Topographic Correlations Within Lunar Swirls in Mare Ingenii

The Moon's bright albedo markings, known as swirls, are defined by broad, bright, on‐swirl areas separated by darker off‐swirl lanes. Their formation mechanism has long been debated and is key for understanding the processing of the lunar surface, the mobility of the lunar soil particles, and the effects of the space environment on planetary surfaces. Here we present, for the first time, evidence that these features do not necessarily cross the surface without regard to topography or local terrain. Within portions of Mare Ingenii on the lunar far‐side, brighter on‐swirl areas have statistically lower mean elevations than adjacent, darker, off‐swirl lanes. These topographic characteristics provide constraints on the plausible formation mechanisms for the swirls in Mare Ingenii, which in turn provide insight into lunar soil migration and evolution. We believe this correlation with topography argues for highly mobile dust transport across the lunar surface.

. Swirl regions also do not represent a mixture of local components; they display their own distinctive spectral properties (Pieters et al., 2014;Pieters & Noble, 2016). Case in point: bright on-swirl regions display very little difference in absorption band strength compared to dark lanes and nearby mature soils (Pieters & Noble, 2016), in addition to a wavelength-independent increase in albedo (Pieters et al., 2014(Pieters et al., , 2021Pieters & Noble, 2016). However, measures of optical maturity using reflectance versus reflectance ratio properties in the Vis-NIR (Lucey et al., 2000a(Lucey et al., , 2000b show they are less mature than the dark lanes (Kramer et al., 2011b;Lemelin et al., 2019).
On-swirl regions in our study areas are higher in feldspar and orthopyroxene (Lemelin et al., 2019) and are depleted in FeO (Lemelin et al., 2019), TiO 2 (Sato et al., 2017), and OH (Hess et al., 2020;Kramer et al., 2011a). Of particular interest, is the abundance of submicroscopic (≤1 μm) iron particles. It is the presence of these particles, created through both solar wind ion and micrometeoroid bombardment, which cause the spectral changes ascribed to space weathering. These particles fall into two categories, nanoscale (<∼40 nm) and microscale (>∼40 nm), each affecting the spectral properties differently. Radiative transfer modeling indicates that the on-swirl regions contain significantly lower abundances of nanoscale iron than surrounding soils, but similar abundances of microscale iron (Trang & Lucey, 2019). This is based on the assumption of a uniform grain size and particle density across the lunar surface (Trang & Lucey, 2019). Spectral analyses in the near-ultraviolet (NUV) through the near-infrared (NIR) also support the lower abundance of nanoscale iron in the on-swirl regions compared to the nearby, normal mature regolith, with the added constraint of an increased deficiency in the smaller (<∼15 nm) size range (Blewett et al., 2021). In contrast, examination of M 3 spectra of Reiner Gamma by Pieters et al. (2021) supports a decrease in the microscale size fraction as opposed to the nanoscale size fraction.
Compaction can also cause variations in brightness. More compact soils display a higher albedo without any changes to the spectral slope or absorption band depths. Hess et al. (2020) examined regolith compaction within swirl regions and found on-swirl areas were more compact.
Several processes are proposed to explain swirl formation: (a) magnetic shielding of the surface from the solar wind to retard soil maturation (Hood et al., 1979;Hood & Schubert, 1980;Hood & Williams, 1989), (b) levitation and transport of fine-grained dust through electrostatic charging (Garrick-Bethell et al., 2011;Pieters & Garrick-Bethell, 2015), (c) sorting and relocation of darker, magnetized materials (Pieters & Garrick-Bethell, 2015), and (d) surface scouring by comet impacts (Pinet et al., 2000;Schultz & Srnka, 1980;Syal & Schultz, 2015;Starukhina & Shukratov, 2004). Each process has both supporting and contraindicating evidence. Here we present a newly discovered topographic correlation between on-swirl and off-swirl regions within Mare Ingenii that may illuminate the relative roles of these processes in forming swirls and inform the contribution by each process to swirl formation in these areas.
Our results support prior studies that suggest variations in composition and compaction of the optically active portion (top few micro-to-millimeters) do play a key role in the swirl albedo patterns, in addition to surface interactions with the local magnetic field. Topography can affect the compositional and size segregation of materials and sustain them for geologically significant timescales. The observed topographic correlation may be key in resolving and interpreting these observational properties and understanding the relative contributions of these swirl formation processes.

Methods and Approach
The Mare Ingenii swirls (33.7°S, 163.5°E) are located within the southwest corner of the Ingenii basin. Two study areas (A and B; Figures 1 and 2, respectively) were chosen for detailed examination. Study area A represents an area with a more diffuse, lower-contrast albedo boundary and study area B represents an area with a sharper, higher-contrast albedo boundary.
Digital elevation models (DEMs) of the two study areas were created using Lunar Reconnaissance Orbiter Camera (LROC) narrow angle camera (NAC) images employing stereophotoclinometry techniques (Gaskell, 2008;Palmer et al., 2016; Text S1 in Supporting Information S1). Stereophotoclinometry combines the highly accurate absolute position of a stereo solution, with the high-resolution relative position of a photoclinometric solution. Stereo heights were determined every 50-60 m and all other heights were determined by photoclinometry relative to the stereo height. DEMs of both study areas at 70-80 cm/pixel vertical and horizontal resolutions were produced. Stereo height errors are 1.36 m for study area A and 1.89 m for study area B. Since stereo solutions are independent of each other, heights that are separated by large horizontal distances (i.e., a few kilometers) will have the same relative error as heights separated by small horizontal distances (i.e., 50-60 m). Photoclinometric height errors will be similar to stereo height errors.
Regional slopes of up to 0.5° in both study areas were identified and corrected to prevent slope bias. Individual impact craters down to 50 m diameter and other larger topographically distinct geologic features were identified, mapped, and their areas masked from the slope-corrected data. This removes extreme high and low elevation values from both on-swirl and dark lane sub-regions ( Figure 1 and Figure S2 in Supporting Information S1). The final elevation values within defined on-swirl and off-swirl (dark lane) subregions in each study area were then mosaic with defined on-swirl and two concentric off-swirl subregions (off-swirl1 and off-swirl2) and the location of a high-resolution (80 cm/pixel) DEM strip (blue box). (middle right) Cumulative frequency distribution plot of the high-resolution slope-corrected and crater/feature-masked topography for on-swirl (blue), off-swirl1 (red), and off-swirl2 (green) regions. The color-shaded areas surrounding each cumulative frequency distribution line represent the error bars: slight color variations indicate where error bars overlap. (upper right) Slope-corrected, crater-masked DEM with the location of a topographic profile perpendicular to swirl regions shown in purple. Colourized topography has an applied linear stretch over 3 standard deviations of the mean. (bottom) Example topographic profile from the purple line, highlighting on-swirl and off-swirl subregions, with the median elevation of each region demarcated by a dashed line. A boxcar filter 100 pixels wide was applied over the entire profile to smooth the overall shape. The vertical exaggeration is 44x. exported for statistical analyses. For study area A, two concentric off-swirl subregions were defined, each with a comparable number of data points to the on-swirl subregion. For study area B, the on-swirl and a single, off-swirl dark lane subregion cover the full study area. The mapped boundaries between on-swirl and off-swirl subregions were done based on the qualitative tonal differences in global LROC wide angle camera imagery and NAC Example topographic profile from the purple line, highlighting on-swirl and off-swirl regions, with the median elevation of each region demarcated by a dashed line. A boxcar filter 100 pixels wide was applied over the entire profile to smooth the overall shape. Topography and albedo suggest that the smaller, central, off-swirl region area sampled in the profile may be a transition zone. The vertical exaggeration is 58x. 10.1029/2021GL095285 5 of 11 reflectance albedo data within the study region. These mapped boundaries should be considered approximate due to varying, and sometimes subtle, albedo contrast in the images (subregion location information is provided as a Geotiff in the Supporting Information S1).
To investigate the topographic data, we compared cumulative distributions between on-swirl and off-swirl locations within each study area. This method retains more information than standard histogram binning, which has arbitrary boundaries, and it provides a straightforward graphical representation of key characteristics and distribution shapes. We evaluated the statistical significance of the topographic differences between on-swirl and off-swirl (dark lane) subregions using Kuiper's variant of the Kolmogorov-Smirnov (K-S) test (Press et al., 2007). When dealing with large data sets, here between 3.67 and 9.76 million points per subregion, even small differences in distributions are statistically significant. We then calculated the mean height for each subregion, including propagation of the errors. The error on the mean height is inverse of the number of data points; therefore, the mean height of each subregion achieves millimeter accuracy even though the errors on individual points are at a meter-scale. To quantify the difference in the mean heights between the subregions, we derived a confidence interval assuming independent samples with unknown but equal population variances. We used the Z score, based on the cumulative standard normal distribution, and report the difference in mean heights for a 95% confidence interval.

Results
The topographic distributions for each of the high-resolution study areas are plotted in Figures 1 and 2. The height for each pixel is plotted in terms of the cumulative distribution, along with error bars (errors are 1.36 and 1.89 m per pixel for areas A and B, respectively). The K-S test results represent a confidence level of greater than four sigma that the on-swirl and off-swirl topographic data sets are not drawn from the same samples at either study area. In study area A, 98% of the on-swirl heights are lower than the inner, off-swirl1 and outer, off-swirl 2 data. In study area B, 99% of the on-swirl heights are lower than the off-swirl data. The mean heights for each subregion are as follows: study area A on-swirl = −3565.5997 ± 0.0005 m, off-swirl1 = −3563.2138 ± 0.000 4 m, off-swirl2 = −3561.1242 ± 0.0004 m; study area B on-swirl = −3493.4499 ± 0.0005 m, off-swirl = −3 490.8101 ± 0.0007 m. From the confidence interval analysis, the mean of the on-swirl heights in study area A is 2.386 ± 0.005 m lower than off-swirl1 and 4.475 ± 0.005 m lower than off-swirl2; implying a progressive decrease in elevation from off-to on-swirl. For study area B, the mean of the on-swirl heights is lower than the off-swirl, dark lanes by 2.640 ± 0.004 m.
Histograms of the topographic data, with Gaussian fits (Figure 3), show the best fit Gaussian means to the topographic data are lower in the on-swirl subregion in study area A by 2.7 ± 0.4 m compared to the inner, off-swirl1 Figure 3. Histograms of the high-resolution topographic data, divided into 40 height bins, for study areas A (left) and B (right). Gaussian fits to each of the on-swirl and off-swirl regions are plotted as dashed lines. The decreasing mean heights from off-to on-swirl are apparent, as are the different data set sizes (see Table S2 in Supporting Information S1 for Gaussian fit parameters). The same color scheme has been used as that in the cumulative frequency distribution plots in Figures 1 and 2: slight color variations indicate where data are overplotted. subregion and by 3.7 ± 0.4 m compared to the outer, off-swirl2 subregion. Similarly, the best fit Gaussian means for study area B show the topographic data are lower in the on-swirl subregion by 2.7 ± 0.2 m compared to the off-swirl, dark lanes. These fits to the binned data provide a second measurement of the differences in the height distributions and are confirmation that the on-swirl subregions are indeed lower than their surroundings by a few meters.

Discussion
Stereophotoclinometry has enabled the measurement of lunar topographic features at submeter scale both horizontally and vertically. In contrast, the lunar digital elevation model derived from the Lunar Orbiter Laser Altimeter (LOLA) and SELENE Terrain Camera has a resolution of 3-4 m (Barker et al., 2016a), which would not detect the topographic differences discovered here using the stereophotoclinometric technique. Of the proposed swirl formation mechanisms, dust transport is the one most affected by topography. Here, we explore the idea that these topographic lows might trap and enable the collection of submicron to micron-sized dust, the size fraction that most highly affects the spectral properties (Pieters, 1993). However, in order to trap lunar dust grains, there must first be a mechanism for migrating lunar dust across the Moon's surface.
The lunar plasma environment includes photoemission on the sunlit side, collection of electrons and ions from the solar wind and terrestrial magnetotail, and secondary electron emission from occasional hot electron populations. The relative strengths of these currents vary throughout the Moon's rotation and revolution (e.g., Stubbs et al., 2014). The smallest, micron-to-submicron-sized particles of the regolith are particularly susceptible to nongravitational forces. Therefore, electrostatic lunar dust dynamics may occur as a result of the interaction between small, charged particles and the plasma environment. Particles can be lifted from the surface through impacts and/or electrostatic forces, either following ballistic trajectories or hovering above the surface if the electric force balances gravity (e.g., Colwell et al., 2007). The sizes of particles that could be lifted from the lunar surface are not well constrained. The repulsive force generated in the patched-charge model is sufficient to loft particles tens of microns in diameter (Schwan et al., 2017;Wang et al., 2016).
Dust grain motion above the surface of the Moon has been inferred on multiple occasions. A horizon glow, at roughly 0.3 m high, was detected by Surveyors 5, 6, and 7 (Rennilson & Criswell, 1974). The Lunar Ejecta And Meteorite (LEAM) experiment deployed on the lunar surface by Apollo 17 recorded evidence for vertical and horizontal dust migration (Berg et al., 1974(Berg et al., , 1976. More recent analyses indicate that the LEAM nighttime signals were not caused by charged dust grains moving across the surface, while the daytime data require more analyses (Grün & Horányi, 2013).
Experiments on dust transport have not yet been conducted at the km scales of our subregions and at the relatively shallow depth differences between on-swirl and off-swirl regions, but there is support for electrostatic dust collection in topographical lows on airless surfaces. Laboratory work has demonstrated that dust particles can be levitated and transported above surfaces with plasma sheaths and into depressions (e.g., Sickafoose, 2002;Sickafoose et al., 2002;Wang et al., 2009Wang et al., , 2010Wang et al., , 2016. Numerical simulations of electrostatic dust transport in a photoelectron sheath near a 7-m diameter, 1-m deep crater show that dust grains accumulate within the crater due to more complex electric fields associated with the crater's edge (Poppe et al., 2012b). The crater in this simulation can be thought of as a "topographic pocket," analogous to the topographic lows associated with the on-swirl regions, albeit slightly shallower. Poppe et al. (2012b)'s study shows that dust can migrate into the crater and be trapped: in transport simulations with dust grains ranging from 10 nm to 10 μm, the crater pocket traps larger grains at higher efficiency than smaller grains due to the varying relative balance between electrostatic and gravitational forces as a function of grain size. Similarly, transport of micron-sized particles in a photoelectron sheath has been proposed as an explanation for dust "ponds" that were observed in 20-m to 300-m wide craters on asteroid Eros (Colwell et al., 2005). Micron-sized dust transport has further been suggested as a global surface smoothing mechanism on Saturn's 30-km diameter moon Atlas, by filling in and erasing craters (Hirata & Miyamoto, 2012). Unlike the other examples, Atlas' plasma surface environment includes immersion in a magnetosphere.
The presence of a local magnetic field at a lunar swirl creates an environment in which solar wind protons can be reflected through a combination of magnetic and electrostatic effects. Simulations have shown that these fields mainly govern the electrostatic interaction at altitudes >100 m while the near-surface plasma environment discussed above dominates at lower altitudes (Poppe et al., 2021a). The role that electrostatic fields play in governing the reflection at higher altitudes has been well studied (e.g., Deca et al., 2018;Fatemi et al., 2015;Saito et al., 2012). The most recent models extend down to the swirl near-surface region and find that the plasma environment differs vastly with altitude and depends critically on upstream plasma parameters (Deca et al., 2021). It has been proposed that this unique environment can attract or repel charged dust into or out of the swirls (Pieters & Garrick-Bethell, 2015). Thus, while there are multiple methods for transporting dust; one is directly correlated to the magnetic field presence at lunar swirls. The presence of a local magnetic field on electrostatically levitated dust has not been fully examined through simulations or experiments. Nonetheless, experiments of a plasma sheath with a magnetic dipole suggest that electric fields in the regions of magnetic anomalies on the lunar surface may enhance the transport of small dust particles (Wang et al., 2012).
Characteristics of distinct topographical changes that can affect dust motion, such as electric fields at crater edges and sharp shadow boundaries, are not likely to occur in the shallow height differences we have detected. However, the motion of lofted dust particles in near-surface plasma sheaths does follow topography. The topographic pocket need not be a crater, any depression can serve to trap and accumulate dust. We note that the change in slope from a crater's rim is steeper than the topographic slope change between on-swirl and off-swirl. The boundary in swirl regions can be very gradational or diffuse compared to a crater's rim. This is seen in Swirl Area B (Figure 2), where the tip of the off-swirl "tongue" near A′ is close in albedo to the adjacent on-swirl region, and may represent a transitional area between on-swirl and off-swirl. Simulations taking these differences into account are beyond the scope of this study, however photometric studies, as discussed next, support the structural differences expected from the entrapment of fine-grained dust.
Photometric studies of lunar swirl regions suggest millimeter-scale roughness and compaction differences between on-swirl and off-swirl regions (Barker et al., 2016b;Hess et al., 2020;Kaydash et al., 2009;Kreslavsky & Shkuratov, 2003;Pinet et al., 2000) which are ascribed to the removal of fine-grained lunar dust and the destruction of the "fairy-castle" structure of lunar soils (Syal & Schultz, 2015;Wu & Hapke, 2018). This has been used to argue for comet impact as the formation mechanism of lunar swirls. Alternatively, if the fine-grained fraction of dust is transported away from those bright areas where the magnetic field is parallel to the surface, then this could disrupt and (or) degrade the "fairy-castle" structure and also be commensurate with the difference in compaction derived by Hess et al. (2020). Electrostatic dust transport simulations also constrain the relative grain size of the lunar dust trapped in the on-swirl pockets compared to the off-swirl regions, in addition to affecting the soil roughness and compaction due to the deposition of dust grains. These constraints, combined with simulation results, imply that it is not the very finest fraction (<1 μm) of the lunar dust that is trapped in the on-swirl topographic pockets, but a larger size fraction (>10 μm) dust grain that would form a soil structure less porous than the fairy-castle structure ubiquitous to the lunar surface. The finest fraction could continue to migrate globally across the lunar surface until it encounters a trap 10-100 s of meters deep (Colwell et al., 2007), such as some of the craters within the swirl regions. Roughness measurements derived from LRO's Mini-RF synthetic aperture radar (SAR) observations detect no surface roughness variations within swirl regions at the centimeter-to-decimeter-scale (Neish et al., 2011), thus the soil structure differences are at the micrometer to millimeter-scale sensitivity of the spectral and photometric measurements. These observations argue that the swirl albedo pattern is shallow and consistent with a very thin surface layer less than several decimeters thick (Neish et al., 2011), providing a constraint on the depth of the dust layer that can accumulate within the on-swirl topographic pockets.
Swirl formation mechanisms must also explain the maturity and compositional properties. Maturity measurements support surface shielding from the solar wind, as does the orientation of the fields with respect to bright and dark areas (Hemingway & Garrick-Bethell, 2012), the abundance of OH/H 2 O of bright areas relative to the nearby, background surface (Hess et al., 2020;Kramer et al., 2011b), and the correlation of OH/H 2 O abundance with magnetic field strength (Hess et al., 2020). These same observed properties also support the removal of the uppermost, very thin, mature layer of the regolith by cometary gas, leaving behind a less mature regolith that will undergo reduced space weathering due to magnetic shielding (e.g., Hess et al., 2020). While there is evidence supporting a role for magnetic shielding in swirl formation, the spectral signatures require the inclusion of additional physical processes (Hess et al., 2020;Pieters et al., 2014Pieters et al., , 2016Pieters et al., , 2021. For example, the on-swirl areas display steeper NIR continuum slopes and shallower NUV slopes than fresh material from background lunar regolith (Blewett et al., 2021). The newly detected topographic correlations in this study argue for contributions from grain sorting; by electrostatic levitation, magnetic sorting, or both. 10.1029/2021GL095285 8 of 11 Modeling of the associated magnetic fields shows they can reduce the impinging solar wind ion flux between 0% and ∼50% depending on the strength of the magnetic anomaly and solar wind conditions (Lue et al., 2011;Saito et al., 2010Saito et al., , 2012Wieser et al., 2010) and lower the energy of the incoming ions by ∼20% (Farrell et al., 2017;Fatemi et al., 2015;Poppe et al., 2016;Zimmerman et al., 2015). The timescales for the two dominant space-weathering processes are 10 4 -10 6 years for solar wind radiation and 10 8 -10 9 years for micrometeorite bombardment (Vernazza et al., 2009). Each of these weathering processes produces rims on the soil grains. Examination of solar flare track density measurements for mature lunar soils indicate both types of rims accumulate in ∼10 6 -10 7 years (Keller & Zhang, 2015;Pieters & Noble, 2016), suggesting that neither process dominates the maturation process. These timescales are much smaller than the 2-4 billion year age of the background surface of most swirls (e.g., Garrick-Bethell et al., 2011), and the accumulation of the weathering rims is also shorter than the <10 8 yr age of the cross-cutting relationships observed in some swirl regions (Schultz & Srnka, 1980;Syal & Schultz, 2015). Even with a reduction of solar wind radiation by 50%, the surface in swirl regions will have been exposed to the weathering environment over a sufficient time span to have optically matured unless there is a mechanism for refreshing the surface. The timescales for dust migration over distances corresponding to swirl region scales are not constrained by current observations or models, nor are the lifetimes for dust grains within the on-swirl topographic pockets or dust traps. It is feasible that migration of dust into these traps operates on timescales shorter than the solar wind maturation process (Garrick-Bethell et al., 2011), thus the accumulated lunar dust has been sufficiently shielded from the solar wind to explain the swirl maturity properties.
The weathered fraction of the lunar soil contains submicroscopic iron. Studies of anorthite (Ca-rich endmember feldspar) suggest that micrometeorite bombardment dominates the production of nanoscale iron (Keller & Zhang, 2015;Trang & Lucey, 2019), and thus at first glance would suggest this size fraction of submicroscopic iron should be the same on-swirl as in the background regolith, commensurate with the studies of Pieters et al. (2021), but contradictory to the works of Trang and Lucey (2019) and Blewett et al. (2021). However, the presence of nanoscale iron may magnetize these grains if the domains are magnetically aligned, and be of sufficiently low density to be susceptible to removal by magnetic sorting, or a combination of electrostatic levitation and magnetic removal. The larger, heavier, microscale grains (such as those found in agglutinates) may not be removed, thus explaining their similar concentration on-swirl as off-swirl. Thus, the on-swirl pockets may be more effective at accumulating the less mature component of the lunar soil's dust while the dark off-swirl regions form a repository for the more mature fraction.
Questions that remain, and would benefit from laboratory and theoretical work beyond the scope of this study, include: 1. What is the size/density fraction of grains preferentially trapped in on-swirl pockets? 2. How does this size/density fraction compare to those grains that would be preferentially trapped in craters within the swirl regions? 3. What are the magnetic properties of submicroscopic iron (do they form magnetically aligned domains)? 4. If the lofted grains are magnetic, how does the magnetic field affect where they are deposited? 5. How does the deposition of these lofted materials affect the compaction/porosity of the regolith?

Conclusions
The topographically low, higher albedo, on-swirl regions observed in Mare Ingenii support the process of dust migration across the lunar surface, contributing to swirl formation. This process is consistent with the spectral and photometric properties for on-swirl regions. From the two study areas in Mare Ingenii, we find that the bulk topography is 2-3 m lower on-swirl than the immediate surrounding off-swirl dark lanes. Based on this discovery and the plausible surface processes for on-swirl regions, these may serve as traps for intermediate-sized (10-1,000 μm) lunar dust grains. Within these traps, the grain size and deposition process form a more compact soil structure compared to the average lunar surface. Future examination of other swirl regions will potentially clarify the correlation of regional topographic differences within swirls, especially in cases where swirls appear on much steeper slopes and drape over impact ejecta. Additional studies will place boundaries on the relative role of dust migration and trapping versus solar wind shielding in creating the thin albedo variations known as swirls.

Data Availability Statement
Data used include Lunar Reconnaissance Orbiter Narrow Angle Camera (LROC-NAC) images. The specific images used are listed in the supplementary materials. These images are publicly available through the Planetary Data System Cartography and Imaging Sciences Node (pds-imaging.jpl.nasa.gov). Compositional and optical maturity maps used in this study are publicly available from the LROC Quickmap public site (https://quickmap. lroc.asu.edu/). The stereophotoclinometry technique and software is described in Gaskell (2008) and Palmer et al. (2016). The topography is included in the supplementary materials as Geotiffs. Geotiffs defining the regions within both Study Areas A and B are being prepared for delivery to the Planetary Data System for calendar year 2022. Prior to delivery they can be obtained from Zenodo at doi:10.5281/zenodo.5794193. The Digital Elevation Models (DEMs) examined in this study (low resolution and higher-resolution strips), including slope-corrected and crater plus feature-masked products, are part of a larger project that will be archived with the Planetary Data System at the completion of the project, however the images and software used to create them are in the public domain, as stated above. Requests for these DEMs prior to archive in the PDS can be sent to the lead author.