Detecting meteoroid streams with an in-situ dust detector above an airless body

The Lunar Dust Experiment (LDEX), aboard NASA’s Lunar Atmosphere and Dust Environment Explorer (LADEE) successfully mapped the dust density distribution over the lunar surface up to an altitude of ∼ 250 km. LDEX detected dust grains launched off the surface in ejecta plumes generated by impacts of cometary and asteroidal micrometeoroids striking the Moon. While on average LDEX detected particles at a rate of 1 min −1 , periodically it measured bursts of particles at a rate exceeding the average value by up to two orders of magnitude. The timing and location of the most intense period of bursts is used here to independently determine the radiant for the Geminids meteoroid stream. The method is proposed to be of general interest to characterize meteoroid streams bombarding any of the airless bodies in the solar system using in-situ dust detectors. © 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).


Introduction
Every planetary body in the inner s olar s ystem is continually bombarded by interplanetary dust particles (IDP) originating primarily from asteroid collisions and cometary activities. Thick atmospheres protect Venus, Earth, and Mars, ablating the incoming IDPs into 'shooting stars' that rarely reach the surface. The surfaces of airless bodies near 1 AU are directly exposed to the high-speed, v 1 km/s, impacts of IDPs with a characteristic radius of a 100 μm and mass flux of F 1 . 5 × 10 −15 kg/m 2 /s ( Grün et al., 1985 ).
The total mass influx to Earth is on the order of 10 5 kg/day, hence the Moon is expected to be bombarded by 5 × 10 3 kg/day of IDPs arriving with a characteristic speed of 20 km/s ( Taylor, 1996 ). High-speed dust impacts into solid surfaces generate plasma ( Dietzel et al., 1973 ) and neutral ( Collette et al., 2014 ) gas clouds, as well as solid secondary ejecta dust particles ( Hartmann, 1985 ). Ejecta particles with sufficient speeds escape from their parent body and have been identified as sources of planetary rings at Jupiter ( Ockert-Bell et al., 1999 ), for example. Particles ejected with speeds below the escape speed follow bound orbits and return to the surface. Before LDEX visited the Moon, bound ejecta clouds forming dust exospheres were observed only around the icy m oons of Jupiter ( Krüger et al., 1999 ) and Saturn's m oon Enceladus, though in the latter case active geysers are the dominant source of particles ( Spahn et al., 2006 ). LDEX has since confirmed the existence of an asymmetric dusty exosphere engulfing the Moon, which responds to the local influx of micrometeoroids bombarding the lunar surface .
Fully characterizing the meteoroid environment at 1 AU remains a challenging and active area of research. Meteoroid influx at Earth is measured via ground-based visual ( Jenniskens, 1994 ) and radar observations Campbell-Brown, 2008 ), which are highly sensitive to the mass and speed of incoming particles. Until LADEE, meteoroid flux to the lunar surface was monitored by visual light flash observations from large impactors with masses > 1 kg ( Suggs et al., 2014 ). Meteoroid influx was also measured by the Apollo lunar seismic station, which operated from 1969 to 1977 and had an estimated mass sensitivity of 10 −1 to 10 3 kg ( Oberst and Nakamura, 1991 ) The previous lunar impact observations were able to detect much larger impacts than those that regularly sustain the lunar dust cloud given the larger cross sectional detection area required to measure an appreciable number of such impacts. The Moon acts as a large area dust detector, amplifying the amount of material impacting its surface by ejecting significantly more mass as outgoing solid ejecta . LDEX measured the distribution of this impact generated The difference between 1 day and 1 week rolling averages of the impact rate as a function of time for a > 0.3 & 0.7 μm, respectively. The gray bar indicates 3 σ error bars. Peak rates which exceed 3 σ are indicated by red dots. Bottom: Gray dots show γ (20, t ) evaluated for each consecutive 20 impacts. A 1.5 day running histogram shows the total number of bursts for probability cuts of γ 0 = 3; 6; 9; and 12; in purple, indigo, yellow, and red, respectively. The 6 unusual periods which satisfy Criteria 1 (gray) or both Criteria (blue) are shown with the vertical lines, labeled A-F. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article). ejecta cloud and provided a novel way of observing the meteoroid influx to the Earth-Moon system.

The dust environment at the Moon
The dust environment at 1 AU is dominated by grains shed from asteroids and comets mainly within the orbit of Jupiter. These sources include comets, both long period Halley Type Comets (HTC) and short period Jupiter Family Comets (JFC), asteroids, Oort Cloud Comets (OCC), and the Edgeworth-Kuiper Belt (EKB). At 1 AU, the population of EKB grains is negligible, as most of these grains get ejected from the s olar s ystem by Jupiter during their migration towards the Sun ( Han et al., 2011;Poppe, 2016 ). This dust/meteoroid environment is broken up into 2 distinct groups, the meteoroid streams and the sporadic background.

Meteoroid streams
When grains are shed, their initial orbital elements are similar to their parent body's. In addition to the gravitational forces by the Sun and the planets, the dynamics of a small dust particle is influenced by additional forces that are size-dependent, including solar wind and Poynting-Robertson drags, radiation pressure, and the Lorentz force ( Han et al., 2011 ). The combination of these forces causes the ejected grains to decouple from their parent bodies and follow divergent trajectories over time. However, large enough (radii > 100 μm) grains preferentially disperse along the trajectory of their parent body, and may fill its entire orbital loop ( Fox et al., 1983 ).
Once the orbit of a source body has been filled and becomes a 3D 'tube of material', it becomes a meteor stream if the orbit of the Earth intersects the ascending or descending node of this tube. There are hundreds of cataloged meteor showers, including the Geminids producing one of the strongest responses at Earth, first documented in 1862 ( Fox et al., 1982;King, 1926 ).

The sporadic background
Smaller grains that are more susceptible to non-gravitational perturbations disperse, and follow orbits that rapidly diverge from their parent body, forming the 'sporadic background.' The sporadic background has its own structure and is organized by various radiant groupings: (a) the helion/anti-helion; (b) apex/antiapex; and (c) the northern/southern toroidal sources ( Jones and Brown, 1993 ). The relative contributions from each source vary as a function of solar longitude ( Campbell- Brown and Jones, 2006 ). The variation of the sporadic background fluxes influences the spatial and temporal distribution of the dust ejecta cloud they generate impacting the Moon .

Impact ejecta plumes
When micrometeoroids impact the lunar surface, an ejecta plume is created that has many times the mass of the impacting particle. For normal impacts on a purely silica surface, the mass yield Y , the ratio of the mass ejected into the plume to the mass of the impacting particle is where C = 30 for a silicate surface, m imp is the mass of the impacting particle in kg, and v imp is the velocity of the impacting particle in km/s, α = 0 . 2 , and β = 2 . 5 ( Koschny and Grün, 2001;Krivov et al., 2003 ). The angular dependence is derived from an experimental finding that the material excavated by impacts varies as cos 2 ϕ where ϕ is angle between the surface normal and the velocity of the incoming particle ( Gault, 1973 ). While this experiment ( Gault, 1973 ) was performed for impacts into solid rock, which may have different impact physics compared to regolith, we still Table 1 Enhanced Burst Activity Periods. The period corresponds to those labeled in Fig. 1 . a (γ 0 ) = N burst /N sp gives the ratio of the number of bursts in each period with the average number of sporadic bursts with the exception of the first row of data, which gives the sporadic background burst rates N sp , in day −1 . The associated stream or complex which is temporally coincident with each period is given in the last column.  (oCe) is a weaker shower and was added to this list due to its temporal correlation with an observed peak. The peak times have been adjusted from the peak times observed at Earth by taking into account the position of the Moon relative to Earth and correcting for the appropriate lead/lag times. implement its results as it is the most relevant finding on the angular dependence of impact ejecta.
The total mass production per unit area in kg/m 2 is given by where F imp is the number flux of impactors per square meter with characteristic mass m imp , cos ϕ is the projection area factor, and Y is from Eq. 1 . Hence the total mass production per unit area is, The Moon is continually bombarded by IDPs forming meteoroid streams, as well as the sporadic background. Surface regions that are transiently exposed to higher than average IDP fluxes respond with an increased mass production M + during these periods, and generate more frequent and denser ejecta plumes. If LADEE happens to fly through any of these plumes it is expected to observe higher than average impact rates. Hence, a period of unusually large impact rates detected by LDEX can be used to identify the surface region that has been exposed to high incoming IDP fluxes during that period.

Identification of unusual periods
LDEX is an impact ionization dust detector. Particles are detected by measuring the charge they generate impacting the target surface . The conversion from impact charge to radius is based on laboratory calibrations . With an average impact speed of 1.67 km/s, LADEE's orbital speed around the Moon, LDEX can detect particles as small as a 0 . 3 μm in radius. LDEX received impacts above its detection threshold of a > 0 . 3 μm at a rate of μ = 2 . 3 × 10 −2 s −1 during commissioning and μ = 3 . 1 × 10 −2 s −1 during the nominal science mission, which began on 21-Nov-2013 . However, intermittently, LDEX detected "bursts" of tens to hundreds of impacts in a single minute. Particles detected in a burst most likely originate from the same well-timed and well-positioned lunar impact event that occurred just minutes before their detection on the ground-track of LADEE. These bursts are detections of individual ejecta plumes, dense enough to register multiple impacts on LDEX as it transits the plume, and have durations of less than a minute. Plasma events occasionally registered false triggers on the LDEX instrument, which also manifests in bursts of detections. These events are removed from the dataset given their identifiable waveform characteristics. For more information on waveform processing, see Horányi et al. (2014) .
To characterize these bursts, we assume that subsequent impacts are independent of each other, hence the dust detection time series observed by LDEX can be approximated as a Poisson process. The probability of detecting n or more impacts within a time t can be calculated ( Oberst and Nakamura, 1991 ) where n is the number of impacts, t is the total elapsed time for the impacts, and μ is the average impact rate for the entire time series of dust detections. The upper limit of n − 2 in the summation is due to the fact that t begins and ends at individual particle detections. For example the probability of detecting 2 or more particles separated by time t is P (2 , t ) = 1 − e −μ t , as expected. Bursts are short unusual periods that are identified in our time series analysis by setting an optimum value for n, a measure of the number of impacts on LDEX resulting from each burst, and identifying the low probability periods ( Oberst and Nakamura, 1991 ). With n set to large values ( n 20), many bursts will be missed as the bursts LDEX detected contained considerably smaller numbers of particles, including additional impacts from the background raises the probability towards the average. A small value of n identifies too many unusual periods, and makes it cumbersome to recognize if they actually belong to a single impact with a larger number of particles. With values of n near 20, the results are not particularly sensitive to n . We found n = 20 to be a convenient particle number per burst for this analysis, using the most active period discussed below as a training set to determine this number. Unless stated otherwise, P = P (n, t ) with n = 20 will be used through the remainder of this analysis. Given the broad range in the exponent of the probabilities used in this analysis, it is con-venient to express P = 10 −γ in terms of its exponent γ = −log 10 P . Fig. 1 shows γ for each consecutive 20 impact detections. If more than 20 impacts occur in a given burst, only the first 20 are counted. Any impacts occurring less than 30 s after a burst of 20 particles are considered part of this burst and removed from the analysis.
To identify unusual periods in the LDEX data, we set 2 criteria: (1) The impact rate deviation r d exceeds 3 σ above the average, either for a > 0.3 or 0.7 μm (2) The detected burst rate N burst (given in Table 1 ) for a > 0.3 μm exceeds the average sporadic background N sp by a factor of 3.
The impact rate deviation r d is calculated by r d = r day − r week where r day and r week are running averages of the impact rates over a period of 1 day and 1 week, respectively. The 1 week average gives an estimate of the background to be subtracted from the impact rates, and 3 σ is chosen to identify particularly unusual periods. LDEX occasionally observed bursts with atypical size distributions, some of which had significantly more larger particles than the dust cloud. Due to this variation, two size cuts (0.3 and 0.7 μm) are utilized to ensure impact rate enhancements are detected even if bursts have different size distributions.
The sporadic rate, N sp , is determined by taking the average burst rate for bursts with γ > γ 0 and is listed in Table 1 for γ 0 = 3 ; 6 ; 9 ; and 12 . Fig. 1 shows r d for both size cutoffs of a > 0 . 3&0 . 7 μm, and the burst detection rate N burst for the same four γ 0 values. Table 2 lists the known meteoroid showers determined by visual observations given by the International Meteor Organization ( McBeath, 2015 ). Table 1 shows each identified unusual period along with their peak time and associated stream which coincides with each. With the exception of period F, each identified period occurs during a known meteoroid shower. However, temporal coincidence alone is not sufficient to establish the detection of a meteoroid shower. If a meteoroid stream impacts the Moon on the opposite hemisphere to where the concentration of bursts were to occur, it cannot be responsible for the burst rate enhancement. For an unusual burst activity period an estimated radiant can be calculated, and at a minimum, it must be pointing to within the same hemisphere as the temporarily coincident known shower to be classified as a potential meteoroid shower detection.

Radiant determination
During Period C, LDEX observed the largest burst rate enhancement, 8-13 times greater than the sporadic background. We therefore first focus on this period to establish a method to find the radiant of the responsible meteoroid shower. A right ascension, α, and declination, δ, are calculated for each burst by determining the radiant which intersects the burst location normal to the lunar surface. We use the period of ± 1.5 days centered around each peak time, as this was approximately the duration of each period of elevated impacted rates ( Table 1 ).
LDEX's observed impact rates peaked during Period C on 14-Dec-2013 11:34 [UTC]. The expected peak flux from the Geminids was 14-Dec-2013 7:49, less than 4 h (or 2 LADEE orbits) apart. The Geminids is a well constrained and intense shower, its radiant is established precisely by ground-based visual observations. Fig. 2 shows the distribution of bursts detected by LDEX during Period C for an increasing set of γ 0 values. To a good approximation, the meteoroids arrive at the Moon in a parallel beam, hence the theoretical M + given in Eq. 2 can be calculated. We show M + in normalized units, such that it is strictly proportional to cos 3 ϕ. For γ 0 = 1 the burst distribution remains isotropic. This is to be expected as 10% probability events are likely to be related to background sporadic impacts. For γ 0 = 7, the remaining bursts tend to concentrate around higher M + regions, and for γ 0 = 16 , only the most unusual bursts remain, identifying the most dense ejecta plumes. Fig. 2 demonstrates that increasing γ 0 (decreasing the probability cut) gives increasingly better estimates for the radiant, hence it can be used to extract the direction information for a meteoroid stream. Using γ as a proxy for the density of each measured plume, such that higher values of γ indicate lower probability events and therefore higher plume densities, we analyzed the RA and δ distributions as a function of γ 0 . Bursts with larger γ are generated in regions of higher M + and therefore as γ 0 increases, the corresponding radiant estimates becomes more accurate. Fig. 3 shows the mean and standard deviations for α( γ 0 ) and δ( γ 0 ). We use the largest γ 0 with at least 3 remaining bursts to determine the best value for RA and δ, γ 0 = 16 in the case of the Geminids. For γ 0 > 16, we observed no considerable change in burst distributions. With γ 0 = 16 , we estimate the Geminids radiant within 1 σ as ( α, δ) = (92 ± 31 °, 27 ± 8 °) compared to the established radiant of (112 °, 33 °) ( McBeath, 2015 ). Therefore, the burst rate enhancement during Period C was indeed due to the Geminids meteoroid stream.

Application to additional periods
The analysis outlined in the previous section provides a method to calculate the radiant of a meteoroid shower for sufficiently large number of burst detections. However, even the most intense showers can escape detection by this method if their radiant intersects the lunar surface far outside LADEE's selenographic latitude range of ± 23 °. The Geminids hit the lunar surface in an optimal location for LADEE's orbital geometry and generated bursts at a rate up to 13 times higher than the sporadic background. This shower, corresponding to Period C, stands out in the LDEX data as the strongest stream detection. The remaining unusual periods are discussed below and compared to temporally coincident known meteoroid streams.

Period A: Northern Taurids
During this period, LDEX recorded one of the largest impact rate enhancements, second only to the Geminids during Period C. How-ever, unlike the Geminids, which generated a burst rate enhancement of a = N burst /N sp ≤ 13 , an enhancement of a ≤ 1.3 was registered during Period A ( Table 1 ). The bursts measured during this period were unusually dense, with γ values up to 15. Fig. 4 shows the burst distributions during this period. The declination is correctly estimated, however the right ascension is not. The Northern Taurids have a ZHR which is 24 times less than the Geminids and are therefore expected to impact the Moon at a much lower rate.

Period B: Puppid/Velids
The Puppid/Velids stream is also known to be weak, with a ZHR of 10, and at most registered a burst rate 1.3 times the sporadic burst rate. Additionally, its radiant impacts the lunar surface at a low selenographic longitude of −45 °. Due to the geometry of the LADEE orbit, throughout each orbit LDEX essentially flys through iso-M + or iso-ϕ lines, as shown in Fig. 5 . Given this geometry and the relative weakness of the stream, extracting the radiant for this stream is difficult, but still its declination is correctly estimated.

Period D: Quadrantids
The Quadrantids is one of the strongest observed showers on Earth, similar in ZHR magnitude to the Geminids, and was predicted to peak approximately 6.5 h after LDEX's observed peak in Period D. Fig. 6 shows the burst distributions during this period. The radiant of this stream intersected the lunar surface at a very high lunar latitude, 63 °in selenographic coordinates. Due to the geometry, the declination for this radiant cannot be accurately determined as LDEX did not visit the relevant δ range. However, LDEX did visit a large range of α in this period and an accurate estimate for the α can be extracted from the data.

Period E: Omicron Centaurids
An additional stream which generated a significant enhancement in LDEX impact rates, as shown in Fig. 1 , was the Omicron Centaurids (oCe). Like the Quadrantids, this stream intersected the lunar surface at an unfavorable selenographic latitude of −51 ° (  Fig. 7 ). Due to the unfavorable geometry and lower burst rate en-hancement for this period of 0.8 to 2.6, radiant estimation was challenging.

Period F: Unidentified
Several of the documented streams produced significant enhancements in impact rate at the expected time. Surprisingly, an uncharacteristically large impact rate enhancement, rivaling the Geminids, was also observed on 25-Mar-2014 that does not correspond to any established shower. If this impact rate enhancement is due to a meteoroid shower, its radiant can be estimated following the analysis outlined in the previous sections.  shower. However, this stream is relatively weak and remains fairly unconstrained. The Meteor Data Center ( Porubcan and Jopek, 2015 ) gives the following radiant parameters: λ= 5 °and ( α, δ) = (266 °, −6.3 °). The α value is within 1 σ of the LDEX calculated radiant, with δ within 2 σ and λ is within 1 °(or one day) of the observed lunar peak time. However, the SonotaCo meteor orbit database gives a solar longitude for the ζ -Serpentids of λ= 365 °, with ( α, δ) = (266 °, −6 °) ( Greaves, 2012 ). The radiant direction given in Greaves (2012) could be consistent with the LDEX results, however the solar longitude is considerably different. Additionally, the lunar response to the unidentified stream is similar to the intense impact rates observed during the Geminids. This is not consistent with the low magnitude of the ζ -Serpentids which remains poorly characterized by ground-based observations. Table 3 summarizes the LDEX radiant estimates of the meteoroid showers. Of the 6 identified periods, the Geminids produced the largest burst rate enhancement. The LDEX data from this period unambiguously verifies the detection of the lunar re-sponse and successfully extracts both radiant parameters as well as the peak time. LDEX can only resolve a maximum in impact rate within a few LADEE orbits. Here, we use 3 orbits as our error criteria, corresponding to approximately 6 h or 0.3 °in solar longitude. For Periods A, B, D, and E, which correlate temporally to known showers, the radiant estimates were more difficult to extract. These difficulties arose from unfavorable geometry, low relative meteoroid stream strength, or both. The Quadrantids, which is comparable in magnitude to the Geminids as observed at Earth, generated the 2nd highest burst rate detected throughout the mission. However, due to its high selenographic latitude, it's declination can only be poorly reproduced.

Discussion
Many of the streams listed in Table 2 did not generate significant burst rate enhancements. While the non-detection of these streams is largely unsurprising due to their low ZHR, the Leonids is strongest amongst these and should have registered a burst rate enhancement given the favorable geometry and its larger ZHR. However, LDEX turned off a few hours before the Leonids peak time and remained off for a few days due to spacecraft operational constraints, therefore missing this stream.  Table 3 Extracted Meteoroid Stream Parameters. The established three letter identification code is id, λ is the peak time in solar longitude, RA is right ascension, δ is the declination, and N (3) is the number of bursts with a probability cut of γ 0 = 3 . Earth observed values ( McBeath, 2015 ), propagated in time to the position of the Moon at each peak time. The error on λ for LDEX measured values was calculated assuming LDEX could not resolve a maximum in impact rate within three LADEE orbits, corresponding to approximately 6 h or 0.3 °in solar longitude. Highlighted in bold are the values for which the estimates are within 1 σ .

Per.
id Lat In addition to the six periods discussed in this work, we note there are two additional periods which fell just shy of our identification criteria, Nov. 24-28, 2013 andJan. 22-27, 2014. As discussed in depth in Szalay and Horányi (2015) , the majority of the ejecta detected by LDEX was from three sporadic meteoroid sources, helion, apex, and anti-helion. The apex source was found to be the most dominant producer of impact ejecta due to its large impact velocity. The two additional periods not marked on Fig. 1 are enhancements in approximately the apex direction. These enhancements could be from random fluctuations in the apex source, or additional unidentified meteoroid streams, weaker than that of Period F.

Conclusions
Using Poisson statistical methods to quantitatively identify unusual periods in the LDEX impact rate data, a method similar to that outlined in Oberst and Nakamura (1991) is proposed to characterize meteoroid streams. By analyzing the distribution of right ascension and declination of groupings of impacts, the radiant for a strong and established meteoroid stream (the Geminids) was successfully reproduced within 1 σ error. Partial radiants and/or peak times are correctly estimated for 4 other meteoroid streams.
An unidentified meteoroid stream is observed by the LDEX instrument aboard the LADEE mission, peaking on 25-Mar-2014. Using the methods outlined in this work, an estimate for the radiant of this putative stream is calculated as ( α, δ) = (268 ± 41 °, -22 ± 13 °), with a peak solar longitude of λ = 4.1 ± 0.3 °. However, this radiant estimate may not be reliable due to geometric constraints. Additionally, while LDEX observed a handful of dense ejecta plumes during this period, the rate of detected bursts was not significantly higher than the sporadic background.
Detecting and measuring the orbital properties of meteoroid streams is currently undertaken via multiple methods, each with its own strengths and weaknesses. The meteoroid stream charac-terization outlined in this work provides a novel method to measure the local meteoroid environment using the Moon as large surface area dust detector, by exploiting the large magnification factor in the density of the ejecta plumes. Future longer duration lunar missions carrying an LDEX type instrument, and following orbits with higher inclinations than LADEE could greatly enhance our knowledge about the meteoroid environment at 1 AU. Spacecraft carrying a dust instrument orbiting, or performing multiple flybys, of other airless bodies could be used to learn about the meteoroid environment throughout the s olar s ystem in a manner unique to dust detectors.