic fields, we show that the energy flux
profile produces a pattern similar to Reiner Gamma's alternating bright and darkly colored bands, but only
when integrating over the full lunar orbit. We additionally show that including He2+ as a self-consistentplasma species improves the match.

Plain Language Summary The Moon is dotted with visually distinctive brightness variations,called “lunar swirls.” Measurements have shown that all swirls are colocated with some of the tinymagnetic fields that are present on the surface. One of the most famous regions, in this respect, is theReiner Gamma swirl. Simulating the plasma environment surrounding Reiner Gamma, using also theobserved magnetic fields from two recent spacecraft missions to the Moon, we find that the flux of energy
to the surface is consistent with the optical brightness pattern when the proton and helium componentsof the solar wind are both included. Detailing how certain areas of the lunar surface are shielded better
than others from impinging plasma could help us understand better how space weathering processes alter
the optical properties of exposed surfaces over time. The morphology of swirls may be telling us about thefine-scale near-surface magnetic field structure, thus helping to constrain the origins of the underlying
crustal magnetic sources and how they relate to the early thermal and magnetic history of the Moon. In
addition, understanding the plasma environment near Reiner Gamma is imperative, as it is one of theprime targets for future low-orbiting spacecraft or even lunar landers.

1. Introduction
The Moon is dotted with visually distinctive, high-albedo surface features, called “lunar swirls”(Blewett
et al., 2011; El-Baz, 1972; Hood & Schubert, 1980; Hood & Williams, 1989; Kramer et al., 2011; Schultz &Srnka, 1980). Measurement campaigns have shown that all known swirls are colocated with lunar magnetic anomalies (LMAs). The opposite, however, does not hold (Blewett et al., 2011; Denevi et al., 2016),
and the evolutionary scenario of these enigmatic features has been debated since the Apollo era (Pieters &Noble, 2016).
©2020. American Geophysical Union.
All Rights Reserved.

DECA ET AL.

The three possible lunar swirl formation mechanisms that have received the most attention in the literature are as follows: (1) Recent cometary and micrometeoroid impacts might have left behind remnant
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magnetization and fine-grained, unweathered material that locally brightens the surface (Pinet et al., 2000;
Schultz & Srnka, 1980; Starukhina & Shkuratov, 2004; Syal & Schultz, 2015); (2) high-albedo dust may belofted and then electrostatically sorted (Garrick-Bethell et al., 2011; Hendrix et al., 2016) or magneticallysorted (Pieters et al., 2014) on the lunar surface, or the uppermost soil grains may be structured differently
at swirls, due to the unique electromagnetic and plasma environment, thereby producing unique spectral
properties (Pieters et al., 2014); (3) the presence of LMAs causes the solar wind to “standoff,” locally altering
the weathering patterns by solar wind ions and the subsequent darkening of the regolith by the formationof nanophase iron (np-Fe0 ) (Blewett et al., 2010, 2011; Deca et al., 2018; Glotch et al., 2015; Hemingway &Garrick-Bethell, 2012; Hemingway et al., 2015; Hood & Schubert, 1980; Hendrix et al., 2016; Kramer et al.,2011, 2011; Pieters & Noble, 2016). Note, however, that one mechanism does not necessarily exclude theother. For example, the increased amount of charged particle flux a regolith surface receives might be a necessary precursor and controlling factor that determines the rate of surface weathering by micrometeoriod
impacts (Blewett et al., 2011; Glotch et al., 2015).
Although they so far appear to be unique to the Moon, swirls have potentially broad implications for both
space weathering and planetary magnetism. If the solar wind standoff model is correct, swirls can help todistinguish between the optical effects of exposure to solar wind versus micrometeoroids (which are notaffected by the presence of magnetic fields), thereby helping us to understand how space weathering processes alter the optical properties of exposed surfaces over time (Hemingway et al., 2015; Pieters & Noble,
2016; Sim et al., 2017). Furthermore, the morphology of the swirls may be telling us about the fine-scalenear-surface magnetic field structure, thus helping to constrain the origins of the underlying crustal magnetic sources and how they relate to the early thermal and magnetic history of the Moon (Hemingway &Tikoo, 2018). For both of these applications, a key component of the explanation relates to the way the crustal
fields affect the access of the solar wind plasma to the surface, which is the focus of this study.
Possibly the most well-known swirl formation is Reiner Gamma, a tadpole-shaped albedo marking with an
overall length of about 70 km, located west of the crater Reiner on the Oceanus Procellarum (7.5◦ N, 59.0◦
W; see figure 1 of Lee et al., 2019). The tadpole's head is characterized by an inner bright lobe and two outerbright lobes, set apart by two narrow dark lanes (see figures 1a and 1b of Poppe et al., 2016). Reiner Gamma's
magnetic topology produces a minimagnetosphere (Deca et al., 2018) in which the dark lanes correspondto the areas where the crustal magnetic field is primarily oriented vertically with respect to the surface andthe bright lobes are colocated with a more horizontal topology (Hemingway & Garrick-Bethell, 2012; Poppeet al., 2016). Deca et al. (2018) have shown that the geometry and magnitude of the magnetization have a
key role in generating the charge-separation (Hall) electric field that regulates the charged particle fluxes
to the surface. Assuming that the energy flux the surface receives is inversely proportional to the surface
brightness (Poppe et al., 2016), the fully kinetic model by Deca et al. (2018) reinforces the formation of
the Reiner Gamma swirl accommodated by solar wind standoff. Note that there need not be a one-to-one
correlation between the amount of energy the surface receives and the optical albedo. The exact relationshipmight depend on additional factors (beyond the scope of this work), such as the surface topology and theion energy threshold needed to form np-Fe0 in the regolith grains.
Here we extend the initial results by Deca et al. (2018). The study revealed that the magnetic morphology, that is, the structure and magnitude of the surface field, could be one reason why not every magnetic
anomaly forms a distinct albedo marking (another explanation might be that swirls can only form where
magnetic sources are shallow; Hemingway & Tikoo, 2018). The study also found qualitative correlations
with the simulation results in both optical remote observations of the lunar albedo and in situ measurementsof reflected solar wind. However, the outer bright lobes of the swirl pattern were not well resolved, and thebrightness of the inner bright lobes was overestimated. One explanation to these discrepancies could be that
Deca et al. (2018) focused solely on a scenario where the Reiner Gamma region is exposed to a quiet solar
wind impinging on the lunar regolith parallel to the surface normal, while the real lunar albedo pattern
would have formed over time and over a wide range of plasma conditions in the lunar orbit.
In order to more accurately estimate the long-term surface effects of the plasma interaction with the LMA
that is colocated with the Reiner Gamma swirl, we integrate the energy flux profiles over the entire lunar
orbit, including the solar wind, magnetosheath, tail lobe, and plasma sheet crossings. The Reiner Gamma
region may be a prime area of interest for one of the next lander and/or low-orbiting missions to the Moon
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Table 1
Overview of the Plasma Parameters Used in the Different Simulation Cases

Casen (cm−3 )T (eV)|v𝑓 low |𝛼𝛿Panels(e− , p+ , He2+ )(e− , p+ , He2+ )(km/s)(◦ )(%)

in Figure 2

SW - A75

SW - BSW - Ca, b, c60
(3.15, 3, 0.15)(13, 3.5, 3.5)

350

45

d, e, f93.5

g, h, iSW - D30

j, k, lSW - E15m, n, oSW - F0MS - G(10.5, 10, 0.5)(50, 100, 100)

150

TL - /

0.05(50, 50, 50)

PS - /

0.5(500, 1,000, 1,000)

55

p, q, r5s, t, u

50

1.5

/

100

<0.01

/

Note. See also table 18.1 in Harada and Halekas (2016). 𝛼 is the incidence angle of the flow with respect tothe surface normal. 𝛿 presents an estimate of the amount of energy flux Reiner Gamma receives based on
the density, the magnitude of the flow velocity, plasma temperature, and incidence angle. SW, MS, TL, andPS indicate the solar wind, magnetosheath, tail lobe, and plasma sheet, respectively. Note that the TL andPS cases have not been modeled. Slash (/) means that the simulation cases TL and TS have not been run.

(Blewett et al., 2019; Garrick-Bethell et al., 2019; Stubbs et al., 2018), making a detailed understanding of
the near-surface plasma environment and its response to varying upstream plasma conditions paramount.

2. Methods
We simulate the solar wind interaction with the Reiner Gamma magnetic anomaly using the 3-D fully
kinetic, electromagnetic particle-in-cell code ipic3d (Markidis et al., 2010). The code implements theimplicit moment method (Brackbill & Forslund, 1982; Lapenta et al., 2006; Mason, 1981) on a Cartesianmesh and a set of open boundary conditions that allows a flowing Maxwellian plasma to be injected at the
upstream and side boundaries of the computational domain (Divin et al., 2007; Deca et al., 2015). ipic3d is
optimized to work well for a wide variety of plasma conditions and self-consistently resolves the dynamics
of all simulated ion and electron species (e.g., Deca et al., 2015, 2017). In contrast to explicit particle-in-cellcodes, the numerical algorithm allows us to overstep the Debye scales when investigating non-Debye-scale
physical processes.
The Reiner Gamma magnetic topology is constructed using a Surface Vector Mapping (SVM) model basedon all available magnetic field measurements from the Kaguya and Lunar Prospector missions (Deca et al.,2018; Tsunakawa et al., 2014). Although the 3-D spherical harmonic model is corrected for the solar windpressure and interplanetary magnetic field influences (Tsunakawa et al., 2015), it remains an extrapolationfrom magnetic field measurements at observed altitudes (ranging between 20 and 32 km in altitude above
the Reiner Gamma region) to the lunar surface. Hence, the SVM model does not capture the finest structuresin the near-surface field and therefore provides only a lower bound on the magnitude and an upper boundon the spatial scale of those features (Halekas et al., 2010; Hemingway & Tikoo, 2018). Specifically for theReiner Gamma LMA, it was found that the magnetic topology spatially overestimates the size of the observed
colocated albedo patterns (Deca et al., 2018). In this study we have therefore artificially reduced the spatial
scale of the magnetic model 2.5 times to match the size of the observed albedo patterns. We do not scale themagnetic field magnitude, assuming that only the spatial scale mismatch is an artifact of the SVM model.
The magnetic field anchor points of the main dipolar-like magnetic structure have been lined up with theobserved dark lanes. The lunar surface itself is approximated by a sphere with a radius of 1,737.1 km thatabsorbs all computational particles that pass its boundary. The details on the implementation are available
in the methods section of Deca et al. (2018) and references therein. All simulations reported in this work
implement a domain size of 200 × 650 × 650 km3 with a resolution of 1.35 × 1.35 × 1.35 km3 . We include
three plasma species: electrons, protons, and alpha particles using 64 computational particles per cell per
species, each weighted by the respective density of the species (Table 1). The time step is 1.75 × 10−5 s.
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As the Moon is tidally locked to Earth, no single patch of regolith iscontinuously exposed to the solar wind plasma. Due to the westerly
selenographic location of Reiner Gamma on the lunar surface, pristine
solar wind would impinge on the region from waxing gibbous to waning
crescent, were it not for the terrestrial magnetosphere that intersects thelunar orbit up to waning gibbous (Figure 1). The Moon spends roughly
4.93 days of its 27.3-day orbit in the magnetosheath and a similar combined 4.47 days in the magnetotail and tail lobes (Poppe et al., 2018). From
Apollo 14 surface plasma measurements, the probability to encounter themagnetotail plasma sheet is estimated to range between 10% and 70%,
varying with geomagnetic activity (Rich et al., 1973).
In order to obtain an integrated surface flux profile for the Reiner Gamma
region that is representative for one “typical” lunar orbit/day, we divide
the Moon's trajectory around Earth in different segments. For each segment we simulate the plasma interaction with the SVM model using afixed plasma incidence angle, flow velocities, and temperatures that are
representative for the respective local plasma environment (Table 1). The
location of Reiner Gamma on the lunar surface is such that for only
one fourth of the orbit (six 15◦ segments), the region is exposed to pristine
Figure 1. The location of the Reiner Gamma region on the lunar surface
solar wind plasma (Figure 1). Note that numerical stability constraints(indicated with a dark blue dot) during the various phases of the Moon's
prevented us from simulating a steady-state environment where the solar
orbit around the Earth. The simulated cases are indicated in green.
wind plasma arrives precisely parallel to the surface. This case, however,Segments of the lunar orbit when no or an insignificant amount of particle
flux reaches the region are indicated in red and orange, respectively. The
can be safely ignored, as it would contribute little to the integrated promagnetopause and bow shock positions are taken from Shue et al. (1997)
file and not affect the general conclusions of this work. In addition, onlyand Fairfield (1971).
while traveling through the dawnside magnetosheath (YGSE > 0), a significant amount of plasma can reach the region. During all other phasesof the lunar orbit, Reiner Gamma receives either no (indicated in red on Figure 1) or an insignificant amountof energy flux (indicated in orange on Figure 1). The 𝛿 parameter in Table 1 estimates the theoretical maximum amount of energy flux that each region of the orbit may receive, using the upstream density, the flowor thermal velocity (plasma temperature), and the incidence angle of the plasma flow. In order to simplify
the simulation setup, we also neglect both the interplanetary and the magnetosphere magnetic field components. In other words, we only keep the contribution from the SVM model. The resulting energy fluxes
to the surface of all simulated cases are then added together and weighted according to the fraction of theorbit spent in each segment. Note that Deca et al. (2015) show that the interplanetary magnetic field hasa relatively small effect on the weathering patterns. In contrast, they also show that the solar wind speed
could significantly affect the shielding efficiency of an LMA (although the effect is less pronounced as compared to a change of the incidence angle of the impinging plasma). Even more, in reality also the solar winddensity, temperature, and alpha-to-proton ratio can vary significantly. We chose to work here only with average plasma conditions in order to keep the number of needed simulations within reason, hence making theassumption that the extreme events that could cause a significantly different flux profile as presented here
are rare and are assumed to have a minimal effect on the long-term albedo variations.

3. Results
Figure 2 presents maps of the simulated energy flux to the surface for the seven cases defined in Table 1
and shows the proton, helium, and combined flux (p+ + He2+ ), respectively. All maps are normalized either
to the upstream solar wind proton energy flux (the p+ and He2+ maps) or the combined energy flux(the combined p+ + He2+ maps). The energy flux maps are constructed using the particle data recorded
less than 1.35 km above the spherical lunar surface after the simulation has reached steady state (Decaet al., 2018). To reduce the particle-in-cell noise for the quasi-steady state configuration, we averaged theresults using the output from six individual time steps, each a thousand computational cycles apart and wellexceeding the period of any observed instabilities.
Focusing on the first six rows of Figure 2, that is, the cases where the Reiner Gamma region is exposed to thepristine solar wind at decreasing incidence angles, it is clear that a smaller 𝛼 corresponds to a greater energy
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Figure 2. Maps of the energy flux to the lunar surface for the seven runs outlined in Table 1. The left, middle, and rightcolumns show the proton (p+ ), helium (He2+ ), and combined energy flux (p+ + He2+ ), respectively. The maps arenormalized to the upstream solar wind proton energy flux (left and middle columns) and the combined energy flux
(right column). The He2+ fluxes have been exaggerated five times. The position of the Moon from top to bottom are
identified in Table 1 and Figure 1.

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Figure 3. Comparison of the relative darkening (inverse relative brightness) of Reiner Gamma with the simulated
energy flux to the surface, integrated over one lunar orbit. (a) Inverse of the LRO-WAC empirically normalizedreflectance image (Boyd et al., 2012; Robinson et al., 2010). A smaller number indicates a brighter surface. The
brightness values are normalized to the mare background averaged over the illustrated region. Equivalently, a larger
value indicates more darkening assuming an initially bright surface prior to weathering. (b–d) Integrated, combined,
normalized energy flux profile to the surface combining p+ and He2+ , p+ , and He2+ , respectively. The normalization is
identical to Figure 2. The He2+ fluxes have been enlarged five times. The black boxes indicate the part of the domainused to construct Figure 4.

flux to the lunar regolith. At 𝛼 = 75◦ (first row, case A in Table 1), the surface receives four times less energy
than at normal incidence (sixth row, Case F). Independent of the incidence angle, the areas not shielded fromthe impinging plasma (i.e., the dark lanes) consistently appear at the same location, that is, at the magnetic
field anchor points. The local wake-like structure that appears downstream of the southern-most dark lanes
becomes systematically shorter and less pronounced with decreasing incidence angles. This trend is consistent for the proton, helium, and the combined flux profiles. He2+ ions have only half the charge-to-mass
ratio of the incident protons, resulting in a more narrow weathering pattern. The electric field that forms
when the impinging plasma encounters the magnetic structure is less efficient to deflect alpha particles.
As a result, compared to the proton profiles, the inner bright lobe is less shielded from He2+ , and the tailnortheast (Y > 0 ∧ Z > 0) of the tadpole's head is less prominent.
The seventh row of Figure 2 depicts the situation in between the bow shock and magnetopause (Case G).
Although the plasma in this region of the magnetosphere is hotter and denser, the slower flow velocity
reduces the incident energy flux to the Reiner Gamma region by a factor of 5 compared with the normal
incidence upstream of the bow shock. Nevertheless, the large-scale features of the energy flux pattern are
still present. The “mini-wake” structure observed at a similar incidence angle in the solar wind, however,is absent. In addition, the electric field formed above the magnetic structure is 50% weaker in magnitude
as compared to a solar wind case with similar incidence angle (figure not shown). The latter is consistent
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with the analysis of Run F in Deca et al. (2015), which discusses thesolar wind interaction with a horizontal dipolar magnetic topology for
low-velocity plasma flow.
We characterize the observed brightness variations of the Reiner Gamma
albedo pattern using the empirically normalized reflectance image fromthe Lunar Reconnaissance Orbiter Wide Angle Camera (LRO-WAC; Boydet al., 2012; Robinson et al., 2010). Figure 3 shows the inverse of therelative brightness or, equivalently, the relative darkening, next to theintegrated surface energy flux maps compiled from the simulations. The
integrated results are obtained by averaging the 2-D profiles from Runs
A–G in Figure 2, weighting the respective quantities of each run by thesegment of the lunar orbit they represent (see also the final paragraph ofsection 2). The relative darkening is normalized to the mare backgroundand the maximum brightness in the illustrated 200 km × 200 km region.
A smaller value indicates a brighter area; a larger value indicates moredarkening assuming the surface was initially bright. At first glance, there
are only minimal differences between Case F (Figures 2q–2r) and theorbit-integrated results. This is not entirely unexpected, as the largest conFigure 4. Comparison of the LRO-WAC empirically normalized reflectance tribution to the total flux arrives along the surface normal. Comparing(blue dashed line), the inverse of the proton energy flux (magenta dotted
Figures 2a and 2d, the He2+ profile matches better the observed ratiosline; Deca et al., 2018), and the integrated profiles of the proton (black),
between the dark lanes and the bright lobes (the inner bright lobe in parHe2+ (green), and combined (red) inverse energy flux computed from theticular). This is consistent with the results of a 𝜒 2 estimate (pixel-by-pixel
boxes indicated on Figure 3 (see text for details).
correlation) that uses the inverse relative brightness as the expected value
and the simulation results as the observed data. In addition, we assume
three free parameters to compute the minimum 𝜒 2 values: a translation in Y and Z and the scaling factor
that is originally set to 2.5 by hand. No significant deviations from the initial values set for the free parameters (0 km, 0 km, 2.5) are identified by the 𝜒 2 minimization algorithm. The relative 𝜒 2 values for the p+(90◦ incidence), p+ (Figure 2c), He2+ (Figure 2d), and combined integrated profile (Figure 2b) are 2.84, 1.51,
1.00, and 1.32, respectively. We elaborate further in the discussion of Figure 4. The plasma interaction withthe magnetic field topology overestimates the plasma shielding in Reiner Gamma's tail region, perhaps suggesting that the surface fields in the tail region have been relatively overestimated in the Tsunakawa et al.
(2015) model. Given the resolution of the latter magnetic field model, the fact that the weaker magnetic
signature is present in the model could be seen as an accomplishment of the SVM technique. Most likely,
only in situ measurements of the field structure at altitudes below current-day nominal spacecraft orbits orobservations at the surface will allow a better agreement between the models and the swirl patterns in very
weakly magnetized areas (Blewett et al., 2019; Garrick-Bethell et al., 2019; Stubbs et al., 2018).
To further quantify the results drawn from the 2-D maps, in Figure 4 we construct a profile across the headof the Reiner Gamma swirl (cf. Poppe et al., 2016), averaging the respective variables along the width of theblack box that is overlaying the four panels of Figure 3. For reference, the inverse of the proton flux profile
obtain by Deca et al. (2018) for a solar wind impinging normal to the simulated lunar surface is included
here as well. Note that we do not assume a one-to-one correlation between the surface energy flux and therelative darkening but rather expect the two quantities to reveal similar trends if indeed solar wind standoff is the mechanism responsible for the surface brightness variations. Keeping the initial normalization
adopted in Figure 3, we have subsequently multiplied the simulated inverse energy flux profiles such that
their average values at the location of the inner bright lobe line up with the latter's relative brightness. Comparing with the result from Deca et al. (2018), it is clear that integrating over a full lunar day is required
to shield the surface from the impinging plasma at the location of the southern (Z < 0) outer bright lobe.
The simulated width and brightness of the outer bright lobes, however, are still not well characterized by
the integrated results from the simulation. In reality, the outer lobes are almost twice as bright as the inner
lobe, but the integrated proton simulation shows lobes that are less than a third the brightness of the innerlobe. The He2+ profile offers a closer match to the ratios between the dark lanes and the inner and outerbright lobes with respect to the background brightness away from the swirl region. In other words, the characteristics of the He2+ energy flux profile are more similar to the in situ LRO-WAC counterpart. Althoughthe He2+ energy flux to the surface is responsible for only 20% of the total incident energy deposited on the
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regolith, it may be an important component that shapes the weathering profile. Alternatively, the magnetic
field model is sufficiently uncertain that it is not possible to separate the effects of including He2+ versus
the sculpting of the bulk plasma flow by near-surface fields. For example, two competing models of themagnetic source body geometries have been published, each with different near-surface fields and each consistent with orbital-altitude observations (Garrick-Bethell & Kelley, 2019; Hemingway & Garrick-Bethell,2012). Apart from these limitations of the magnetic field model, we speculate that to activate the formation of np-Fe0 in the regolith grains, a certain threshold energy needs to be exceeded. The amount of energy
deposited at the location of the inner bright lobe is smaller than at the outer bright lobes, but the averageenergy per computational particle that penetrates the central density halo and reaches the surface is greater.

4. Conclusions
Using the fully kinetic particle-in-cell code, iPIC3D (Markidis et al., 2010), coupled with a downwardcontinued model of the near-surface magnetic field structure (Tsunakawa et al., 2015), we have shownthat the major albedo features of the Reiner Gamma swirl—namely, its alternating bright lobes and darklanes—can be explained in terms of the integrated energy flux at the lunar surface (Figures 3 and 4). The simulated weathering pattern consists of broad lobes, where the energy flux to the surface is weak, interrupted
by narrow lanes, where the surface energy flux is at a maximum. We have shown that the best-matchingenergy flux and albedo patterns emerge only when integrating over all solar wind incidence angles andplasma environments that contribute to the total energy flux reaching the location of the swirl. Additionally,
we showed that He2+ might be a key factor required to obtain a one-to-one correlation between the observed
albedo patterns and the plasma weathering pattern generated by the standoff of the impinging solar wind
(Figure 4). An unexplained observation is that the energy flux at the outer bright lobes predicted by themodel is only <50% of the brightness of the inner lobe, when in reality, LRO-WAC albedo data show thatthe outer bright lobes are almost twice as bright as the outer lobes. The mismatch may arise in part from thefact that the Tsunakawa et al. (2015) surface field model may be missing some of the finest structures in thetrue near-surface magnetic fields.
Acknowledgments
J. D. and M. H. gratefully acknowledge
support from NASA's Lunar Data
Analysis Program, Grant
80NSSC17K0420. A. D. was supported
by RFBR Grant 19-02-00993. This
work was supported in part by NASA's
Solar System Exploration Research
Virtual Institute (SSERVI): Institutefor Modeling Plasmas, Atmosphere,
and Cosmic Dust (IMPACT), Grant
NNA14AB06A. Resources supporting
this work were provided by the NASA
High-End Computing (HEC) Program
through the NASA Advanced
Supercomputing (NAS) Division atAmes Research Center and by TGCC
and CINES under the DARI Project
A0050400295. I. G.-B. acknowledges
support from the BK21 plus programof the National Research Foundation(NRF) funded by the Ministry of
Education of the Republic ofKorea.Part of this work was inspired bydiscussions within International Team
437: “Negative Ions in the Solar
System” at the International Space
Science Institute, Bern, Switzerland.
J. D. thanks H. J. Lim for her
suggestions, which helped improving
the manuscript. All data necessary tovalidate the findings presented in thismanuscript can be found at https://doi.org/10.5281/zenodo.3631616 inaccordance with the FAIR data project.

DECA ET AL.

Although the details of solar wind-induced physical and chemical alteration of lunar soil are beyond thescope of this work, we note that no part of the lunar surface is completely shielded from the impinging
plasma. This suggests either that partially shielded lunar surfaces may require long time periods before
becoming saturated and fully darkened or that some additional processes, such as regolith gardening bysmall impacts, work to counteract the darkening effects such that the steady-state optical properties represent some balance between these processes (Hemingway et al., 2015; McFadden et al., 2019), with thebalance depending on the integrated solar wind energy flux.
Our simulations establish a clear link between the Reiner Gamma albedo pattern and the way the impinging
plasma is affected by the near-surface magnetic fields. Our results thus support the solar wind standoff
hypothesis for the formation of swirls (Hood & Schubert, 1980) and suggest that the albedo patterns may
be used to inform models of the finely structured near-surface magnetic fields where swirls are present(Hemingway & Tikoo, 2018). Finally, an improved understanding of the plasma environment at the Reiner
Gamma swirl is particularly valuable, as this is likely to be a prime target for future low-orbiting spacecraft
or even landers (e.g., Blewett et al., 2019; Garrick-Bethell et al., 2019; Stubbs et al., 2018).

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