A meteoroid stream survey using meteor head echo observations from the Middle Atmosphere ALOMAR Radar System (MAARSY)

Icarus 309 (2018) 177–186

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A meteoroid stream survey using meteor head echo observations from the Middle Atmosphere ALOMAR Radar System (MAARSY) Carsten Schult a,∗, Peter Brown b,c, Petr Pokorný d,e, Gunter Stober a, Jorge L. Chau a a

Leibniz Institute of Atmospheric Physics at the Rostock University, Schloss-Str. 6, Kühlungsborn 18225, Germany Department of Physics and Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada c Centre for Planetary Science and Exploration, University of Western Ontario, London, Ontario N6A 5B7, Canada d Department of Physics, The Catholic University of America, Washington, DC 20064, USA e Space Weather Laboratory, Code 674, NASA Goddard Space Flight Center, Greenbelt, MD 20771, Maryland b

a r t i c l e

i n f o

Article history: Received 19 December 2017 Revised 23 February 2018 Accepted 28 February 2018 Available online 9 March 2018 Keywords: Meteors Asteroids Comets Radar observations Interplanetary dust

a b s t r a c t Results from a meteor head echo shower survey using the quasi continuous meteor observations of the high power large aperture radar MAARSY, located in northern Norway (69.30°N, 16.04°E) are presented. The data set comprises 760 0 0 0 head echoes detected during two and half years sensitive to an effective limiting masses below 10−8 kg. Using a wavelet shower search algorithm, we identified 33 meteor showers in the data set all of which are found in the IAU meteor shower catalog. We find ∼ 1% of all measured head echoes at these masses are associated with meteor showers. Comparison of shower radiants from this survey with the observation of the Canadian Meteor Orbit radar (CMOR) transverse scattering radar system shows generally good agreement, although there are large differences in the measured durations of some meteor showers. Differential mass indices (s) of ∼ 1.5–1.6 are measured for the Perseids (PER), Geminids (GEM) and Quadrantids (QUA) showers. The Orionids (ORI) show a much steeper mass index of 2.0, in agreement with other observations at small particle sizes, suggesting the Halleyid showers, in particular, are rich in very small meteoroids. © 2018 Elsevier Inc. All rights reserved.

1. Introduction Meteor showers, in contrast to sporadic meteors, are released from a common parent body, either a comet or asteroid. Study of meteor showers is particularly valuable as the meteoroids released from a single parent body provide direct samples of those particular parents. More generally, understanding how meteoroid streams form and subsequently evolve provide insight into the timing and mode of decay processes of small solar system bodies (Williams and Ryabova, 2011). Historically, most meteor shower surveys were conducted using optical instruments (Hemenway et al., 1973) or transverse scattering meteor radar systems (e.g. Sekanina, 1970; Brown et al., 2008; Younger et al., 2009; Janches et al., 2013). More recently, shower surveys have been undertaken with dedicated networks such as the Cameras for Allsky Meteor Surveillance project (CAMS) (Jenniskens et al., 2016) and the Southern Argentina Agile MEteor Radar (SAAMER) (Pokorný et al., 2017). Brown et al. (2008) provides an overview of the past shower surveys and the history of

∗

Corresponding author. E-mail address: [email protected] (C. Schult).

https://doi.org/10.1016/j.icarus.2018.02.032 0019-1035/© 2018 Elsevier Inc. All rights reserved.

meteoroid orbit surveys in general while Jenniskens (2017) provides a contemporary review of the subject. Surveys to date have resulted in a total of 112 meteor showers being designated as established by the International Astronomical Union (IAU)1 . An additional 589 working showers are also listed by the IAU. Meteor showers are generally richer in larger meteoroids compared to the sporadic background. The fraction of all meteoroids which belong to showers is estimated to rise to a maximum exceeding 50% at cm-sizes and falls to less than 10% at sub-mm sizes (Jenniskens, 2006). However, the small-size end of the meteoroid stream spectrum is of interest for several reasons. The very smallest meteoroids in a stream are removed due to the effects of radiation pressure (Burns et al., 1979; Dohnanyi, 1970). This is potentially a very sensitive statistical probe for meteoroid properties (such as bulk density), particularly for highly eccentric orbits. Additionally, streams which are rich in small meteoroids must either be young or have some production source for very small meteoroids (e.g. fragmentation/thermal sintering) as small particles evolve out of a stream most quickly. Streams rich in small particles may also have

1

https://www.ta3.sk/IAUC22DB/MDC2007/.

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dynamical effects which preferentially deliver only small meteoroids to Earth intersection (eg. the 2012 Draconids (Ye et al., 2013)). To date no dedicated survey has explored which streams remain detectable at the very smallest meteoroid masses (≤ 10−10 kg), though some recent measurements demonstrate that at least some showers contain meteoroids in the order of these masses or smaller. The meteor shower survey described by Galligan (20 0 0) remains to date the only survey to very faint magnitudes (M ≈ +13) performed on a nearly complete ‘virtual’ year comprised of half a million orbits detected with the multi-station transverse scattering Advanced Meteor Orbit Radar (AMOR). This survey, to a limiting mass of order 10−10 kg, found only half a dozen streams with significant . They estimate that less than 1% of all meteoroids in their survey could be linked to a definite shower (Galligan, 20 0 0). Observation of meteor head echoes using high power large aperture (HPLA) radars is a unique method to measure accurate atmospheric trajectories for large numbers of very small meteoroids. Yet, this technique has not been systematically used to survey which streams are present at very small masses. However, using meteor head echoes to obtain information about meteor showers is not a new idea. Hey et al. (1947) were the first to use meteor head echoes to estimate the velocity of the Draconid meteor shower. More recently, HPLA head echo observations of some showers include: the Perseid and Leonid meteoroids with the ALTAIR system (Close et al., 20 0 0; 20 02), the detection of the Eta Aquariids and Perseids with the Jicamarca VHF radar (Chau and Galindo, 2008) and the Orionids and Geminids which have been detected with the MU radar system (Kero et al., 2011, 2013). The Middle Atmosphere ALOMAR Radar System (MAARSY) detected the Geminid meteor stream during a sounding rocket campaign in 2010 (Stober et al., 2013; Schult et al., 2013). These studies collectively demonstrate that very small meteoroids are present in several of the major streams, but the extent and strength of streams at head echo masses is unclear. To date, all meteor head echo shower campaigns were initiated for specific known showers and were operational on time scales of hours or days, not covering the entire shower period. A complete meteor head echo shower survey has not been done, in part because of a lack of daily observations of head echoes from HPLA radar systems for a period of a year or more. In November 2013, we started a quasi continuous monitoring experiment with MAARSY on the Northern Norwegian island Andøya (69.30°N, 16.04° E). This experiment configuration is still running and a first analysis on the overall count rate, detection heights, velocities and the dynamical masses of the sporadic meteor background and a comparison with a meteor input function has been presented by Schult et al. (2017). In this complementary work we identify meteor showers detectable among these 0.7 million orbits using a wavelet approach to identify meteor showers in the same data. This survey comprises the first equivalent full-year shower survey based on meteor head echo observations. 2. MAARSY: meteor head echo observation methodology and analysis Table 1 summarizes the radar parameters used for the experimental setup in this study. The procedure followed in the raw data analysis shown as a step-by-step process as applied to an example head echo using the same experimental mode as used in this study is detailed in Schult et al. (2017). Here we only briefly summarize the basic interferometric analysis of particular importance in determining radiant accuracy and refer the reader to Schult et al. (2017) for more details.

Table 1 Experiment parameters for the meteor head echo observations used in this study. The experimental setup is also used in the study from Schult et al. (2017). Note that during the first months of the collection period in No. 2013 the experiment was separated into a zenith beam and a 12.4° off-zenith beam (25. November 2013 to 22. March 2014). Here PRF refers to the Pulse Repetition Frequency and IPP the Inter-Pulse Period (IPP). PRF

10 0 0 Hz

Code Pulse length IPP Duty cycle Sampling start range Sampling end range Sampling resolution Range gates Beam direction

16-bit Complementary Code 16 × 300 m 1 ms 3.2 % 49.8 km 134.7 km 300 m 283 0° zenith

MAARSY is an HPLA consisting of 433 single Yagi antennas with a peak power of about 800 kW and an antenna gain of 33.5 dBi. On reception 16 different channels, representing 16 different antenna subarrays (each of at least seven Yagi antennas) for interferometric calculations are available. The smaller baselines between the subarrays are used to get a first coarse estimate of the individual head echo direction on a pulse to pulse basis, while the longer baselines are later included to provide higher directional precision. Using the smallest interferometric baselines, the angular ambiguity starts 15.6° from the pointing direction, which includes the main beam and the first three side lobes of the full array radiation pattern (see Latteck et al. (2012); Chau et al. (2014) for details of the beam pattern and procedures used for interferometric solutions). The position of the meteor head echo within the radar beam is calculated for every pulse resulting in a time resolution of 1 ms. Depending on the entry angle, velocity and signal strength of the meteor head echo, the number of data points differ greatly and lie between 15 to 400 (median: 72) with corresponding paths extending from 0.5 to 15 km (median 3.8 km) in length. As it moves through the radar beam, the meteor head echo passes areas with very different antenna gains. In most cases, the detection of the meteor head echo starts with low signal strength at the edge of the main beam. Approaching the center of the radar beam the SNR increases, resulting in lower uncertainty of the head echo direction. As the meteor leaves the radar beam or the ablation process ceases and the SNR typically decreases again. Using the interferometric calculation of the meteor location on the plane of the sky together with the known range to the head echo for each pulse, a robust fit is made to the data points versus time for vx , vy and vz to provide an estimate of the trajectory as described in Schult et al. (2013). This takes the form of apparent entry angle and average velocity for each head echo. Points further away from the mean straight-line trajectory get lower weight in the fitting procedure reducing the influence of outliers and the effects of scatter on the fit due to low SNR areas. Independent validation of the robustness of the resulting radiants and speeds has been presented by Brown et al. (2017). That study shows that optical trajectories (determined from triangulation of two camera stations) and MAARSY head echoes had radiants and speeds which agreed to within a degree and ∼ 0.5 km/s respectively. Figure 1 shows the distribution of the standard errors (one sigma) of the trajectory angles and velocities in relative counts. The figure shows that the elevation angle has on average a smaller statistical error than the radiant azimuth angle. This is because the radiant azimuth is mainly determined by the interferometric analysis while the radiant elevation angle is more linked to the range rate and range resolution. Meteor head echoes with speed errors

C. Schult et al. / Icarus 309 (2018) 177–186

0.07

normalized counts

Table 2 The maximum value of σ wave for the five strongest showers detected by MAARSY. Here the combination of spatial σ ang and velocity σ vel probe size at the solar longitude of shower maximum λmax together with the resulting σ wave are given for each shower. The three letter designation follows that used by the IAU Meteor Shower Catalogue (e.g., LYR for Lyrids).

Δ azi: median: 3.8° Δ ele: median: 2.2° Δ vel: median: 2.2 km/s

0.06 0.05

Name

0.04

LYR PER ORI GEM QUA

0.03 0.02 0.01 0 0

2

4 6 error (degree−km/s)

8

Fig. 1. Distribution in relative count rates of the standard errors (bin size 0.2 km/s) in meteor head echo determined radiant elevation angle (ele), azimuth angle (azi) and velocity (vel).

greater than 10 km/s were removed and are not included in our analysis. Note that the statistical errors for head echoes from a specific meteor shower might differ due to a more limited range in the entry angle and velocities than the population as a whole which were used to construct Fig. 1. For the meteor shower survey all meteor head echo data collected from the beginning of MAARSY observations (November 2013) through March 2016 was stacked together in integer solar longitude bins to form a ‘virtual’ year, similar to the procedure used by Galligan (20 0 0) and Brown et al. (2010). Fig. 2 shows the stacked counts per solar longitude bin and the cumulative observation time in hours per bin. In total, about 760,0 0 0 meteor head echoes are included in this study with a mean of ∼ 20 0 0 head echoes per degree of solar longitude. 3. 3D wavelet of the radiant distribution Meteor showers are localized enhancements in the density of radiants in time-velocity-radiant coordinates compared to the background. While no formal quantitative definition of a meteor shower exists, Galligan (20 0 0) was the first to apply wavelet analysis to detection of meteor streams in orbital meteor data. Building on this earlier work, the procedure used in the current study to localize meteor showers using the wavelet transform was presented in Brown et al. (2010) and updated in Pokorný et al. (2017). All radiant data in every 1° bin in solar longitude is analysed using the wavelet equation:



1

Vg max



∞



∞

f (x, y, Vg ) Vgmin −∞ −∞ σ   (x0 − x )2 + (y0 − y )2 (Vg0 − Vg )2 3− − σang 2 σV2    (x0 − x )2 + (y0 − y )2 (Vg0 − Vg )2 exp −0.5 − dxdydVg , (1) σang 2 σV2

W [x0 , y0 , Vg0 ] =

( 2π )

3/2

1/2 ang V

σ

with x = (λ − λ0 ) and y = β (radiant coordinates in degree). σ ang is the spatial probe scale, Vg is the geocentric velocity and σ V the corresponding velocity probe scale. f(x, y, Vg ) is the observed radiant distribution and W[x0 , y0 , Vg0 ] the corresponding wavelet coefficient at the location (x0 , y0 ) and the velocity (Vg0 ). This produces a wavelet ‘map’ of the sky for each solar longitude bin, with radiant overdensities producing larger wavelet coef-

179

λmax

λ − λ0 (degs)

Vg (km/s)

β

σ ang

σ vel

(degs)

(degs)

(degs)

(%)

32 140 209 262 283

240.5 283 246.6 208.3 276

57.0 38.5 7.5 11 64

46.4 59 65 32.8 40

4.5 4.6 2.6 3.8 4.2

7.5 6.0 15 14 5

σ wave 45 110 78 115 67

ficients (Wc ). For each test radiant, speed pair, the significance of the resulting Wc is assessed by computing Wc for every other solar longitude bin at the same test radiant,speed location and finding the yearly median and standard deviation of Wc . This is used to define a background and expected variance. The number of standard deviations (termed σ wave ) is the particular Wc above the median Wc and forms a relative measure of the shower’s significance compared to the background. To begin the analysis, an estimate of the optimal spatial and velocity probe size is required. This varies between datasets and is determined by the spread in the radiant compared to the background. For comparison, Brown et al. (2010) adopted a spatial probe size of 4° and 10% in speed for the wavelet search of CMOR transverse scattering meteor data while Pokorný et al. (2017) used 2.5° and 15% in speed for Southern Argentina Agile Meteor Radar (SAAMER) survey. An optimal choice of probe size ideally will maximize the σ wave value for meteor showers. However, the radiant shape and spread changes with shower speed as does the background, so some compromise value must be used (or the search performed over multiple probe sizes, which though possible, becomes computationally expensive). Here we follow Pokorný et al. (2017) and use the strongest showers detectable by MAARSY as a basis for choosing probe sizes. We compute σ wave as a function of spatial and velocity probe size in the solar longitude bin of the maximum activity of these reference showers and isolate the combination producing the largest σ wave . Fig. 3 shows an example of the variation as a function of probe size of σ wave for the Lyrids shower. A similar plot is shown in Bruzzone et al. (2015), where the wavelet coefficient (Wc ) is maximized. Table 2 summarizes the optimal probe sizes for the five strongest showers in the MAARSY dataset. In several cases (notably the Perseids) there is a broad maximum covering a large range of σ vel in particular. We chose σang = 3◦ and σvel = 8% as a broad compromise. In general, σ wave values above 3.0 have been used in past analyses to identify localized maxima and we adopt this cutoff as well. For every solar longitude, such local maxima were identified and then the radiants linked with maxima in adjacent solar longitude bins to form chains which may be showers. We have done two variations of such shower linkages (List 1 and 2 in the supplementary material2 ) similar to the process in Pokorný et al. (2017) using two different linkage parameters. Successive maxima were linked if they fell within 2° in radiant location (λ − λ0 and β ) and 10% in speed. We term this “List1”. Shower list 2 was constructed as a second check; it is less restrictive with maxima linked if they are within 3° spatially and 15% in speed. These automated searches resulted in 92 possible showers for List 1 and 111 showers in List 2. The lists and the corre-

2

ftp://aquarid.physics.uwo.ca/pub/maarsy.

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meteors

6000

4000

2000

obs. time / h

0 60

40

20

0 0

50

100

150 200 solar longitude

250

300

350

Fig. 2. Meteor head echo counts and measurement time per degree of solar longitude for the data set used in this study. Data gathered for the years 2013–2016 are stacked into an equivalent “virtual” year.

Fig. 3. Value of σ wave (color coded) for the Lyrids (LYR) as a function of angular probe size (vertical axis) and relative velocity probe size in % (horizontal axis). Here the values for σ wave are computed for =32° centred at sun-centred radiant coordinates of x=240.5° and y=57.0° for Vg =46 km/s. The cross represents the maximum value of σ wave .

sponding figures and tables are included in the supplementary material. Using these provisional lists as a starting point, the next step was manual verification of the automated linkages including additional linkages among shower chains within the automated list. That is, some showers are artificially “broken” into several chains, usually because either there is too much radiant scatter or the wavelet coefficient initially slightly above the 3σ threshold drops just below this threshold in some solar longitude bins, breaking a chain. Another possibility is that some of these automatically formed showers might not be real, often the result of low radiant counts or measurement artifacts. In that case if the radiant drift is inconsistent or unphysical as discussed in Brown et al. (2010) and Pokorný

et al. (2017), these showers are assumed to be artifacts and removed. Once all automated showers are examined for these potential issues, the final list of probable showers was then compared with the IAU Meteor Shower Catalogue and common showers flagged. The final shower list is shown in Table 3 and the corresponding orbital parameters are shown in Table 4. Included are all showers from the list which passed the manual selection and last longer than two solar longitude bins. Also included are shorter duration showers if similar showers are seen in the CMOR data set. In these cases we are more confident that the detections are real because of the independent estimate from another survey. The first column in Table 3 shows the IAU code of the corresponding meteor shower and the second column the linked shower

C. Schult et al. / Icarus 309 (2018) 177–186

181

60

30° 40

°

0

−30°

°

30

°

330

°

°

270

210

°

v / km/s

Ecliptic latitude

60°

20

150

−60° 0

Sun−centered ecliptic longitude Fig. 4. Radiant locations for the 33 meteor showers of Table 3. The size of the dots represents the σ wave above the background and the geocentric velocity is color coded. The full width half maximum of the sporadic sources as observed with MAARSY are represented with dashed lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

4. Results and discussion We identified 33 showers which have been documented in the IAU list and have been reported in previous radar surveys (e.g. Brown et al., 2010; Pokorný et al., 2017; Jenniskens et al., 2016). Fig. 4 shows the location of all detected showers in a radiant map ((λ − λ0 )g , βg ) color coded by geocentric velocity (Vg ). The size of the symbol represents the significance of the shower at its time of maximum relative to the annual background activity (σ wave ). The dashed lines show the location of the full width half maximum of the sporadic sources as observed with MAARSY (Schult et al., 2017). The number of detectable showers is lower than previous meteor shower surveys using specular radar systems, except for the AMOR survey (Galligan, 20 0 0). The CMOR survey reported 117 different showers (Brown et al., 2010), while the SAAMER survey detected 58 showers (Pokorný et al., 2017). This discrepancy is probably the result of three different reasons. First, MAARSY, like other HPLA head echo detecting radars, is most sensitive to high speed meteors (Baggaley, 2002). Due to the high geographic latitude (69°) of MAARSY, this results in a strong seasonal detection sensitivity. This is shown in Fig. 2 where the highest count rates occur between 90° to 270° solar longitudes. During this time frame (start of the summer to start of the winter) the Earth’s Apex has locally the highest elevation angle of the year and meteors with the highest geocentric speeds are most observable. During the other half of the year the Apex direction has poor observational geometry throughout the whole day. Therefore high speed meteor showers, which are concentrated in the Apex, remain undetected. This also effects meteor showers with radiants in the Helion or Antihelion sporadic source region. Only the North Toroidal meteor source region is observable during the whole year (Schult et al., 2017). For radars located at lower latitudes, this effect is smaller (Janches et al., 2006). Secondly, a difference between other specular radar meteor shower surveys and the present study is the total number of meteors in the surveys. A larger data set of MAARSY head echo observation would lead to detection of weaker showers.

70 geo. velocity MAARSY / km/s

numbers particular to the data set. The beginning and end solar longitudes (λs and λe ), the solar longitude with the highest wavelet coefficient (λm ) and the duration (dur = λe − λs ) are also shown. The radiant (α g , δ g ), radiant drift ( α g , δ g ), geocentric velocity (Vg ) and the wavelet coefficient (Wcmax ) are referred to as λm . The showers having too few days of detection to calculate a radiant drift are marked with a zero in the corresponding columns.

60

50

40

30

20 20

30

40 50 60 geo. velocity CMOR / km/s

70

Fig. 5. Geocentric velocity of common MAARSY showers compared to CMOR observations (Brown et al., 2010). The mean deviation between the two data sets is 0.54 km/s. Note that in contrast to the MAARSY data, the CMOR data are corrected for deceleration.

Finally and perhaps most significantly, is the difference in the detected particle sizes between the surveys. As meteor showers contain in general larger particles, they are easier to detect with specular systems which have higher mass thresholds. MAARSY is more sensitive and typically observes at least one to two orders of magnitude smaller masses (representative masses of order 10−9 kg (Schult et al., 2017; Brown et al., 2017)) than the CMOR system (10−7 kg at 30 km/s (Brown et al., 2008)). The comparison of common shower geocentric velocities with the CMOR survey (Brown et al., 2010) shows no systematic offset over the whole velocity range, as shown in Fig. 5 (not included: zeta Cygnids (ZCY), Orionids-zeta Taurids (ORI-ZTA), Leonis Minorids (LMI), Part of Coronae Borealids (CB), Part of April rho Cygnids (ARC)). This is interesting because Brown et al. (2010) used a height, velocity dependant deceleration correction (Brown et al., 2008) while for the MAARSY data the direct observed (average) velocity is used. This implies that MAARSY detects the meteor head echoes before significant deceleration occurs. This conclusion is supported by the fact that the mean detection height of MAARSY head echoes is around 100 km (Schult et al., 2017) as compared to around 90 km for typical CMOR specular echo observation (Jones and Campbell-Brown, 2005). This large height differ-

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Table 3 Meteor showers identified in the MAARSY head echo survey. The table shows shower number from the wavelet analysis (No.), solar longitude of first/end detection (λs and λe ), solar longitude of the wavelet maximum λm , duration, geocentric right ascension/declination (α g /δ g ), radiant drift and errors ( α g / ± ( α )/ δ / ± ( δ )), wavelet coefficient at the maximum (Wcmax ), geocentric velocity (Vg ). IAU code

No.

λs

λm

λe

duration

αg

δg

α g

± ( α )

δ g

± ( δ )

Wcmax

σ wave

Vg

BTA PPS TPR PER ZCY ZCA KLE DPL STA-TA ORI LMI CTA-ETT NTA-TA NOO LEO GEM MON HYD DAD-NID DLM URS JLE QUA LBO XCB Part of CB TCB Part of ARC LYR ETA NOC ZPE ARI

1 90 92 88 25 46 789 10 11 24 13 16 17 15 18 19 21 29 22 23 26 36 37 25 28 27 31 35 32 34 40 39 41 42 45 43 46 47 48 49 50 51 53 54 55 56 58 62 59 60 61 63 64 65 66 67 70 68 69 71 72 73 74 75 82 83 85 86 91 76 77 78 79 80 81 84 87 89

85.5 99.5 105.5 112.5 10.5 151.5 162.5 174.5 181.5 189.5 192.5 203.5 217.5 231.5 233.5 246.5 255.5 256.5 256.5 264.5 270.5 281.5 281.5 284.5 291.5 293.5 298.5 30.5 31.5 34.5 44.5 53.5 66.5

98.5 111.5 108.5 140.5 14.5 163.5 181.5 176.5 195.5 210.5 210.5 222.5 227.5 244.5 236.5 261.5 257.5 257.5 256.5 268.5 270.5 281.5 283.5 292.5 293.5 295.5 298.5 31.5 32.5 45.5 47.5 86.5 82.5

102.5 116.5 113.5 148.5 18.5 164.5 196.5 177.5 218.5 225.5 215.5 226.5 231.5 258.5 238.5 270.5 257.5 257.5 256.5 279.5 270.5 284.5 287.5 300.5 298.5 301.5 298.5 34.5 35.5 65.5 55.5 96.5 88.5

18 18 9 37 9 14 35 4 38 37 24 24 15 28 6 25 3 2 1 16 1 4 7 17 8 9 1 5 5 32 12 44 23

85.7 23.1 45.9 48.6 300.4 139.7 162.2 147.2 30.4 97.2 161.4 64.8 56.7 88.7 154.4 113.1 100.2 125.9 205.8 162.7 221.9 148 230.3 214.9 248.2 229 232.9 317.1 272 337.5 10.4 69.8 47.1

21.1 30.9 48.7 58.2 39.7 11.7 15.7 9 7 16 37.2 26 22.2 15.4 20.8 32.6 6.3 2.1 61.5 30.1 75 24.4 49.9 46.7 29.6 36.6 35.7 42.8 33.6 –1.6 17.3 26.4 27

0 0.75 0 1.32 0 0 0.77 0 0.77 0.85 1.16 0.74 0.93 0.67 0.88 1.19 0 0 0 0.9 0 0 0.6 0.76 0.48 0.8 0 0 0.53 0.7 0 0 0.37

0 0.07 0 0.03 0 0 0.04 0 0.03 0.01 0.09 0.34 0.07 0.02 0.09 0.03 0 0 0 0.06 0 0 0.13 0.13 0.09 0.2 0 0 0.17 0.01 0 0 0.13

0 0.61 0 0.32 0 0 –0.3 0 0.3 0.03 –0.66 0.14 0.05 –0.06 –0.52 –0.17 0 0 0 –0.39 0 0 0.16 –0.33 –0.04 –0.22 0 0 –0.38 0.35 0 0 0.45

0 0.08 0 0.01 0 0 0.03 0 0.02 0.01 0.06 0.14 0.05 0.02 0.21 0.03 0 0 0 0.03 0 0 0.08 0.09 0.09 0.21 0 0 0.06 0.01 0 0 0.1

71.3 160.6 33.2 1140.2 76.4 43.1 104 30.3 82.8 430.5 79.1 38.8 79 103.7 105.9 1018.2 29.4 27 67.7 78.5 123.6 89.3 659.3 79.9 59 53.2 82 45.3 208.1 346.9 40.5 83.8 193.3

15.7 7.6 9.3 109.1 11.9 12.2 24.7 9.1 16.7 64 10.2 9.8 14.7 27.3 9.7 101 9.6 9.8 11.2 9.8 32.3 27.1 65.1 13.6 10.1 8 11.5 8 40.2 29.8 9.8 14.4 27.9

29.2 62.7 50.8 58.7 42.5 42.5 42.9 43.8 28.1 64.6 59.3 40.2 27.9 42.7 69.3 33.1 38.6 56.7 40.8 61.7 32.6 50.6 40 40 44.9 36.4 36.4 41.4 46.2 64.3 36.6 27.7 38.6

4.5

70

4

60

3.5 50 3 40

v / km/s

log10(5*Wc) MAARSY

ence is an artifact of the different detection biases between radial and transverse meteor scatter; the latter are particularly affected by initial trail radius which produces an artificial height ceiling for detection (Ceplecha et al., 1998). However, the deceleration correction applied to CMOR data seems to be a good approximation in a statistical sense, given the agreement with shower speeds measured by MAARSY. The MAARSY shower list does not include any meteor showers with a geocentric velocity smaller than 27 km/s, although there are several known and also reported by other radar systems. This again we attribute to the detection biases inherent in radial meteor scattering which favours higher speeds. Though MAARSY in general observes meteors with slower velocities but the count rates are low. The strong decrease in the ionization coefficient of these slow meteors requires larger meteoroids to produce enough scattered signal to be detectable. Because of the much smaller observation volume of the system, in comparison to all sky radars, it is much less likely to observe many higher mass (slow) meteoroids. Fig. 6 shows a comparison of the wavelet coefficients of the MAARSY and the CMOR survey with color coded geocentric velocity. The MAARSY coefficient is multiplied by a factor of 5 to account for the discrepancy in the total count rate. MAARSY has on average 20 0 0 orbits per solar longitude while the CMOR analysis was done with about 10,0 0 0 orbits per bin. It can be seen that nearly all the blue dots, meaning slow velocity meteor showers, have larger wavelet coefficients in the CMOR data. In contrast, the red symbols correspond to the faster meteor shower and have the same or higher wavelet coefficients than in the MAARSY data. MAARSY clearly detects faster meteor showers more efficiently than CMOR. This is also the case for the sporadic meteor sources, where the fast North/South Apex dominate the meteor head echo

2.5 30

2 1.5 1.5

2

2.5 3 3.5 log10(Wc) CMOR

4

4.5

20

Fig. 6. Comparison of the wavelet coefficients (Wcmax ) from MAARSY with the CMOR system. Because of the larger statistics of the CMOR survey, the MAARSY coefficient is multiplied by a factor of 5. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

observations (e.g. Chau et al., 2007; Janches et al., 2006; Kero et al., 2012), while for specular systems the Helion/Antihelion complex has a stronger relative signal (Jones and Brown, 1993; CampbellBrown and Jones, 2006). This is also a consequence of the initial trail radius effect for specular meteor radar systems. A longer set of meteor head echoes or a meteor head echo shower survey closer

C. Schult et al. / Icarus 309 (2018) 177–186

183

Table 4 Orbital elements of the detected meteor showers. Semi-major axis (a), eccentricity (e), perihelion (q), inclination (i), argument of perihelion (ω), argument of ascending node () and number of orbits used to calculate the wavelet coefficient (Norb ) on the day of the peak. All angular elements are J20 0 0.0. The number of individually extracted shower head echoes (Nm ), their mean dynamical mass (in units of log10 (mass[kg]) and the standard deviation (widthm ) of the log10 (mass[kg]) distribution is also shown. Finally, the mean height (in km) of the head echos for each shower (mean z) and the width of the height distribution (in km) widthz is given in the final two columns. IAU code

λm

a

e

q

i

ω



Norb

Nm

mdyn

widthm

mean z

widthz

BTA PPS TPR PER ZCY ZCA KLE DPL STA-TA ORI LMI CTA-ETT NTA-TA NOO LEO GEM MON HYD DAD-NID DLM URS JLE QUA LBO XCB Part of CB TCB Part of ARC LYR ETA NOC ZPE ARI

85.5 99.5 105.5 112.5 10.5 151.5 162.5 174.5 181.5 189.5 192.5 203.5 217.5 231.5 233.5 246.5 255.5 256.5 256.5 264.5 270.5 281.5 281.5 284.5 291.5 293.5 298.5 30.5 31.5 34.5 44.5 53.5 66.5

2.22 2.56 2.98 11.72 4.79 5.02 8.39 2.87 1.74 4.22 4.44 3.53 2.06 10.09 4.3 1.25 3.43 4.92 2.59 4.5 4.47 3.19 2.6 1.45 3.35 0.97 1 3.68 14.74 4.44 1.44 1.7 1.71

0.85 0.653 0.86 0.919 0.815 0.984 0.987 0.986 0.819 0.874 0.863 0.971 0.826 0.989 0.771 0.879 0.939 0.954 0.622 0.878 0.789 0.984 0.623 0.361 0.768 0.079 0.107 0.776 0.938 0.874 0.927 0.809 0.953

0.334 0.889 0.419 0.949 0.887 0.082 0.107 0.039 0.315 0.533 0.607 0.103 0.358 0.11 0.985 0.151 0.209 0.224 0.98 0.55 0.945 0.051 0.98 0.928 0.777 0.896 0.89 0.825 0.919 0.559 0.105 0.325 0.081

2.9 143.4 100.5 112.8 73 13.5 24.2 21.7 6.2 164.2 122.2 13.5 2.6 24.8 163.3 22.5 35.3 125.2 72.2 134 52.3 101.3 70.3 75.7 78.2 74.5 73.9 71.6 78.8 164.4 34.1 5.2 31.2

242.5 133 74.2 150.3 138.4 211.6 37 200.7 121.3 89.8 99.1 325 294.2 141.8 172.4 324 128.8 125.6 189.6 266.7 204.5 335.8 172.1 218.2 121.1 77.2 90.7 126.2 214.7 92.5 30.5 58.6 27.6

278.5 111.5 108.5 140.5 14.5 343.5 181.5 356.5 15.5 30.5 210.5 222.5 227.5 64.5 236.5 261.5 77.5 77.5 256.5 268.5 270.5 281.5 283.5 292.5 293.5 295.5 298.5 31.5 32.5 45.5 47.5 86.5 82.5

37 464 46 440 94 42 56 40 50 246 111 45 41 49 444 274 31 35 71 177 40 48 279 89 103 108 143 68 93 183 40 62 110

77.0 237.0 19.0 501.0 43.0 32.0 92.0 17.0 94.0 582.0 75.0 39.0 56.0 103.0 108.0 465.0 13.0 2.0 0 100.0 0 30.0 209.0 70.0 57.0 86.0 0.0 14.0 31.0 180.0 23.0 112.0 199.0

–7.0 –8.3 –7.9 –8.0 –7.9 –7.2 –7.6 –7.6 –7.7 -9.0 –8.7 –7.9 –7.3 –7.7 –8.7 –7.2 –8.0 –7.9 0 –8.7 0 –7.5 –7.3 –7.4 –7.3 –7.2 0 –8.3 –8.1 –9.2 –7.8 –7.3 –7.4

1.2 1.5 0.9 1.3 1.0 1.2 1.2 0.9 1.2 1.5 1.3 1.5 1.7 1.2 1.3 1.2 1.2 0.0 0 1.7 0 0.7 1.2 1.0 1.3 1.2 0 0.9 1.1 1.8 1.1 1.4 1.3

97.9 103.9 97.6 106.6 97.8 96.9 97.8 98.1 99.8 106.6 103.5 96.2 96.3 98.7 106.2 96.1 100.0 101.8 0 104.4 0 97.8 98.1 95.3 96.8 94.4 0 100.3 104.8 107.0 97.6 97.2 97.0

2.9 6.6 2.2 6.7 4.3 4.0 3.9 3.0 4.2 7.1 4.9 4.4 5.2 4.3 5.9 4.5 4.4 3.2 0 6.3 0 3.4 4.1 4.3 4.2 4.8 0 3.9 5.3 6.6 5.0 3.0 3.3

Table 5 Comparison of the radiants of the Geminids and Orionids with the observation of an other HPLA (MU radar), a specular system (CMOR) and optical measurments (CAMS).

70

50

60

Geminids (GEM)

40 50 30 40

v / km/s

duration MAARSY / sol. long.

60

20 30

10 0 0

10

20 30 40 50 duration CMOR / sol. long.

60

20

Fig. 7. Comparison of the duration of the meteor showers as recorded by MAARSY versus CMOR, color coded velocity. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to the equator would help to refine information on high velocity meteor showers. In Fig. 7 the duration of common meteor showers between MAARSY and CMOR are compared. The scattering in the plot is in some cases very large and can reach the order of weeks. The largest discrepancies are observed for showers with lower veloc-

System

αg

δg

Vg

MAARSY MU (Kero et al., 2013) CMOR (Brown et al., 2010) CAMS (Jenniskens et al., 2016) Orionids (ORI) MAARSY MU (Kero et al., 2011) CMOR (Brown et al., 2010) CAMS (Jenniskens et al., 2016)

113.1 112.8 112.5 113.5

32.6 32.6 32.1 32.3

33.1 34.9 34.5 33.8

97.2 94.8 95.5 95.5

16 15.4 15.2 15.7

64.6 67 65.4 66.3

ities; faster showers are closer to the line of equality. For example, in the case of the Quadrantids, MAARSY observed the shower for 7° in solar longitudes, which is mainly around the traditional sharp peak. In contrast, CMOR detects this shower for several weeks (in total for 60° of solar longitude) with a much lower σ wave (Brown et al., 2010). Either CMOR is more sensitive to this broader part of the stream or the total statistical data set of the MAARSY observation is not sufficient to extract such weak signals. In general, only two of the slower showers MAARSY observed a longer duration than detected by CMOR. In Table 5 the radiants and geocentric velocities at the times of maximum for the Geminids and the Orionids are compared with the results of the HPLA MU radar, the specular radar CMOR and the optical CAMS network. These two showers were chosen for

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5 log10 cumulative counts

4.1. Shower mass indices

measurement fit

By estimating the mass of individual head echoes we may measure the differential mass index power law, s, of particles in the stream. We assume the number, dN, of meteoroids with mass between m and m + dm follows dN = Cm−s dm, where C is a normalization constant (see Ceplecha et al. (1998) for more details). To measure shower mass indices, we first extracted all head echoes that were within 3° of the radiant drift corrected position, estimated by the wavelet analysis and also within 3 km/s in speed for each shower. The dynamical mass was then computed following the procedure described in Schult et al. (2017). Note that the dynamical masses as calculated assume no fragmentation and are based on the average observed deceleration and speed over the entire path. Therefore, they generally represent lower bounds to the true masses. We also restrict the head echoes used to those which have measurement errors which result in a total uncertainty ≤ 50% of the mass value. The overall statistics of dynamical masses per shower are give in the last five columns of Table 4. For the strongest four showers (GEM, PER, QUA and ORI), there are enough individual head echo events to estimate the mass index of the showers at MAARSY masses. We first examine the dynamical mass distribution of all head echoes measured by MAARSY with individual mass measurement errors less than 50% for comparison to shower indices. Collectively these form a comparatively high precision dataset maintaining large number statistics. The curve fits use the Multi-Nest algorithm using the procedure described in Pokorný and Brown (2016). The resulting distribution and fit is shown in Fig. 8. The roll-off below ≈ 10−7 kg is instrumental. The value for s of 2.07 is consistent with the values in the model of Grun et al. (1985). This is a bit surprising as MAARSY head echo measurements are dominated by high speed meteoroids with over representation of material from Oort cloud and Halley type comets (Nesvorny et al., 2011; Pokorny et al., 2014) compared to mass limited surveys. The Grun et al. (1985) flux at these masses is primarily from in-situ satellite impact measurements, which should better reflect the lower speed meteoroid population. This surprising agreement was also noted by Schult et al. (2017). Fig. 9 shows the mass index fits for head echoes in three sets of 5 km/s wide bins, spanning the range of speeds for the showers measured. For the first two velocity populations, fits are close to s=1.7, spanning masses from 10−6 kg at low speeds (33–38 km/s) to 10−8 kg. At the highest speeds (63–68 km/s), the latter where the peak in head echo numbers occurs, the mass index is about 2. Unfortunately, the distributions are not simple power laws, but show a distinct change in apparent slope at larger masses. Using the same quality criteria as used in Fig. 9, four shower mass distributions are shown in Fig. 10. Most values are slightly

4 s=−2.067 all meteors

3

2

1 −12

−10

−8

−6 −4 log10 m / kg

−2

0

Fig. 8. Power law fit to the dynamical mass (in kilograms) distribution for all head echoes with ≤ 50% mass uncertainty.

validation of the MAARSY radiant locations because they were observed with several different systems, in particular another HPLA radar with a similar sensitivity. For the Geminid meteor shower the MAARSY determined radiant matches well the other datasets. However, MAARSY observed the lowest average velocity for the Geminids of 33.1 km/s. For comparison, the MU Geminid velocity is given as 34.9 km/s (Kero et al., 2013). However, the MU Geminid speed is extrapolated with a linear fit to a common altitude of 109.5 km. Without this extrapolation of 0.11 km/s per km in altitude the discrepancy is actually smaller than 1 km/s and the variability between the surveys almost certainly due to differences in deceleration. For the Orionids, MAARSY records the maximum at a solar longitude of 210.5°; this is 2° later in solar longitude than the traditional maximum. This shift could reflect a mass-dependent sorting, but our number statistics remain too small to conclude this with confidence. Referenced to a common solar longitude of 208.5 °, MAARSY observes the same radiant as the other studies with αg = 95◦ and δg = 15.8◦ . The measured velocity of 64.6 km/s is 0.8 km/s slower than the (deceleration-corrected) CMOR observation and 2.4 km/s slower than the MU observations. Here we strongly suspect deceleration is playing a major role, as the Orionids are a southern hemisphere shower with a radiant which never exceeds a maximum elevation angle of 32°. Due to the very low elevation angle, noticeable deceleration occurs as these head echoes enter the beam at a shallow angle. 4.5 measurement fit

log

10

cumulative counts

4 3.5 3

4.5

4.5

4

4 3.5

3.5 s=−1.701 33−38 km/s

3

s=−1.686 40−45 km/s

3

2.5

2.5

2.5

2

2

2

1.5

1.5

1.5

1 −12

−10

−8

−6 log

10

−4 m / kg

−2

0

1 −12

−10

−8

−6 log

10

−4 m / kg

−2

0

1 −12

s=−1.988 63−68 km/s

−10

−8

−6 log

10

−4 m / kg

−2

0

Fig. 9. The mass index fit to all head echoes with less than 50% measurement error having speeds from 33 to 38 km/s (left), 40–45 km/s (middle) and 63–68 km/s (right). All masses are in kilograms.

C. Schult et al. / Icarus 309 (2018) 177–186

measurement fit

log10 cumulative counts

2.2

2

1.8

1.8 s=−1.95 ORI

1.6

1.4

1.4

1.2

1.2

1 −12

log10 cumulative counts

2.2

2

1.6

−10

−8

−6

−4

2.2

2

2

1.8

1.8 s=−1.56 QUA

1.6

1.4

1.4

1.2

1.2

1 −12

−10

−8 log10 m / kg

−6

−4

s=−1.64 GEM

1 −12

2.2

1.6

185

−10

−8

−6

−4

−6

−4

s=−1.45 PER

1 −12

−10

−8 log10 m / kg

Fig. 10. Power law fit to the dynamical mass (in kilograms) distribution for various shower head echoes with ≤ 50% mass uncertainty. Shown are fits for the ORI (top left)[s=1.95], GEM (top right)[s=1.64], QUA (bottom left) [s=1.56] and PER (bottom right) [s=1.45].

lower or similar to the sporadic background at similar speeds. Virtually all these values are smaller than shower mass indices derived at larger sizes, which are typically > 1.6 (Blaauw et al., 2011). The notable exception are the ORI, which have a comparatively high mass index, a finding similar to Kero et al. (2011) who directly estimated a mass index from MU RCS measurements of ORI head echoes to be slightly larger than 2.0. This apparent excess of small meteoroids in the ORI may simply be an artifact of the higher sensitivity of MAARSY and MU to higher speed head echoes or it may be intrinsic to the stream. The latter possibility is suggested by the shower survey results of AMOR (Galligan, 20 0 0), which are at a similar limiting mass to the present survey. AMOR’s strongest stream detection is that of the Eta Aquariid stream. The shower was so strong in AMOR data that it was used as calibration for AMOR initial system testing as noted by Taylor (1991). The Halleyid showers may in fact be intrinsically rich in small meteoroids with masses below 10−8 kg. The lower mass indices measured for these showers at small masses compared to shower measurements at larger masses are expected. The smallest meteoroids in eccentric streams will be lost due to radiation pressure, the so-called beta-cutoff (Dohnanyi, 1970), which should remove most meteoroids below 10−11 kg for streams with eccentricities above 0.9. It is worth emphasizing the sensitivity of mass index measurements to uncertainties, notably fit ranges which may be affected

by small number statistics/larger errors in the distribution wings, as noted by Hughes (1987). 5. Conclusion In this paper we demonstrated that HPLA head echo radar observations are able to detect and measure properties of a variety of meteor showers. The presence of meteoroids in streams having masses as low as 10−9 kg to as small as 10−10 kg, for faster meteor showers, is directly demonstrated by their visibility in these head echo data. We find mass indices near 1.5–1.6 for the PER, QUA and GEM showers. The Orionids show a much steeper mass index close to 2.0, suggesting smaller meteoroids in this Halleyid stream. In total we identified 33 meteor showers all of which were previously known and documented in the IAU meteor shower catalog. The head echoes associated with these showers represent ∼ 1% of all head echoes measured in our survey to an equivalent limiting mass of 10−8 kg. A comparison of the geocentric radiants of the detected showers with CMOR observations shows generally good agreement. Shower velocities differ by as much as a few km/s, though the mean difference is ∼ 0.5 km/s. Larger differences are found between the duration of the meteor showers in the MAARSY and the CMOR surveys. This may correspond to the differences in statistical sizes or may be due to the different observed particle sizes (radar sensitivity). Additional

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factors can include biases in the observation geometry (elevation angle and radiant time below the horizon) which we have yet to analyse in detail. This will be left for a future publication. Acknowledgements The technical support by the Andøya Rocket Range (ARR) is acknowledged. Furthermore we thank the IAP staff for the technical support, operations and maintenance of MAARSY. This work was supported by grant STO 1053/1-1 (AHEAD) of the Deutsche Forschungsgemeinschaft (DFG). PGB was supported by the NASA Meteoroid Environment Office through co-operative agreement NNX15AC94A. Supplementary material Supplementary material associated with this article can be found, in the online version, at 10.1016/j.icarus.2018.02.032. References Baggaley, W., 2002. Radar Observations. In: Murad, E. and Williams, I. (Ed.), Meteors in the Earth’s Atmosphere. Cambridge Univ Press, Cambridge, U.K, pp. 123–147. chapter Radar Obse Blaauw, R.C., Campbell-Brown, M.D., Weryk, R., 2011. A meteoroid stream survey using the Canadian Meteor Orbit Radar - III. Mass distribution indices of six major meteor showers. Mon. Not. R. Astron. Soc. 414 (4), 3322–3329. doi:10. 1111/j.1365-2966.2011.18633.x. Brown, P., Stober, G., Schult, C., Krzeminski, Z., Cooke, W., Chau, J., 2017. Simultaneous optical and meteor head echo measurements using the Middle Atmosphere Alomar Radar System (MAARSY): Data collection and preliminary analysis. PSS 141, 25–34. Brown, P., Weryk, R., Wong, D., Jones, J., 2008. A meteoroid stream survey using the Canadian Meteor Orbit Radar: I. methodology and radiant catalogue. Icarus 195 (1), 317–339. doi:10.1016/j.icarus.20 07.12.0 02. Brown, P., Wong, D., Weryk, R., Wiegert, P., 2010. A meteoroid stream survey using the Canadian Meteor Orbit Radar II: identification of minor showers using a 3d wavelet transform. Icarus 207, 66–81. Bruzzone, J.S., Brown, P., Weryk, R.J., Campbell-Brown, M.D., 2015. A decadal survey of the daytime arietid meteor shower using the canadian meteor orbit radar. Mon. Not. R. Astron. Soc. 446 (2), 1625–1640. doi:10.1093/mnras/stu2200. Burns, J., Lamy, P., Soter, S., 1979. Radiation forces on small particles in the solar system. Icarus 40 (1), 1–48. doi:10.1016/0019- 1035(79)90050- 2. Campbell-Brown, M.D., Jones, J., 2006. Annual variation of sporadic radar meteor rates. Mon. Not. R. Astron. Soc. 367, 709–716. Ceplecha, Z., Borovicka, J., Elford, W.G., Revelle, D.O., Hawkes, R.L., Porubcan, V., Simek, M., 1998. Meteor phenomena and bodies. Space Sci. Rev. 84, 327–471. Chau, J., Renkwitz, T., Stober, G., Latteck, R., 2014. MAARSY multiple receiver phase calibration using radio sources. J. Atmos. Sol. Terr. Phys. 118, 55–63. doi:10.1016/ j.jastp.2013.04.004. Chau, J.L., Galindo, F., 2008. First definitive observations of meteor shower particles using a high-power large-aperture radar. Icarus 194 (1), 23–29. doi:10.1016/j. icarus.2007.09.021. Chau, J.L., Woodman, R.F., Galindo, F., 2007. Sporadic meteor sources as observed by the Jicamarca high-power large-aperture vhf radar. Icarus 188, 162–174. Close, S., Hunt, S.M., McKeen, F.M., Minardi, M.J., 2002. Characterization of Leonid meteor head echo data collected using the VHF-UHF Advanced Research Projects Agency Long-Range Tracking and Instrumentation Radar (ALTAIR). Radio Sci. 37 (1), 9–1–9–9. doi:10.1029/20 0 0RS0 02602. Close, S., Hunt, S.M., Minardi, M.J., McKeen, F.M., 20 0 0. Analysis of Perseid meteor head echo data collected using the Advanced Research Projects Agency LongRange Tracking and Instrumentation Radar (ALTAIR). Radio Sci. 35 (5), 1233– 1240. doi:10.1029/1999RS002277. Dohnanyi, J., 1970. On the origin and distribution of meteoroids. J. Geophys. Res. 75 (17), 3468–3493. Galligan, D.P., 20 0 0. Structural Analysis of Radar Meteoroid Data. Canterbury Doctoral. Grun, E., Zook, H., Fechtig, H., Giese, R., 1985. Collisional balance of the meteoritic complex. Icarus 62 (2), 244–272.

Hemenway, C., Millman, P., Cook, A., 1973. Evolutionary and physical properties of meteoroids. In: Hemenway, C., Millman, P.M., Cook, A. (Eds.), Evolutionary and Physical Properties of Meteoroids. NASA SP-319, p. 386. Hey, J.S., Pasrsons, S.J., Stewart, G.S., 1947. Radar observations of the Giacobinid Meteor Shower. R. Astron. Soc. 107, 176–183. Hughes, D., 1987. P/Halley dust characteristics - a comparison between Orionid and Eta Aquarid meteor observations and those from the flyby spacecraft. Astron. Astrophys. (ISSN 0 0 04–6361) 187, 879. Janches, D., Heinselman, C.J., Chau, J.L., Chandran, A., Woodman3, R., 2006. Modeling the global micrometeor input function in the upper atmosphere observed by high power and large aperture radars. J. Geophys. Res. 111, A07317. Janches, D., Hormaechea, J., Brunini, C., Hocking, W., Fritts, D., 2013. An initial meteoroid stream survey in the southern hemisphere using the southern argentina agile meteor radar (saamer). Icarus 223 (2), 677–683. doi:10.1016/j.icarus.2012. 12.018. Jenniskens, P., 2006. Meteor Showers and their Parent Comets. Cambridge Univ Press, Cambridge, U.K. Jenniskens, P., 2017. Meteor showers in review. Planet. Space Sci. 143, 116–124. doi:10.1016/j.pss.2017.01.008. Jenniskens, P., Nnon, Q., Albers, J., Gural, P., Haberman, B., Holman, D., Morales, R., Grigsby, B., Samuels, D., Johannink, C., 2016. The established meteor showers as observed by CAMS. Icarus 266, 331–354. doi:10.1016/j.icarus.2015.09.013. Jones, J., Brown, P., 1993. Sporadic meteor radiant distributions: orbital survey results. Mon. Not. R. Astron. Soc. 265, 524–532. Jones, J., Campbell-Brown, M., 2005. The initial train radius of sporadic meteors. Mon. Not. R. Astron. Soc. 359 (3), 1131–1136. doi:10.1111/j.1365-2966.2005. 08972.x. Kero, J., Szasz, C., Nakamura, T., 2013. MU head echo observations of the 2010 Geminids: radiant, orbit, and meteor flux observing biases. Ann. Geophys. 31 (3), 439–449. doi:10.5194/angeo- 31- 439- 2013. Kero, J., Szasz, C., Nakamura, T., Meisel, D.D., Ueda, M., Fujiwara, Y., Terasawa, T., Miyamoto, H., Nishimura, K., 2011. First results from the 2009-2010 MU radar head echo observation programme for sporadic and shower meteors: the Orionids 2009. Mon. Not. R. Astron. Soc. 416, 2550–2559. Kero, J., Szasz, C., Nakamura, T., Meisel, D.D., Ueda, M., Fujiwara, Y., Terasawa, T., Nishimura, K., Watanabe, J., 2012. The 2009–2010 MU radar head echo observation programme for sporadic and shower meteors: radiant densities and diurnal rates. Mon. Not. R. Astron. Soc. 425, 135–146. Latteck, R., Singer, W., Rapp, M., Vandepeer, B., Renkwitz, T., Zecha, M., Stober, G., 2012. MAARSY: The new MST radar on AndyaSystem description and first results. Radio Sci. 47 (1), 1–18. doi:10.1029/2011RS004775. Nesvorny, D., Vokrouhlicky, D., Pokorny, P., Janches, D., 2011. Dynamics of dust particles released from oort cloud comets and their contribution to radar meteors. Astrophys. J. 743 (1), 37. Pokorný, P., Brown, P., 2016. A reproducible method to determine the meteoroid mass index. Astron. Astrophys. 592 (A150), 1–12. doi:10.1051/0 0 04-6361/ 201628134. Pokorný, P., Janches, D., Brown, P.G., Hormaechea, J.L., 2017. An orbital meteoroid stream survey using the Southern Argentina Agile MEteor Radar (SAAMER) based on a wavelet approach 290, 162–182. doi:10.1016/j.icarus.2017.02.025. Pokorny, P., Vokrouhlicky, D., Nesvorny, D., Campbell-Brown, M., Brown, P., 2014. Dynamical model for the toroidal sporadic meteors. Astrophys. J. 789 (1), 25. Schult, C., Stober, G., Chau, J.L., Latteck, R., 2013. Determination of meteor-head echo trajectories using the interferometric capabilities of maarsy. Ann. Geophys. 31, 1843–1851. Schult, C., Stober, G., Janches, D., Chau, J.L., 2017. Results of the first continuous meteor head echo survey at polar latitudes. Icarus 297, 1–13. Sekanina, Z., 1970. Statistical model of meteor streams II. Major showers. Icarus 13 (3), 475–493. Stober, G., Schult, C., Baumann, C., Latteck, R., Rapp, M., 2013. The geminid meteor shower during the ecoma sounding rocket campaign: specular and head echo radar observations. Ann. Geophys. 31, 1–15. Taylor, A., 1991. A Meteor Orbit Radar. Ph.D. thesis. University of Canterbury. Williams, I.P., Ryabova, G.O., 2011. Meteor shower features: are they governed by the initial formation process or by subsequent gravitational perturbations? Mon. Not. R. Astron. Soc. 415 (4), 3914–3920. doi:10.1111/j.1365-2966.2011.19010.x. Ye, Q., Wiegert, P., Brown, P., Campbell-Brown, M.D., Weryk, R., 2013. The unexpected 2012 Draconid meteor storm. Mon. Not. R. Astron. Soc. 437 (4), 3812– 3823. doi:10.1093/mnras/stt2178. Younger, J.P., Reid, I.M., Vincent, R.A., Holdsworth, D.A., Murphy, D.J., 2009. A southern hemisphere survey of meteor shower radiants and associated stream orbits using single station radar observations. Mon. Not. R. Astron. Soc. 398 (1), 350. doi:10.1111/j.1365-2966.2009.15142.x.