Lunar Meteoritic Gardening Rate Derived from in Situ LADEE/LDEX Measurements, Geophys

Geophysical Research Letters

RESEARCH LETTER Lunar meteoritic gardening rate derived from in situ 10.1002/2016GL069148 LADEE/LDEX measurements

Key Points: 1 2,3,4 • LDEX directly samples the material Jamey R. Szalay and Mihály Horányi reblanketing the lunar surface 1 2 •Thelunardustdensityhasanaverage Southwest Research Institute, San Antonio, Texas, USA, Laboratory for Atmospheric and Space Physics, University of scale height of approximately 200 km Colorado Boulder, Boulder, Colorado, USA, 3Department of Physics, University of Colorado Boulder, Boulder, Colorado, • 40 μm/Myr of lunar soil is USA, 4Institute for Modeling Plasma, Atmospheres, and Cosmic Dust, Boulder, Colorado, USA redistributed near the equatorial plane by meteoritic bombardment, primarily driven by the apex sporadic source Abstract The Lunar Atmosphere and Dust Environment Explorer (LADEE) orbited the Moon for approximately 6 months, taking data with the Lunar Dust Experiment (LDEX). LDEX was uniquely equipped to characterize the current rate of lunar impact gardening as it measured the very particles Correspondence to: J. R. Szalay, taking part in this process. By deriving an average lunar dust density distribution, we calculate the rate [email protected] at which exospheric dust rains back down onto the lunar surface. Near the equatorial plane, we find that approximately 40 μm/Myr of lunar regolith, with a cumulative size distribution index of 2.7, is redistributed Citation: due to meteoritic bombardment, a process which occurs predominantly on the lunar apex hemisphere. Szalay, J. R., and M. Horányi (2016), Lunar meteoritic gardening rate derived from in situ LADEE/LDEX measurements, Geophys. Res. Lett., 43, doi:10.1002/2016GL069148. 1. Introduction The surfaces of airless bodies are continually bombarded by micrometeoroids, which eject and redistribute Received 13 APR 2016 the surface material in a process called impact gardening [Gault et al., 1974; Arnold, 1975; Morris, 1978]. Impact Accepted 9 MAY 2016 gardening is ubiquitous throughout the solar system and plays a critical role in how surfaces are modified Accepted article online 16 MAY 2016 and evolve over time. Without any appreciable atmosphere, airless bodies are exposed to their ambient plasma environments and undergo space weathering processes [Pieters et al., 2000; Taylor et al., 2001], with an efficacy that depends on the competing impact gardening rate at which the lunar material is resurfaced. Impact gardening plays a role in the evolution of volatiles trapped in permanently shadowed regions, mixing and potentially covering them over time [Hodges, 2002; Hurley et al., 2012]. This process is also expected to be relevant at Mercury [Morgan et al.,1988],wheremeteoroidimpactspeedsandtheirsubsequentimpact ejecta generation can be considerably larger than the Moon [Marchi et al.,2005].Lunarswirls,peculiaralbedo markings on the surface of the Moon, represent an active area of research with multiple competing pro- posed source mechanisms [Kramer et al., 2011; Garrick-Bethell et al., 2011; Glotch et al., 2015; Syal and Schultz, 2015; Poppe et al., 2016]. Any explanation for such albedo markings must be consistent with known impact gardening/resurfacing rates. Scientific instruments or solar panels deployed on the lunar surface are subject to the accumulation of dust from meteoritic bombardment, degrading their performance over time. The Apollo and Lunokhod retroreflectors placed on the surface of the Moon have degraded considerably. The most likely explanation for this degradation is the accumulation of dust partially covering the reflectors, reducing their ability to reflect [Murphy et al., 2010, 2014]. Data from the Apollo Dust Detector Experiments were used to estimate solar cell degradation as well as buildup of dust on vertically facing solar cells by measuring their output as a function of time [Hollick and O’Brien,2013].Whilefutureinstrumentshavebeenproposedtobetterunderstand these fluxes [Li et al., 2015], currently, quantitative estimates for the buildup of impact ejecta on such surfaces remain relatively unconstrained.

©2016. The Authors. The Lunar Dust Experiment (LDEX) [Horányi and et al., 2014] was an impact ionization dust detector aboard This is an open access article under the the Lunar Atmosphere and Dust Environment Explorer (LADEE) [Elphic et al., 2014]. LDEX recorded average terms of the Creative Commons Attribution-NonCommercial-NoDerivs impact rates of ∼1 hit/min of particles during the lower altitude science phase, with radii of a ≳0.3 μm. Using License, which permits use and the data taken during approximately 6 months of operation, LDEX was able to characterize the dust density distribution in any medium, provided distribution of the lunar dust cloud as a function of time, altitude, and local time (LT). LDEX discovered a the original work is properly cited, the use is non-commercial and no permanently present, asymmetric dust cloud [Horányi et al., 2015]. The grains detected by LDEX return to the modiﬁcations or adaptations are made. surface on timescales of a few minutes and are the very same grains which reblanket the lunar surface.

SZALAY AND HORÁNYI LUNAR METEORITIC GARDENING RATE 1 Geophysical Research Letters 10.1002/2016GL069148

Figure 1. Lunar dust density for each local time denoted by the colored dots and error bars. The diagram in the top corner shows the local time range for each color. The grey curve with error bars in the bottom panel shows the average over all local times. The dashed line shows the best exponential ﬁt to the average in the bottom panel, replicated in each of the above panels. Each panel covers the same range of arbitrary linear units.

The lunar dust density distribution in the equatorial plane was found to be primarily generated by three known sporadic sources: the helion (HE), apex (AP), and antihelion (AH) [Szalay and Horányi, 2015a], with a minor contribution potentially coming from the antiapex (AA) source [Herschel, 1911; Janches et al., 2000; Campbell-Brown, 2008]. The ejecta cloud was observed to be sensitive to small changes in impactor ﬂuxes and velocities. During several of the known meteoroid showers, LDEX observed temporary enhancements of the lunar dust cloud, localized to the hemisphere exposed to the incident meteoroid shower ﬂux [Szalay and Horányi, 2016].

2. Determining the Average Lunar Dust Density Profile To determine the impact gardening rate, an average vertical structure of the dust density profile must be derived. First, we select data taken during the months of January to April 2014, as this is the time period with minimal meteoroid shower activity [Szalay and Horányi, 2016] and most indicative of the cloud’s average behavior. We calculate the density as a function of altitude for local time (LT) bins of 1.5 h for all available local times. Normalizing each density to the 6 LT profile, we determine an average dust density profile as a function of altitude (Figure 1). For the purposes of this study, an exponential fit is found to be in good agreement, with −h∕" the form n(h)=n0e , where h is the altitude in kilometers above the lunar surface, n0 is the density at h=0, and =200 km is the scale height. The altitude distribution of the dust is then f(h)= 1 e−h∕". " " As a first approximation, f(h) was calculated by averaging all observations over the local times LADEE visited [Horányi et al., 2015, Methods]. Due to LADEE’s orbital characteristics, each sampled local time covers a different distribution of altitudes. Here we present an improved method to determine the distribution function by removing the correlation between local time and altitude. Assuming all LDEX detections are for particles at their vertical turning points [Horányi et al.,2015],wecancalculatethevelocityparticleswillreimpactthe surface from any altitude from energy conservation. With the approximation that all grains undergo purely vertical motion, the corresponding one-dimensional velocity distribution function at the surface is

R∕" dh 2Rv − 2 f(v)=f (h(v)) = e (ve∕v) −1 , (1) dv 2 2 2 "ve 1 −(v∕ve)

( ) R where ve =2.4 km/s is the lunar escape speed, R=1737 km is the radius of the Moon, and h(v)= 2 from (ve∕v) −1 energy conservation. This distribution function diﬀers from previous work [Horányi et al., 2015, Methods] due to the additional analysis of the local time dependence (Figure 2).

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As mentioned, we restrict our analysis to LDEX data taken during January to April 2014. However, during the commissioning phase of LADEE’s orbit, the spacecraft reached altitudes up to ∼250 km until late November 2013. While the LDEX data during late 2013 are more variable due to increased meteoroid stream activity, the exponential fit derived here is consistent with the high-altitude data profile observed by LDEX, reinforcing our methodology. The differential mass distribution of lunar ejecta measured by LDEX remained inde- pendent of the altitude, and had the form 1 f(m)∝m−( +#), where # =0.9; hence, the differential size distribution is f a f m Figure 2. The velocity distribution function from equation (1) (black) ( )∝ ( ) dm Ca−(1+3#), with the normalization along with the previously derived distribution (grey) from Horányi da = et al. [2015, Methods]. The vertical dashed line indicates the velocity −3# −3# (C =3)#∕(a0 −amax). LDEX measured parti- to reach the highest altitude visited by LDEX of 250 km. For velocities cles above a threshold size of ath ≈0.3 μm. ≳840 m/s, the distribution function derived in this work is an extrapolation. The average lunar dust density profile in Figure 1 shows the dust density for parti-

cles with radii a ≥ ath. Since the measured dust distribution is a simple power law for a > ath [Horányi et al., 2015], we assume the power law to remain valid to a critical value a0≤ ath [Kolmogorov, 1941]. The dust density −3# for particles with radii greater than a is given by n(h, a)=n(h)(a∕ath) where n(h) is ﬁt to the LDEX-derived densities for a≥ath and is assumed to remain valid for all sizes with a≥a0. During the months of October 2013 to March 2014, LDEX observed an asymmetric dust cloud, with a peak density slightly canted toward the Sun [Horányi et al., 2015]. The location of this peak density was found to vary throughout the LADEE mission, following the Earth-observed variations between the HE and AH sources [Campbell-BrownandJones, 2006]. The direction of the cant was predicted to point slightly antisunward during some of the nonobserved months. During the last month of the LADEE mission, when the HE and AH sources are observed on Earth to be comparable in magnitude, LDEX did in fact ﬁnd the peak density to be located at 6LT[Szalay and Horányi, 2015a]. Therefore, we treat the lunar dust cloud to be symmetric with respect to the apex direction for the purposes of averaging over timescales much longer than a few months. Following the analysis in Szalay and Horányi [2015a], we assume that the azimuthal dependence is governed by the sum of the known sporadic sources in the ecliptic plane. The complete average dust density distribution is −3 a # n(h a)=e−h∕" n w cos3( − )Θ( − ∕2) (2) ,$, a w s $ $s $s % , ( th ) s ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟∑ n0($)

where s represents each source, $ is the angle from apex, Θ is the Heaviside function, $s is the characteristic ∘ ∘ ∘ ∘ −3 −3 angle for each source radiant (65 ,0 , −65 , and 180 )[Campbell-Brown, 2008], nw = 8.5 × 10 m , and ws is the relative weight (0.24, 0.49, 0.24, and 0.03) for the HE, AP, AH, and AA sources, respectively. The normaliza- ∘ −3 −3 tion nw was determined by setting n0(0 )=4.5 × 10 m , the low-altitude density at 6 LT observed in April 2014 and a representative value for the average cloud. The AA source is included in this analysis to be consistent with the observed nonzero density near the vicinity of 18 LT; however, its contribution is not particularly signiﬁcant to our results. The relative ratios of AP to HE/AH sources are derived from LDEX measurements during the month of April when the dust cloud was approximately symmetric about the apex direction. Figure 3 shows the derived average lunar dust density distribution from evaluating equation (2).

3. Calculating the Impact Gardening Rate To determine the ﬂux of all returning grains incident to the surface, we calculate the average ejecta surface ve impact velocity, v̄0 = ∫0 vf(v)dv = 670 m/s. The ﬂux as a function of local time is then given by 3 a − # F( a)=n0( )v̄0 (3) $, $ a ( th )

SZALAY AND HORÁNYI LUNAR METEORITIC GARDENING RATE 3 Geophysical Research Letters 10.1002/2016GL069148

and shown in Figure 4. Using the turning point approximation to calculate F($, a) via equation (3) introduces ∼10–20% error compared to using the true velocity distribution [Horányi et al., 2015, Methods] for a similar cal- culation. Integrating equation (3) over all local times, we derive an average

flux for all sizes (a≥a0), −3# a0 F = F (4) 0 a , ( th ) −2 −1 where F0 =1.2 ± 0.7 m s . The error is calculated by incorporating a 20% error from the turning point approximation with the average 35% error from the fitted and observed values of n(h). To determine the impact gardening rate, the characteristic cross-sectional area for this flux is calculated by inte- Figure 3. The annually averaged lunar dust density distribution, given grating over the distribution function, in equation (2), for particles with a ≥ 0.3 μm in a reference frame where the Sun is in the −x direction and the apex motion of the Moon about the Sun is in the +y direction.

−(3 −2) −(3 −2) amax a # a # 2 3#% 0 − max 3 2 + = f(a)%a da = ≈ %a (5) 3 2 −3# −3# 3 2 0 ∫a0 # − [ a0 − amax ] # −

where the approximation has been made for amax ≫ a0. The accumulation timescale, after which the surface will be entirely covered by a single layer of impact ejecta is

1 3# − 2 3 −2 - = = a # (6) F 3# 0 + 3%F0ath with a characteristic thickness of d ≈ +.Therefore,thedepthaccumulationrateis √ 3 3∕2 3# 3% 2 3(1−#) . = d∕- = F+ = F0a a (7) th 3# − 2 0 ( ) The size distribution for lunar regolith has been accurately measured down to a few microns [Heywood, 1971; Görz et al., 1971], and recent analysis indicates that the lunar ﬁnes are lognor- mally distributed with a peak at radius 0.1 to 0.3 μm[Park et al., 2008], indi-

cating that a0 is lower than the LDEX observation threshold ath. However, determining the size distribution for grains with a < 1 μm remains chal- lenging [Liu and Taylor,2011].Labora- tory impact experiments found impact ejecta fragments down to 50 nm in radius [Buhl et al., 2014]; therefore, we investigate the impact gardening rates for a in the range of 0.05 to 0.3 m. Figure 4. The total number ﬂux of ejecta particles onto the surface as 0 μ afunctionoflocaltime.Thedashedlineshowstheaveragevalueof Table 1 shows - and . for critical radii 2 1 2 1 1.2 m− s− and the grey portion indicates the error of 0.7 m− s− . of 0.05, 0.1, and 0.3 μm.

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Table 1. The Accumulation Timescale - and Depth Accumulation Rate . a for a Select Set of Critical Radii a0,GiveninEquations(6)and(7) 3 6 a0 (μm) - (10 years) . (μm/10 years) 0.05 6 ± 330± 16 0.1 10 ± 637± 20 0.3 22 ± 12 51 ± 28 a Errors are calculated by propagating the error in F0 to - and ..

4. Discussion and Conclusions Using a data-driven model of the lunar dust density distribution, we find that approximately 40 μm per 106 years of lunar soil is redistributed from meteoritic bombardment. This result is not particularly sensitive 0.3 to the critical size cutoffof the dust distribution (. ∝ a0 ) and is applicable for periods when the meteoroid environment at 1 AU would be comparable to its present state. The dust falling back to the lunar surface has a cumulative size distribution proportional to a−2.7; however, we cannot address the modification of the size distribution if grains stick to each other after reaching the lunar surface. Meteoritic gardening predominantly takes place on the apex hemisphere of the Moon. We note that these results are derived from data taken near the Moon’s equatorial plane. At high latitudes, where permanently shadowed regions exist, the meteoroid fluxes and subsequent impact gardening rates could be considerably different. A comprehensive model of lunar bombardment including all known sporadic sources such as the northern and southern toroidal sources would better address the impact gardening rates in these permanently shadowed regions and is suggested as a future line of study. This work could be extended to derive gardening rates at other airless bodies in the solar system, such as Mercury, asteroids, Phobos, and Deimos, by further understanding the difference in meteoroid environments and subsequent ejecta generation at these bodies compared to the Moon.

This work analyzes the rate at which high-altitude (h >1 km) dust rains back down onto the lunar surface; however, there could be additional processes contributing to the gardening of the regolith. While electrostatic lofting was not found to eject particles to high altitudes [Szalay and Horányi,2015b],measurementsfrom the Lunar Ejecta and Meteorites instrument [Berg et al., 1973; Grün et al., 2011; Grün and Horányi, 2013] and the Surveyor cameras [Criswell, 1973; Rennilson and Criswell,1974]suggestthatsmallscaleelectrostaticdust transport may occur close to the surface at altitudes h≪1 km. To perform the calculations outlined in this work, some key assumptions were made, namely, that all grains undergo purely vertical ballistic motion. The impact gardening quantities - and . are calculated for accumulation on a flat plate on the lunar surface. To calculate more accurate accumulation times for recessed features, such as retroreflectors, the horizontal velocities should be taken into account. With a nonzero horizontal velocity component, recessed features would experience a reduced flux, as their effective cross-sectional area to a flux of nonvertically moving grains would be decreased. For the Apollo and Lunokhod retroreflectors placed on the lunar surface in the 1970s, we do not expect that an appreciable amount has accumulated from meteoritic bombardment. If dust has accumulated on these surfaces, it must come from either very low altitude impact ejecta, small scale electrostatic transport, or both. Constraining the flux of lunar dust onto retroreflectors would aid in the analysis of the existing lunar ranging experiments and help guide future development and operation of instruments and/or solar panels deployed to the lunar surface. Acknowledgments LDEX measurements can be used to improve our models of the distribution of interplanetary meteoroids and LDEX data are available through NASA’s Planetary Data System. their subsequent ejecta. Similar measurements near the moons Phobos and Deimos have been suggested M. Horányi was supported by the to map the dust flux near Mars. An LDEX type instrument sent to any airless body in the solar system would Institute for Modeling Plasma, gather critical information about its local meteoroid environment and constrain its surface impact gardening Atmospheres, and Cosmic Dust of NASA’s Solar System Exploration processes. Research Virtual Institute. We thank Cesare Grava for insightful References discussions on exospheric distributions. The authors thank two Arnold, J. R. (1975), A Monte Carlo model for the gardening of the lunar regolith, The Moon, 13(1–3), 159–172. anonymous reviewers for constructive Berg, O. E., F. F. Richardson, and H. Burton (1973), Lunar ejecta and meteorites experiment, Apollo 17: Prelim. Sci. Rep. SP-330, p. 16, NASA comments. Spec. Publ., Washington, D. C.

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