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Formation and past evolution of the showers of
96P/Machholz complex
Abedin Abedina,b , Paul Wiegerta,b, Diego Janchesc, Petr Pokorn´yc,d, Peter
Browna,b, Jose Luis Hormaecheae
aDepartment of Physics and Astronomy, The University of Western Ontario, London,
Canada N6A 3K7
bCentre for Planetary Science and Exploration (CPSX), The University of Western
Ontario, London, Canada N6A 3K7
cSpace Weather Laboratory, GSFC/NASA, Greenbelt MD, 20771
dDepartment of Physics, The Catholic University of America, Washington, DC 20064, USA
eFacultad de Cs. Astronomicas y Geofisicas, UNLP, y CONICET, Estacion Astronomica
Rio Grande, Tierra del Fuego, Argentina
Abstract
In this work we model the dynamical evolution of meteoroid streams of
comet 96P/Machholz, and the largest member of the Marsden sunskirters, comet
P/1999 J6. We simultaneously fit the characteristics of eight meteor showers
which have been proposed to be linked to the complex, using observations from
a range of techniques - visual, video, TV and radar. The aim is to obtain a self-
consistent scenario of past capture of a large comet into a short-period orbit,
and its subsequent fragmentation history. Moreover, we also aim to constrain
the dominant parent of these showers.
The fit of our simulated shower characteristics to observations is consistent
with the scenario of a capture of a proto-comet 96P/Machholz by Jupiter circa
20000 BC, and a subsequent major breakup around 100 - 950 AD which resulted
in the formation of the Marsden group of comets. We find that the Marsden
group of comets are not the immediate parents of the daytime Arietids and
Northern and Southern δ-Aquariids, as previously suggested. In fact, the hy-
pothesis that the Northern δ-Aquariids are related to the Marsden group of
comets is not supported by this study.
The bulk of the observational characteristics of all eight showers can be
explained by meteoroid ejection primarily from comet 96P/Machholz between
10000 BC and 20000 BC. Assuming the Marsden group of comets originated
between 100 AD - 950 AD, we conclude that sunskirting comets contribute
mainly to the meteoroid stream near the time of the peak of the daytime Ari-
etids, Southern δ-Aquariids, κ-Velids. Finally, we find that the meteor showers
identified by Babadzhanov and Obrubov (1992) as the α-Cetids, the Ursids and
∗Abedin Abedin
Email address: aabedin@uwo.ca (Abedin Abedin)
Preprint submitted to Icarus October 10, 2017
Carinids correspond to the daytime λ-Taurids, the November ι-Draconids or
December α-Draconids and the θ-Carinids.
Keywords:
1. Introduction1
This work builds on a series of studies aiming to investigate the origin and2
past evolution of the meteoroid complex, related to comet 96P/Machholz (96P3
hereafter). In a previous work, we investigated the formation mechanism and4
the age of the Quadrantid meteoroid stream (Abedin et al., 2015) and more5
recently the origin of the daytime Arietids meteor shower (Abedin et al., 2017).6
Our main goal is to develop a self-consistent scenario of the hierarchical fragmen-7
tation and subsequent evolution of the 96P complex, using detailed observational8
characteristics of the associated Machholz shower complex.9
Comet 96P is unusual among the short-period comets. It has an extremely10
low perihelion distance, grazing the Sun at a distance of 0.123 AU or roughly11
27R, and has been associated with up to eight meteor showers, several other12
comets and at least one object of asteroid appearance. In particular, it is thought13
that 96P shares a genetic relationship with the Marsden and Kracht group of14
sunskirting comets and the Kreutz sungrazers (e.g., Sekanina and Chodas, 2005;15
Jenniskens, 2006). This ensemble of interplanetary bodies is referred to as the16
Machholz interplanetary complex and is believed to have originated from a sin-17
gle split of a larger progenitor prior to 950 AD (Sekanina and Chodas, 2005).18
Despite the association of 96P with the aforementioned bodies, some of their19
present orbital elements differ noticeably, owing to the differential planetary20
perturbations (mainly due to Jupiter). Presently, the Marsden sunskirters ap-21
proach the Sun within 8.8−11.2R(Sekanina and Chodas, 2005), and have22
mean orbital inclination of ≈26◦, whereas the Kracht group of comets have23
perihelia in the range 6.7−11.6Rand inclination of ≈13◦. For comparison,24
the present inclination of 96P is i≈58◦and perihelion distance of 0.123 AU25
(≈27R). Furthermore, 96P is interesting among other comets as it has anoma-26
lous molecular abundances (e.g., A’Hearn et al., 1995; Schleicher, 2008), being27
relatively depleted in CN , C2, C3compared to the OH abundance. That in-28
dicates that 96P has either formed in a region of the early Solar system with29
unusual conditions or is interstellar in origin.30
Comet 96P was mentioned for the first time in the context of meteor astron-31
omy by McIntosh (1990). The author noted the similar orbital evolution of 96P32
and the Quadrantid meteoroid stream, though their evolutionary cycles were33
offset by 4000 years. That led McIntosh (1990) to suggest a sibling rather than34
child-parent relationship.35
Numerical simulations of the long-term evolution of the orbit of 96P were36
performed by Babadzhanov and Obrubov (1992). They were the first to sug-37
gested that within one circulation cycle of the longitude of the ascending node38
Ω and the argument of perihelion ω(≈8200 years), the comet may give rise to39
2
eight different meteor showers. The Earth intersects four of these showers at40
their descending nodes and four at their ascending nodes. The authors identified41
these showers as the Quadrantids, daytime Arietids, Southern and Northern δ-42
Aquariids, Ursids, κ-Velids, Carinids and the α-Cetids. This work was extended43
by Babadzhanov et al. (2008) who considered instead asteroid 2003 EH1as the44
parent (a known member of the 96P complex, see section 1.1.1), where they45
obtained similar results for the first four showers, but the four last showers were46
linked to the α-Draconids, Puppid-Velids, Carinids and α-Piscids respectively.47
In short, the first four showers are well known and constrained. The existence of48
the other showers has remained uncertain, partly due to the lack of systematic49
meteor surveys from the Southern hemisphere.50
Jones and Jones (1993) argued that if comet 96P had been captured by close51
approach with Jupiter, about 2200 years ago, there has been sufficient time for52
the comet to produce most of the observed characteristics of the Quadrantids,53
the daytime Arietids and Southern δ-Aquariids.54
Recent work, carried out by Nesluˇsan et al. (2013b) investigated potential55
streams related to 96P, assuming an initial meteoroid ejection time 4000 years56
ago. They concluded that 96P may indeed produce eight different showers,57
though they were skeptical about the detectability of all of them. Instead,58
they argued that due to the proximity of four of the intersection points with59
the Earth’s orbit, only six showers are expected to be identified. Although60
the authors recognized the ∼8200 years circulation cycle of the longitude of61
the ascending node and the argument of perihelion of the 96P’s orbit, they62
considered only half of that period in their investigation. Moreover, the authors63
did not compare the characteristics of the modeled meteoroid streams in detail64
with available observations.65
Several recent works have suggested that the Marsden group of comets are66
the immediate parents of the daytime Arietids and the Northern and South-67
ern δ-Aquariids (Ohtsuka et al., 2003; Sekanina and Chodas, 2005; Jenniskens,68
2006; Jenniskens et al., 2012). Ohtsuka et al. (2003) noted the similarity in the69
orbital evolution of 96P, the Marsden and Kracht group of sunskirting comets70
and the daytime Arietids, assuming their evolutionary cycles were shifted by a71
few hundred years. The authors suggested that the Arietids are related to the72
Marsden group but hinted that all bodies may be genetically related. Sekanina73
and Chodas (2005) performed numerical simulations to investigate the origin74
of the Marsden, and Kracht group of comets. Based on the tendency of these75
comets to arrive at perihelion in pairs, the authors developed a detailed model76
and suggested that the sunskirting group of comets, along with the Arietids and77
southern δ-Aquariids, originated from a single comet break up, prior to 950 AD.78
However, these authors and earlier works have not attempted to constrain for-79
mation models of the 96P complex using detailed observations of the associated80
meteor showers.81
1.1. 96P/Machholz complex showers82
Some of the individual showers belonging to 96P complex have already been83
studied by several authors, including our series of studies. Below, we provide a84
3
brief summary of each shower, listed according their strengths:85
1.1.1. The Quadrantids86
The Quadrantids are unusual, being among the strongest of the annual show-87
ers with an extremely compact central portion, with a Full Width of Half Max-88
imum (FWHM) of only ≈17 hours, encountered every year between January89
3-4. The short duration alone is a strong evidence that the core of the stream90
is young.91
Due to the presently large difference in the longitude of the ascending nodes92
of the stream and 96P/Machholz, the comet was not recognized as the immedi-93
ate parent of the stream. Comet 1491 I was suggested by Hasegawa (1979) and94
followed up by others (Hasegawa, 1979; Williams and Collander-Brown, 1998;95
Williams et al., 2004; Jopek and Williams, 2013); however the relatively poor96
orbit that could derived from ancient Chinese, Japanese and Korean records97
(Kronk, 1999) makes a clear link difficult. Numerous other cometary parents98
have been considered (see Williams et al. (2004) for a review) but were found99
wanting. Jenniskens et al. (1997) suggested that the parent may be an asteroid-100
like object, hidden in a high inclination orbit. With the discovery of asteroid101
2003 EH1, Jenniskens (2004) noted a striking similarity with the orbit of the102
Quadrantids and suggested a child-parent relationship. Wiegert and Brown103
(2005) performed a nodal regression analysis of the orbits of 2003 EH1and the104
Quadrantids, arguing that the core of the stream is only 200 years old. Williams105
et al. (2004) performed a similar study which concluded the stream was young,106
as 2003 EH1and the Quadrantids were on similar orbits 500 years ago.107
However, recent radar observations of the Quadrantids revealed that there is108
an older component of the stream, lasting from mid-November to mid-January109
(Brown et al., 2010). Using seven high-precision photographic Quadrantids, aug-110
mented with radar observations by the Canadian Meteor Orbit Radar (CMOR)111
we demonstrated, from back-integrations of eight high precision photographic112
Quadrantid and five high-precision radar Quadrantids, that the core of the113
stream is related to asteroid 2003 EH1and most likely formed circa 1800 AD114
(Abedin et al., 2015). This study also found that the older component is asso-115
ciated with comet 96P and is several millenia old. For a more detailed review116
of past works on the Quadrantids, the reader is referred to Jenniskens (2006),117
Nesluˇsan et al. (2013b) and Abedin et al. (2015).118
1.1.2. The Daytime Arietids119
This shower is observed annually between mid-May and late June with a120
broad plateau of peak activity near solar longitude λ= 80.5◦(Bruzzone et al.,121
2015). The shower characteristics have mostly been constrained by radar obser-122
vations, owing to the proximity of the radiant position to the Sun, with some123
recent observations by optical detections. Recently, we addressed the ques-124
tion as to the association of the stream with the Marsden group of comets or125
comet 96P (as discussed above). We performed detailed numerical simulations126
of meteoroids, ejected from 96P and the most notable member of the Mars-127
den group of comets - P/1999 J6. The resulting streams from both comets128
4
were analyzed with respect to which could reproduce the main characteristics129
of the daytime Arietids. As observational constraints for the shower, we used130
data from the 12 year radar survey of the daytime Arietids by CMOR (Bruz-131
zone et al., 2015), along with 14 TV observations by SonotaCo (2009) and 31132
video events recorded by the Cameras for All-sky Meteor Surveillance (CAMS)133
(Jenniskens et al., 2016). Our simulations indicated that the Marsden group134
of comets can not alone reproduce the observed characteristics of the shower135
and thus can not be the sole parents of the stream. Instead, we conclude that136
the broader activity of the daytime Arietids is associated with comet 96P and137
has an age of ∼12000 years, though we demonstrated that the Marsden group138
of comets may contribute to the peak of the shower. An outstanding question139
for this shower relates to the difference in the orbital elements of optical and140
radar sized particles, a discrepancy previously noted by Jenniskens et al. (2012).141
Radar surveys measure systematically lower meteoroid geocentric speeds, and142
thus lower orbital semi-major axis, as compared to those obtained by optical143
surveys. Jenniskens et al. (2012) attributed these differences to insufficient cor-144
rection for deceleration of radar sized (a few hundreds of microns) meteoroids in145
the Earth’s atmosphere. These are normally subject to a greater atmospheric146
drag than larger meteoroids. These differences, if they are real, may imply that147
the daytime Arietids are older than a few tens of millenia (assuming the differ-148
ence in the orbital elements is due to Poynting-Robertson drag). The observed149
discrepancy however, remains unresolved.150
1.1.3. Southern and Northern δ-Aquariids151
The Southern δ-Aquariids are observed every year between late May to early152
July with a peak activity at solar longitude λ= 126◦(Brown et al., 2010).153
Though much weaker, the northern branch is active between late July to late154
August with a maximum activity occurring at λ= 139◦. Although the show-155
ers stand well above the sporadic background and have been well measured,156
their origin has received less attention and is mostly limited to the works by157
Babadzhanov and Obrubov (1992); Sekanina and Chodas (2005); Jenniskens158
(2006); Babadzhanov et al. (2008) and Nesluˇsan et al. (2013b).159
1.1.4. κ-Velids, α-Cetids, Carinids and Ursids160
- The predicted κ-Velids have recently been established as an annual shower161
(Pokorn´y et al., 2017), based on systematic radar observations by the Southern162
Argentina Agile Meteor Radar (SAAMER) (Janches et al., 2013, 2015) and we163
consider this linkage secure.164
The remaining three we will discuss in more detail in this paper, but we note165
that, there is no obvious shower listed in the IAU Meteor Data Center (IAU166
MDC) (http://www.ta3.sk/IAUC22DB/MDC2007/), corresponding to the radi-167
ant, speed and timing characteristics predicted by Babadzhanov and Obrubov168
(1992) for α-Cetids, though there are 19 different showers that are listed as169
Cetids. The Southern Daytime ω-Cetids may correspond to this shower in170
Babadzhanov et al. (2008) where they identify it as the α-Piscids. Likewise,171
there are 4 different showers listed as Carinids, though only θ-Carinids have172
5
been well measured (Pokorn´y et al., 2017). Finally, the association of the Ur-173
sids with 96P is questionable, as the stream has already been confirmed to be174
related to comet 8P/Tuttle (e.g., Jenniskens, 2006), which indicates that the175
stream had been either misidentified by Babadzhanov and Obrubov (1992) or176
it overlaps with another nearby stronger meteor shower and hence can not be177
detected as individual, as previously suggested by Nesluˇsan et al. (2013b).178
In this work, we aim to obtain a broader picture of the origin and past evo-179
lution of the complex of interplanetary bodies, associated with comet 96P. We180
approach that problem by simultaneously fitting the observed shower charac-181
teristics and attempt to answer the following questions:182
1. What is the most dominant parent of the 96P meteoroid complex associ-183
ated, comet 96P/Machholz or the Marsden group of comets?184
2. What is the age and likely parent (comet 96P/Machholz or the Marsden185
group of comets) of the Southern and Northern δ-Aquariids and the recently186
established κ−Velids and θ-Carinids?187
3. Do the Carinids, α−Cetids and Ursids exist or they have been misidenti-188
fied? If they exist, what is their likely age and parent?189
4. Can we obtain a self-consistent scenario as to the epoch when comet 96P190
has been captured in a short period orbit and its past fragmentation history?191
2. Observations192
In this section we present the observational characteristics of the showers193
that we will study and also provide some observational constraints on the parent194
bodies considered in this work.195
Babadzhanov and Obrubov (1992) were the first to note that comet 96P may196
intersect the Earth’s orbit at eight different locations, during one Kozai cycle (≈197
8200 years) of its longitude of ascending node. As a result, it could produce 8198
meteor showers at Earth. Figure 1 shows the intersection points of the descend-199
ing and ascending nodes with the Earth’s orbit, after one full Kozai cycle. Some200
of these showers are well known - The Quadrantids, daytime Arietids, South-201
ern and Northern δ-Aquariids and κ-Velids. Their observational characteristics202
have been constrained by both, radar and optical meteor surveys. However, the203
identification of some of the showers, which Babadzhanov and Obrubov (1992)204
have named the Carinids, α-Cetids and Ursids are uncertain. As noted in the205
previous section, there are no showers in the IAU MDC which match the char-206
acteristics of the Carinids and α-Cetids as given by Babadzhanov and Obrubov207
(1992). The shower designated as Ursids by Babadzhanov and Obrubov (1992)208
is not well documented in the literature and should not be mistaken with the209
00015 (URS) Ursids in the IAU MDC, which is a different shower, unambigu-210
ously associated with 8P/Tuttle (Jenniskens et al., 2002). Therefore, as part211
of this work, we aim to examine the validity of these “misidentified” showers212
by fitting our simulated shower characteristics to the observations of the well213
constrained showers (QUA, ARI, SDA, NDA and KVE) and then performing a214
search for the predicted showers in radar and optical databases.215
6
−2−1 0 1 2
X, (AU)
−3
−2
−1
0
1
Y, (AU)
Figure 1: Backwards time evolution of the ascending (blue dash line) and descending (red solid
line) nodes of the orbit of comet 96P/Machholz for one Kozai circulation cycle (∼8200 years)
of longitude of the ascending node (Ω) and argument of perihelion (ω). The “x” symbols
indicate the starting position of the cycle (present) and the triangle denotes the end position.
For the shower data required in this study, such as shower duration, orbits216
and radiants, we use the orbits measured by the Canadian Meteor Orbit Radar217
(CMOR) (Brown et al., 2010) and by the Southern Argentina Agile Meteor218
Radar (SAAMER) (Janches et al., 2013, 2015). The CMOR dataset includes219
1.5×107orbits obtained between 2002 and 2015, while the SAAMER dataset220
includes 106orbits obtained between 2012 and 2015. For this work we compile221
these dataset into a representative composite year.222
We took the simulation results which predict where shower radiants are223
expected, together with the expected speed and timing and performed a 3D224
wavelet search following the methodology described in Brown et al. (2010) and225
updated in Pokorn´y et al. (2017). For all predicted radiants we extended our226
search ±10 degrees relative to the predicted radiant and ten degrees of solar227
longitude before and after the expected activity dates based on the simulations.228
7
Finally, we searched over a window of ±10 km s−1from the predicted speeds229
for each shower. Our wavelet transforms were computed in steps of 0.2 degrees230
(providing a lower bound to our radiant precision) and in steps of 0.5% in speed.231
We used fixed wavelet probe sizes of 4 degrees in angular coordinates and 12%232
probe size in speed, based on results from Campbell-Brown and Brown (2015)233
and Pokorn´y et al. (2017). From these wavelet computations, we identified lo-234
cal maxima, which we define as being excursions in the wavelet coefficient of235
3σabove the median background based on the year of data outside the shower236
window that fell in our analysis windows. Based on the variance in daily radiant237
location and speed, we estimated our uncertainties to be 1 degree in radiant po-238
sition and 5% in speed - these uncertainties are used for all subsequent estimates239
of error in daily mean shower orbital elements. Finally, we automatically link240
shower maxima together if individual maxima occur withing 2 degrees (or less)241
in solar longitude, have radiants less than two degrees in sun-centered radiant242
coordinates and are less than 10% different in speed. These search results turned243
out to be very clean: there was only one possible maxima each day associated244
with the 96P predicted showers. We also attempted to link each maxima point245
with pre-existing showers listed in the IAU MDC, assuming common radiants246
were within 3 degrees in angular coordinates and 10% in speed.247
As a result of the search and our stream modelling, we have identified three248
observed showers as likely part of the 96P complex and roughly similar to249
the original predictions by Babadzhanov and Obrubov (1992). These are the250
“December α-Draconids” (IAU #00334, DAD) that partially overlaps with the251
“November ι-Draconids” (IAU #00392, NID), the “daytime λ-Taurids” (IAU252
#00325, DLT), “θ-Carinids” (IAU #00785, TCD). The DADs and the NIDs253
belong to the northern toroidal source and are the Ursids counterpart identi-254
fied by Babadzhanov and Obrubov (1992). The DLTs are the southern branch255
of the daytime Arietids and are likely the same shower named α-Cetids by256
Babadzhanov and Obrubov (1992). Finally, the TCD belong to the southern257
toroidal source and have only recently been established as a separate meteor258
shower (Pokorn´y et al., 2017). Analyzing the observed CMOR shower charac-259
teristics of the DAD and NID, we found that the latter two showers are weak and260
partially overlap in time, which renders their identification as separate show-261
ers difficult. We note that these two showers have been identified as separate262
events in the IAU MDC. Furthermore, towards the end of the activity of the263
DAD (λend = 271.5◦), there is significant background activity that overlaps264
with the onset of the Quadrantids. In fact, Brown et al. (2010) argued that265
Quadrantids show a low background activity that last about two months. In266
light of our simulations and more sensitive shower search, we suggest that this267
extended activity is not in fact one long individual shower, but instead likely268
three similar showers of the 96P complex, sharing similar radiant and orbital269
characteristics but slightly offset in nodal times.270
The observational characteristics of all these showers are summarized in271
Tab 1, as derived from radar (CMOR and SAAMER) and optical (CAMS)272
surveys. Generally, radar and optical meteor detections sample different me-273
teoroid sizes, with the former being capable of detecting particles of size of a274
8
few hundreds of microns, whereas the optical techniques detect larger mete-275
oroids (millimeter and larger). Thus, combining radar and optical observations276
enables us to fit our stream modelling to observed shower characteristics, equiv-277
alent to a few hundred micrometers and millimeter size meteoroids, as well as278
to investigate the past evolution of meteoroids of different sizes.279
Shower λstart
λmax
λend λ−
λ
b Vgαgδga q e i ω
(deg) (deg) (deg) (deg) (deg) (km s−1)(deg) (deg) (AU) (AU) (deg) (deg)
QUAa267.5 283.0 291.0 273.0 64.0 41.7 231.0 48.5 2.77 0.977 0.648 71.7 169.5
QUAb270.0 283.0 296.4 277.5 63.7 40.7 230.2 49.5 2.82 0.979 0.657 71.2 171.4
QUAd275.2 283.0 288.6 - - - - - - - - - -
ARIa62.0 80.5 95.0 348.3 7.4 39.1 44.9 25.5 1.71 0.074 0.957 30.6 26.4
ARIb73.0 77.0 89.4 331.6 7.3 41.1 43.9 24.4 2.67 0.078 0.974 27.7 28.7
SDAa114.5 123.5 163.5 210.9 -
7.2
41.3 338.8 -
16.7
2.23 0.058 0.974 31.5 155.7
SDAb117.9 128.0 145.9 208.8 -
7.2
41.3 341.3 -
15.7
2.59 0.069 0.975 29.0 152.9
SDAd109.8 124.5 144.4 – – – – – – – – – –
NDAa126 139 156 208.8 7.8 37.3 345.2 2.6 1.70 0.096 0.944 24.8 329.9
NDAb120.9 141.0 207.5 208.4 6.8 38.4 347.6 2.1 1.97 0.090 0.955 22.3 330.7
NDAd113.4 149.0 151.1 – – – – – – – – – –
DLTa71 86 98 331.2 -
8.6
35.6 52.5 10.1 1.49 0.109 0.927 23.5 211.1
NIDa221.0 241.0 264.0 265.1 61.6 43.0 196.1 65.3 2.44 0.984 0.598 73.7 188.1
NIDb239.3 242.0 267.9 260.9 63.2 42.0 196.5 68.3 3.62 0.973 0.734 72.9 194.7
DADb248.8 256.0 262.6 272.0 62.8 40.8 210.8 58.6 2.48 0.983 0.603 71.8 177.4
TCDc274.0 276.0 280.0 282.3 -
60.3
41.7 156.8 -
59.2
2.38 0.966 0.595 74.5 342.2
KVEc272.0 276.0 286.0 257.8 -
60.5
40.5 141.1 -
51.0
2.08 0.965 0.560 72.9 19.1
Table 1: Geocentric characteristics of the meteor showers, possibly associated with the Mach-
holz complex at their time of maximum activity. The columns denote: 1. The solar longitude
of the start time of the activity profile, 2. The time of maximum activity, 3. The end time
of the activity, 4. Sun-centered ecliptic longitude of the radiant, 5. Ecliptic latitude of the
radiant, 6. Geocentric speed, 7. Geocentric equatorial right-ascension of radiant position
in J2000.0. 8. Geocentric equatorial declination of the radiant in J2000.0. The remaining
columns list the orbital elements at maximum activity. The superscript (a) indicates data
obtained by CMOR, (b) corresponds to CAMS data, (c) observations derived by SAAMER
and (d) corresponds to visual observations by IMO.
In the Sec. 4 we fit the parameters listed in Tab. 1 directly to our simulations.280
By simultaneous match of all eight showers, our goal is to explain the age281
9
Name a e i Ωω
(AU) (deg) (deg) (deg)
P/1999 J6 3.100499137 0.984177313 26.613141 81.613781 21.976803
±0.000027986 0.000015813 0.020234 0.072701 0.080133
96P 3.0339397249395830.9592118287498158.312214235 94.323236311 14.757748401
±0.000000024505 0.000000046985 0.000044922 0.000011819 0.000020956
Table 2: Orbital elements of comet P/1999 J6 and comet 96P/Machholz used in this study,
taken from the NASA’s JPL Horizon System. See the text for more details.
estimates of the showers and put into perspective the origin of the 96P complex.282
2.1. Test parent bodies283
In this work, we consider two parent bodies for testing a child-parent re-284
lationship with the observed meteor showers. These bodies are the comet285
96P/Machholz and the most prominent member of the Marsden group of comets,286
P/1999 J6. The latter was chosen as it has the best constrained orbit among287
other group members. It would be impractical to simulate the meteoroid streams288
originating from each individual member of the Marsden group of sunskirters.289
Comet P/1999 J6 was first observed by the coronograph on-board of the290
Solar and Heliospheric Observatory (SOHO) and according to the NASA’s291
JPL Horizon database has been classified as a Jupiter-Family Comet (JFC)292
(http://ssd.jpl.nasa.gov/sbdb.cgi), despite its low Tisserand parameter293
with respect to Jupiter (Tj= 1.942), a value more typical for Halley type294
comets. Generally, JFCs have typical Tisserand parameters with respect to295
Jupiter of 2 < Tj<3. The present period of the comet is P= 5.46 years and296
based on 267 observations it has the orbital elements listed in Table 2. Presently,297
P/1999 J6 approaches the Sun within q≈0.049 AU or roughly 10R.298
Comet 96P/Machholz was discovered on May 12, 1986 and has also been299
classified as a JFC ((http://ssd.jpl.nasa.gov/sbdb.cgi). According to the300
NASA’s JPL Horizon database it has an orbital period of P∼5.3 years, with a301
Tisserand parameter with respect to Jupiter of Tj= 1.942. Similar to P/1999302
J6, this value is low and typical for Halley type comets. The present orbital303
elements of 96P are listed in Table 2. Presently, the perihelion distance of 96P304
is q≈0.124 AU or roughly 25R.305
The present orbits of the two hypothetical parents, comets 96P and P/1999306
J6, are presented in Fig. 2. It is evident that the two orbits are strikingly similar,307
indicating a possible genetic relationship. Currently, the ascending node of the308
orbit of 96P is located near the Sun, whereas the descending node is between309
the orbits of Mars and Jupiter. In contrast, while the ascending node of P/1999310
J6 is also close to the Sun, the descending node is close to the Earth’s orbit and311
most likely supplies “young” meteoroids that are presently encountered by the312
Earth.313
10
Figure 2: The orbits of comet 96P/Machholz (black line) and comet P/1999 J6 (green line)
viewed from above the ecliptic plane. The solid lines indicate the portion of the orbits above
the ecliptic whereas the dotted lines denote the portions below the ecliptic.
3. Numerical Simulations314
3.1. Solar System model and numerical integrator315
In our simulations, we model the Solar system as comprising the Sun and316
all planets. Effectively, the parents and their synthetic meteoroid streams will317
move under the gravitational attraction from the Sun, where the planets will318
act as perturbing forces on their Keplerian motion. We account for the mutual319
interaction between the planets, while the parent clones and individual mete-320
oroids are considered as test particles. In addition to gravitational effects, the321
meteoroids will be also subjected to non-gravitational forces such as the solar322
radiation pressure force (e.g., Burns et al., 1979) and Poynting-Robertson (PR)323
drag (e.g., Burns et al., 1979; Klaˇcka, 2004; Klaˇcka and Kocifaj, 2008). The solar324
radiation pressure affects the dynamics of micron and millimeter sized particles325
11
and manifests itself as weakening of the solar gravitational attraction force FG.326
Usually, the radiation force is considered via the standard β-parameter and is327
given by Burns et al. (1979) as:328
β=FR
FG
= 5.7×10−4Qpr
ρs ,(1)
329
where ρis the meteoroid’s bulk density in kg m−3,sis the radius of the330
meteoroids in meters and Qpr is the light scattering efficiency, considered to be331
unity in our simulations. The PR drag decreases particle’s semi-ma jor axis and332
eccentricity, due to anisotropic emission of the absorbed solar radiation, in the333
reference frame of the Sun, and causes meteoroids to slowly spiral towards the334
Sun. In this work we do not account for the Lorentz force and solar wind drag335
as they are ∼1000 times smaller than the solar radiation pressure (e.g., Leinert336
and Grun, 1990) for 100 µm particles (the smallest meteoroids considered here)337
and their influence decreases for larger meteoroids.338
The radiation forces are virtually zero for the considered parent bodies.339
The only significant non-gravitational force on comet nuclei is the “rocket”340
like acceleration induced by the sublimation of the cometary volatiles, which341
causes the trajectory of a comet to deviate from pure gravitational motion.342
However, we do not model these forces here, due to their stochastic nature over343
the time scales considered in this work. Thus, the parent bodies will be subject344
to gravitational force only. Furthermore, the orbital evolution of both parents345
96P and P/1999 J6 are in state of Kozai-type oscillation (Sec. 3.3.1). That leads346
to episodically decrease of their perihelia to distances of 0.025 AU or roughly347
5R. For this reason, despite the fact that a body would generally spend348
a very short time near perihelion, we also include general relativistic effects349
(post-Newtonian approximation).350
The equations of motion of all bodies (planets, parent bodies and meteoroids)351
are integrated using the symplectic method of Wisdom and Holman (1991),352
with close approaches handled with the Chambers’ hybrid symplectic scheme353
(Chambers, 1999). During the backward integrations of the orbits of 96P and354
P/1999 J6, we take snapshots of the state vectors of the clones and the planets355
every year. These state vectors will be used as the basis for meteoroid ejections356
at any instant of time from suitably selected clones for both parents.357
3.2. Meteoroid ejection358
The meteoroids are modeled as spherical particles of density ρm= 2500 kg m−3
359
with radii ranging from s= 100 µm (a size appropriate for radar meteors (e.g.,360
Weryk and Brown, 2013)) to s= 1 mm (a typical value for optical or visual361
meteors). They are sampled from a uniform distribution of the logarithm of362
their radii. Although, this is not a realistic size distribution, we aim to sample363
a wide size range of meteoroid sizes in order to investigate the resulting shower364
for radar and optical size meteors. Later, we apply weighting to the number of365
meteoroids as a function of their size (Sec. 3.4.6 and Sec. 3.4.5).366
12
The meteoroids are ejected as a result of cometary outgassing, where the367
ejection speed is modeled according to Brown and Jones (1998) and is given as:368
Vej = 10.2r−1.038ρ−1/3R1/2
cm−1/6(m s−1) (2)
where ris the heliocentric distance in (AU), ρis the bulk density of the369
meteoroid in (g cm−3), Rcis the radius of the comet nucleus in (km) and m370
is the mass of the meteoroid in (grams). The meteoroids are ejected isotrop-371
ically on the sunlit hemisphere independently of the angle to the Sun. Dust372
production rate assumed to be uniform in true anomaly of the parent clones in373
the simulation. Thus, in order to calculate the ejection speeds, we also need to374
know the parents’ physical size.375
Recent studies of the nucleus brightness suggest a radius between R= 2 −376
2.5 km (e.g., Green et al., 1990; Sekanina, 1990; Licandro et al., 2000) and more377
recently R= 3.2 km (Lamy et al., 2004). We model comet 96P as a spherical378
nucleus of a mean radius R= 2.5 km and bulk density of ρ=700 kg m−3.379
Despite, P/1999 J6 being the largest fragment of the Marsden group of comets380
and that has survived at least several perihelion returns, Sekanina and Chodas381
(2005) estimated that the nucleus of the comet is not greater than 45 meters.382
However, Lamy et al. (2013) questioned these estimates based on more recent383
analysis of light-curves of sunskirting comets and concluded that the size of the384
largest fragments must be at least a few hundreds of meters. Following the385
results of that recent work, we assume a radius for P/1999 J6 of R= 0.25 km386
and bulk density of ρ=700 kg m−3.387
For example, the mass of a meteoroid at the lower size range (s= 100µm),388
considered in our simulations, would have a value of m≈10−6grams. The389
magnitude of the ejection speed for such a meteoroid, released from the nucleus390
of 96P/Machholz at a heliocentric distance of 1 AU would be Vej ≈160 m s−1,391
whereas meteoroid of radius s= 1 mm would have a terminal speed of Vej ≈392
50 m s−1. We note, however, that there is no reliable way to know what the393
actual size of the comet was about 20000 years in the past. If the nucleus of 96P394
was as twice as big, 20000 years ago, as its present size, the above values of the395
ejection speeds will translate to Vej ≈226 m s−1for a radar size meteoroid and396
Vej ≈70.5 m s−1for a particle of radius s= 1 mm. However, we do not expect397
that the uncertainty introduced by the lack of knowledge on the original parent398
size 2000 years into the past to be significant. This is because the meteoroids are399
expected to have initial orbits similar to that of the parents, and the difference in400
ejection speeds are much lower than the orbital speeds of the parents. Thus the401
effect on the difference in ejection speeds due to differences in the original parent402
size will be significantly smaller than the errors in the ’true’ orbital evolution403
of the parent over a 20000 year period.404
P/1999 J6 is significantly smaller and fainter than 96P, so it is not unrea-405
sonable to expect that it will have less dust production compared to that of406
96P. However, here we will initially assume dust production rate similar to 96P,407
merely because we need to eject a relatively large number of particles from both408
parents, so we have a good particle number statistics. This seems a reasonable409
13
assumption, since our goal is to test the streams of which parent body will pro-410
duce a better match to the observed width of the activity profiles, which is to a411
first order a proxy as to the age of the shower. The amount of dust production412
is not expected to affect the width of the profiles but only the relative number413
of particles in each bin of the solar longitude. The size of the cross-section of a414
stream, and thus the width of the activity profile, will depend on the differential415
planetary perturbations and non-gravitational forces over time.416
3.2.1. Selecting “clones” for backward integrations417
The first step in meteoroid stream modelling is to integrate the orbit of418
a hypothetical parent back in time to an epoch of interest that will be used419
for meteoroid ejection and forward integrations. Despite the good quality of420
the contemporary small Solar system body observations, their ”true” orbits421
are not exactly known but instead come with a confidence region. Therefore,422
we sample the uncertainty region of the phase space of their orbital elements423
aiming to consider all orbits consistent with the ”true” orbit. Each set of the424
sampled orbital elements is referred to as “clone”. Assuming that we have a set425
of six orbital elements yi= (a, e, i, ω, Ω, M ), and they are correlated, the orbital426
elements for each clone, can therefore be written in the form:427
yi=y0+XikΛk j ξj,(3)
where y0is 6 ×1 column vector of of the nominal orbital elements of the428
body, Xik is 6 ×6 matrix, with columns equal to the eigen-vectors of the co-429
variance matrix of the orbital elements, Λkj is a diagonal matrix with elements430
corresponding to the eigen-values of the covariance matrix and ξjis a random431
number sampled from a normal distribution with mean µ= 0 and standard432
deviation σ= 1. Using that approach, we create 1000 clones for each assumed433
parent body, 96P and P/1999 J6, that is integrated back in time, until an epoch434
for interest.435
3.3. Phase 1: Backward integrations of parent body candidates436
3.3.1. Parent candidate #1 96P/Machholz437
The equations of motion of comet 96P and each clone are integrated back in438
time, until 50000BC, using a force model as described in Sec. 3.1. The lengthy439
backward integration (5×104years) was chosen with the aim of encompassing at440
least a few circulation cycles of the longitude of the ascending node (Ω), allowing441
us to study the resulting meteoroid streams over a long time period. However,442
we emphasize that even though our backward integrations extend to 50000 BC,443
we only consider meteoroid ejection epochs since 20000 BC. The reason for that444
is that the time window of 50 millenia is comparable to the dynamical and445
physical lifetimes of JFC (e.g., Levison and Duncan, 1994, 1997), so backward446
integration until 50000 BC merely aims to illustrate the past evolution of the447
orbit of 96P.448
Our symplectic method (see section 3.1) uses a fixed integration time step.449
We chose ∆t=12 hours to balance speed with accuracy. To be more precise,450
14
prior to the main integrations, we performed sample simulations in order to451
determine an optimal time step for both parents, 96P and P/1999 J6 where the452
method is described in detail in Abedin et al. (2017).453
During the backward integrations, we impose a perihelion cut-off distance of454
5R. Any clone or the parent body that approached the Sun below that limit455
is considered “dead” and removed from the simulations. Comets are unlikely to456
survive at such short distances from the Sun, which is also evidenced by the dis-457
ruption of the Kreutz group of sungrazing comets (Sekanina and Chodas, 2005).458
In fact, the sun grazing stage of the evolution of comets is often considered a459
frequent end state of most comets (e.g., Bailey et al., 1992).460
Figure 3: Backward evolution of the nominal orbital elements of comet 96P/Machholz (red
line), along with 103clones (green dots), over 5×104years.
The evolution of the orbital elements of the 1000 clones and the nominal461
orbit of 96P are presented in Fig. 3. The orbit is stable over a time scale of462
∼7500 years and evolves smoothly, while beyond that time the dispersal of463
the clones becomes significant. Furthermore, the orbit of 96P/Machholz is in464
state of Kozai type oscillation, which manifests itself in a distinct correlation465
between some of the orbital elements. In the Kozai-type orbital evolution, the466
semi-major axis of the orbit is approximately conserved, while there is out-of-467
phase oscillation of the perihelion distance, eccentricity and inclination of the468
orbit. That is, when the orbital inclination is at its maximum value i≈80◦, the469
orbital eccentricity reaches a minimum e≈0.7, while the perihelion distance470
15
is also at its maximum value q≈1 AU. Conversely, when the inclination is471
at minimum i≈15◦, the eccentricity is at its maximum (e≈0.99) while the472
perihelion distance reaches a minimum value of q≈0.05 AU. This oscillation in473
(e, i, q) for 96P occurs with at a period of ≈4100 years, whereas the longitude474
of the ascending node (Ω) and the argument of perihelion (ω) circulate from475
0◦to 360◦, with a period of ≈8200 years (see Fig. 3). The fact the orbit of476
96P is in a state of Kozai-type oscillation will be used for selecting clones for477
meteoroid ejection in Sec 3.4.1.478
3.3.2. Parent candidate #2 P/1999 J6479
Using the approach outlined in Sec. 3.2.1, we created 1000 clones, sam-480
pled from the 6-dimensional phase space of the nominal orbital elements of481
P/1999 J6. Then the orbits of the clones are integrated backwards in time until482
0 AD. This time span is motivated by the hypothesis that the Marsden group483
of comets, ARI, SDA and NDA may have formed between 100-950 AD (Sekan-484
ina and Chodas, 2005). In order to encompass the suggested comet breakup485
time interval, the earliest of these epochs (100 AD) will be used for meteoroid486
ejection onset time from P/1999 J6 and forward integrations of their orbits.487
For the backward integration of the orbit of P/1999 J6, we found an optimum488
fixed time step of ∆t= 4 hours, utilizing the force model as described in Sec. 3.1.489
We note the shorter integration time step used for the orbit of P/1999 J6,490
compared to ∆t= 12 hours for 96P. The reason for that is P/1999 J6 experiences491
more shallow and frequent encounters with Jupiter, so time step of at least492
∆t= 4 hours is needed in order to smoothly sample its motion around the Sun.493
The result from the backward integrations are presented in Fig. 4. The orbit494
of P/1999 J6 quickly becomes chaotic, after only 500 years, owing to frequent495
close encounters with Jupiter. The onset of chaos was verified by Lyapunov496
exponent calculations, and corresponds in Fig. 4 to the time where the orbital497
elements begin to spread significantly. Presently, the perihelion distance of the498
comet reaches its minimum distance of q≈0.05 AU, while the eccentricity is499
almost at its maximum value of e≈0.98 (see Fig. 4). The present value of the500
inclination is i≈26.6◦but only 1.5 millenia ago it was about i≈75◦, where501
the perihelion distance was at its maximum value of q≈1 AU.502
Due to the quick dispersal of the clones of P/1999 J6, it becomes difficult to503
know the true orbit of the comets prior to 100 AD, due to the chaos. However504
a careful selection of clones using the past evolution of P/1999 J6, could still505
provide meaningful results from the forward simulations.506
3.4. Phase2: Forward integration507
3.4.1. Selection of “clones” for meteoroid ejection from parent candidate #1:508
96P/Machholz509
We use the fact that the orbit of 96P is in state of Kozai oscillation in order510
to select clones for meteoroid ejection and forward integrations. This type of511
secular evolution approximately conserves the Kozai energy (e.g., Kozai, 1962;512
Kinoshita and Nakai, 1999) which can be expressed as.513
16
Figure 4: Backward evolution of the nominal orbital elements of comet P/1999 J6 (red line),
along with 103clones (green dots), over 2000 years.
C= (2 + 3e2)(3 cos2i−1) + 15e2sin2icos 2ω, (4)
where eis the eccentricity, iis the inclination and ωis argument of perihelion514
of the orbit respectively. Over the period of interest here (22000 years in the515
past) the argument of perihelion (ω) would have completed roughly 3 precession516
cycles, indicating that the 96P’s osculating value of (ω) can take any value517
between 0◦and 360◦, where as the eccentricity of the orbit would lie between518
e∼0.7−0.97. However, due to the correlation between eand ω, the actual519
values that the orbit of 96P can take, are constrained to a curve called the Kozai520
trajectory for a given value of the Kozai energy C. Figure 5 shows the Kozai521
trajectories for the nominal orbit of 96P/Machholz, in the (e−ω) space, for522
different values of the Kozai energy C. In addition, the orbital elements of all523
clones of 96P, for the epoch of 20000 BC are mapped.524
It is evident from Fig. 5 that the Kozai energy for 96P/Machholz is not525
strictly conserved, owing to the fact that close approaches to Jupiter and plan-526
etary perturbations are not considered in the Kozai formalism. Nevertheless,527
using the information of an approximate conservation of Cprovides a vital infor-528
mation about the appropriate selection of clones for forward simulations. That529
is, during the secular evolution of the orbit of 96P, we expect that the true orbit530
must lie on or near a Kozai trajectory for C= 4. We thus sample our clones for531
17
Figure 5: Snapshot of the Kozai evolution of the orbit of 96P/Machholz in 20000 BC, for
different values of the Kozai energy C. The grey dots denote all the clones, superimposed
over the trajectories of constant C, where the red dots indicate “good” clones, that we select
for meteoroid ejection and forward integrations. Examples of “bad” clones, that are discarded
in our simulations, are denoted with blue dots.
forward integrations along that trajectory (see Fig. 5 for details). Ideally, one532
would select as many clones as possible, covering the entire range of argument533
of perihelion (ω) and eccentricity (e). However, here we sample only 10 clones534
due to the lengthy integrations times. The sampled clones are equally spaced535
in the range of ω= 0◦−360◦, while covering the interval e= 0.7−0.97.536
3.4.2. Selection of “clones” for meteoroid ejection from parent candidate #2:537
P/1999 J6538
Assuming that the primary reason for the dispersal of the clones is due to539
close planetary encounters, we chose to select clones that are situated close to540
the nominal orbit of the comet. The reason for that is that clones that lie541
far from the orbit can not end up on the present orbit of comet P/1999 J6542
and thus produce the observed characteristics of the resulting meteor showers543
(i,e., location of peak activity and spread, radiant location, geocentric speed544
18
etc.). Such an occurrence would require that all or nearly all of the ejected545
meteoroids suffer planetary encounters that place them on the present orbits of546
the observable streams, which cannot happen in practice due to the stochastic547
nature of planetary encounters.548
Using the argument discussed above, we select 10 clones near the nominal549
orbit of P/1999 J6. Clones “near” the nominal orbit are considered as those with550
orbital elements differing by no more than 1% of the orbital elements of P/1999551
J6. That should ensure that meteoroids ejected from these clones, end up in552
or close to the phase space of orbital elements of those meteoroids, presently553
intersecting the Earth.554
3.4.3. Orbit integration of meteoroids ejected from parent candidate #1 96P/Machholz555
Using that approach outlined in Sec. 3.2 3000 meteoroids are ejected at every556
10 perihelion passages (or roughly every 55 years) from ten suitable clones,557
over an arc, assuming the comet activity turns on at a heliocentric distance of558
r≤3 AU. That distance roughly corresponds to the threshold at which the559
water ice begins to sublimate (Delsemme, 1982). Assuming the orbital period560
of 96P (≈5.5 years) does not vary dramatically, and the meteoroid ejection561
onset is ∼20000 BC, that roughly corresponds to meteoroid ejection over ∼400562
perihelion returns, until the present. This amounts in ∼1.2×106particles per563
clone, in the range of their radii s= 100 µm −1 mm.564
Similar to the backward integrations, the equations of motion of the ejected565
meteoroids are integrated forward in time with a fixed time step of ∆t=12 hours,566
until the present. Furthermore, a perihelion cut-off distance of 0.025 AU or 5R
567
is imposed, so meteoroids below that limit are removed from further integra-568
tions. Moreover, only meteoroid having their orbital nodes within 0.01 AU (a569
“sieve” distance) from the Earth’s orbit are considered as capable of producing a570
shower, at the Earth. In reality, only meteoroids actually hitting the Earth can571
be observed as meteors, however due to the unrealistically low number of the572
simulated meteoroids, a nodal distance of 0.01 AU seems a good compromise.573
3.4.4. Orbit integration of meteoroids ejected from parent candidate #1 P/1999574
J6575
Due to the shorter time-scales of integrations here (only 2000 years), 3000576
meteoroids are ejected from 10 clones of P/1999 J6 every fifth perihelion return577
(or approximately every 27 years), so that approximately the same (compared578
to 96P) dust production (∼1.2×106particles per clone) is maintained. That579
results in 73 active perihelion returns of each clone. Finally, only remaining580
difference here is that we use a shorter integration time step of ∆t=4 hours (as581
for the backward simulations), due to more frequent encounters of P/1999 J6582
with Jupiter. All other parameters such as comet activity turn-on distance, per-583
ihelion cut-off distance and meteoroid sieve distance are the same as described584
in Sec. 3.4.3.585
19
3.4.5. Weighting of meteoroids by their perihelion distance at time of ejection586
The comet sublimation rate increases with the heliocentric distance (e.g.,587
Sekanina, 1988, 1992) and is a non-linear process. As comet approaches the588
Sun, sublimation becomes more violent which increases the dust production589
rate (Schulz, 2006) and the meteoroid ejection speeds (Whipple, 1950, 1951;590
Brown and Jones, 1998). Thus, the number of meteoroids will be dependent on591
the perihelion distance of the parent at the time of ejection. We use a weighting592
scheme suggested by Jones (2002), given as:593
Ws=θc(1 −e)2
q2√1−e2(5)
594
where595
θc= arccos q(1 + e)−r0
r0e(6)
596
is the to true anomaly corresponding to the comet-Sun distance r0in AU,597
at which the cometary activity turns on, eis the orbital eccentricity and q598
is the perihelion distance in AU. In the weighting process we set r0= 3 AU599
throughout. It is well known that more volatile components such as, CO and600
CO2begin to sublimate at much larger heliocentric distances e.g., as large as601
r0≈5 AU (see Sekanina, 1988), but it is unlikely that the gas pressure can lift602
millimeter size particles off the comet’s surface.603
Using the weighting scheme given by Eq. 3.4.5 each particle is assigned a604
weight, depending on the perihelion distance of the parent at the time the605
meteoroid is ejected. For example, a meteoroid ejected from a parent with a606
perihelion distance of 1 AU and an eccentricity of e=0.96, assuming r0=3 AU607
will be weighted by Ws≈6, where as a particle released from a parent with a608
perihelion distance of q= 0.1 AU and same eccentricity (orbit size and shape609
similar to 96P/Machholz) will be weighted by Ws≈340. Thus, this weighting610
will be used to correct for the meteoroids’ number distribution.611
3.4.6. Weighting by meteoroid size612
In Sec. 3.2 we mentioned that the ejected meteoroids, in our simulations, are613
sampled from a size distribution which is flat in the logarithm of particles’ size, in614
the range 100 µm - 1 mm, equivalent to radar and optical meteors respectively.615
However, this size distribution is not realistic. Generally, more particles are616
released at smaller sizes, compared to larger ones which is evidenced from meteor617
observations. Following Wiegert et al. (2009), this flat size distribution can618
be calibrated to a differential size distribution, as dN/dr =rα. Thus, the619
weighting that needs to be applied to account for differential size distribution620
is just Wr=rα+1.621
The observed sized distribution of meteors can roughly be approximated622
with a power-law as dN(m)∝m−sdm, where s∼2.34 (see Whipple, 1967;623
Grun et al., 1985) is referred to as mass index of the distribution. Since m∝r3,624
20
then dN(r)∝r−3s+2dr ≈r−5dr. Thus, the needed weighting to correct for the625
meteors’ size distribution is Wr≈r−3s+3 ≈r−4. Finally, the total weighting626
that is needed to be applied to the meteors, in order to account for a realistic627
meteor number distribution, will be the product of particles’ perihelion distance628
at time of ejection and particle size distribution, namely Wtot =WsWr.629
4. Results630
In this section we present the results of the simulated meteoroid streams of631
both parent candidates, 96P and P/1999 J6, and compare the characteristics of632
their resulting showers with wide rage of meteor observations e.g., radar (CMOR633
and SAAMER), optical (CAMS) and visual (IMO) surveys. We first examine634
the simulation-observation fits for each individual meteor shower, produced by635
each individual parent candidate and then provide a qualitative comparison of636
their combined contribution to the common showers.637
For the sake of brevity, we present results for only one clone for each parent638
body, which produces the best fit in our simulations. Moreover, we show the639
results of one single initial meteoroid ejection onset time which yields a best640
match. However, snapshots of the fits for every 1000 years, between 20000 BC641
and the present, are presented in the on-line Supplementary Material (SM). All642
our results are presented only for meteoroids that approach the Earth’s orbit643
within 0.01 AU i.e., for meteoroids considered to produce meteors.644
The width of the activity profile is a rough proxy as to the age of a meteor645
shower. We use that information and attempt to simultaneously fit the observed646
widths and peak location of all resulting showers, from each parent body, in647
order to obtain a self-consistent scenario of the age and formation mechanism648
of the meteoroid complex of 96P.649
Finally, we omit the results for the Arietids that were investigated in a650
previous work (Abedin et al., 2017). However, in Sec. 5 we provide a brief651
discussion as to how the results of that work fit in the context of the present652
study.653
4.1. The simulated meteor showers of parent candidate - 96P/Machholz654
Assuming that 20000 BC is the initial meteoroid ejection onset time, the655
longitude of the ascending node and argument of perihelion, of the orbit of 96P,656
will complete approximately 2.5 Kozai circulation cycles, causing the ejected657
meteoroids to intersect the Earth’s orbit at 8 different locations (cf. Fig. 1658
in Sec. 2). That results in 8 different meteor showers to be detected on the659
Earth, as originally suggested by Babadzhanov and Obrubov (1992). Figure 6660
shows the simulated shower radiants. Four of these showers, QUA, ARI, SDA661
and NDA were identified by Babadzhanov and Obrubov (1992) and are well662
known. The remaining four showers, which we call “filaments”, have relatively663
recently been identified as showers. The Quadrantids and filament 1 are part664
of the northern toroidal source (Brown et al., 2010; Jenniskens et al., 2016),665
whereas filament 2 is the southern branch of the ARI and contributes to the666
21
hellion sporadic source (Brown et al., 2008). The SDA and NDA are part of the667
anti-hellion sporadic source (e.g., Brown et al., 2010; Jenniskens et al., 2016),668
while filaments 3 and 4 are found in the southern toroidal source (Pokorn´y et al.,669
2017).670
−60◦
−30◦
0◦
+30◦
+60◦
ARI
fil.2
NDA
SDA
QUA fil.1
fil.3 fil.4
−60◦
−30◦
0◦
+30◦
+60◦
ARI
fil.2
NDA
SDA
QUA fil.1
fil.3 fil.4
90◦0◦270◦180◦90◦
λ−λ, (deg)
0.15
0.30
0.45
0.60
0.75
0.90
q, (AU)
−18000
−15000
−12000
−9000
−6000
−3000
0
Eject. Epoch, (AD)
Figure 6: Resulting radiant distribution of meteoroids ejected from a single clone of comet
96P with meteoroid ejection onset time 20000 BC. The radiants in top panel are color coded
in terms of meteoroids’ present perihelion distance, and as a function of meteoroid ejection
epoch (lower panel).
An interesting feature is the clear correlation between the perihelion distance671
and the showers’ radiants (Fig. 6). The toroidal showers have perihelion close to672
1 AU, and the intersection with the Earth’s orbit occurs close to that point. The673
ecliptic showers, on the other hand, are in a sunskirting state approaching the674
Sun as close as 0.025 AU or slightly farther than 5R. Figure 6 shows that there675
22
is no strong correlation between the showers’ radiants and the meteoroid ejection676
epoch, though it is evident that cores of some of the showers are dominated by677
younger particles.678
4.1.1. The Quadrantids (QUA)679
In Abedin et al. (2015) we investigated the Quadrantid meteoroid stream.680
We demonstrated that the age of the central part of the stream is only 200 years681
old and is associated with asteroid 2003 EH1. We also showed that the wings of682
the activity profile must be much older and are associated with comet 96P. These683
results had been suggested by several previous studies (e.g., Jenniskens, 2004;684
Wiegert and Brown, 2005; Nesluˇsan et al., 2013a). However, in the current work685
we will mainly concern ourselves with the broader (long-lasting) component of686
the QUA, associated with 96P.687
Fig. 7 shows the simulated weighted activity profile of the QUA, assuming688
meteoroid ejection from comet 96P with initial onset epoch in 10000 BC. The689
location of the peak of the activity profile produced a good match with the690
CMOR and IMO visual observations, though the simulated Full Width of Half691
Maximum FWHM ≈6 days was significantly wider. Figure 8 shows the sim-692
ulated distribution of meteoroids, presently reaching the Earth, as a function693
of their ejection epoch and perihelion distance at that epoch. The perihelion694
distance of 96P was low between 7000 BC and 5000 BC, so meteoroids released695
within that time frame are weighted more, which is the reason for the presently696
wider FWHM. The poor match between the simulated and observed peak of the697
QUA is not surprising, as the contribution of asteroid 2003 EH1is not consid-698
ered here, whose ejecta were shown to have dominated the core of the stream699
(Abedin et al., 2015). That results in a very narrow peak activity consisting of700
relatively large meteoroids, while the extended moderate activity is associated701
with 96P.702
Our interest here is in the wings of the activity profile which produce a703
relatively good match to the CMOR observations. Brown et al. (2010) argued704
that QUA show a significant low level activity in the range 232◦< λ<270◦,705
which was also predicted by simulations. However, we find that the long-lived706
activity identified by Brown et al. (2010), as part of the QUA, may be a results707
from two weak nearby showers that peak in the range 232◦< λ<260◦and708
partially overlap with the wings of the QUA (see Sec. 4.1.4).709
23
275 280 285 290 295 300
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
10000BC
r= 0.947
Figure 7: Simulated, weighted and normalized activity profile (red histogram) of the QUA,
originating from 96P/Machholz with meteoroid ejection onset in 10000 BC. Superimposed are
the observed normalized relative activity profiles by CMOR (grey histogram) and IMO visual
observations (black circles). The quantity rdenotes the sum of the residuals of the fit between
the theoretical and CMOR profile.
270 276 282 288 294 300
λ, (deg)
−1.2
−1.0
−0.8
−0.6
−0.4
−0.2
0.0
0.2
Ejection epoch (- = BC, + = AD)
×104
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
q, (AU)
Figure 8: Solar longitude distribution of QUAs as a function of meteoroid ejection epoch, from
comet 96P/Machholz assuming meteoroid ejection onset in 10000 BC. Individual meteoroids
are color coded in terms of their perihelion distance at time of ejection.
24
The simulated radiant drift of the QUA is presented in Fig. 9, superimposed710
over the measurements by CMOR. The simulated mean radiant position at the711
peak activity λ= 283.5◦was λ−λ= 276.4◦±3.9◦and b= 63.8◦±0.9◦,712
which translates in a mean difference with the CMOR radiant of approximately713
0.8 degrees. Our simulations indicate that the QUA stream seems to be mainly714
dominated by relatively old ejecta (prior to 3000 BC) (see Fig. 8) and mostly715
comprised of small βmeteoroids. The reason for that may be the 2:1 mean-716
motion resonance with Jupiter (e.g., Hughes et al., 1981; Froeschle and Scholl,717
1986; Gonczi et al., 1992; Wiegert and Brown, 2005), which has perhaps scat-718
tered away most of the smaller component of the stream, preferentially leaving719
larger meteoroids. We note that the mean semi-major axis of the stream places720
it just outside of the 2:1 mean-motion resonance (Froeschle and Scholl, 1986;721
Wiegert and Brown, 2005). Also, solar radiation pressure increases the size of722
the orbits of smaller meteoroids. This affects the location of mean-motion res-723
onances, and may even bring them to Jupiter-intersecting orbits, resulting in724
scattering.725
25
Figure 9: Simulated sun-centered radiant drift of QUA, with assumed meteoroid ejection onset
in 10000 BC from comet 96P. The color coding is in terms of meteoroid size. Superimposed
is the observed radiant drift by CMOR (grey squares).
Figure 10 shows the distribution of the orbital elements of the QUA, assum-726
ing meteoroid ejection onset circa 10000 BC from comet 96P, as a function of the727
solar longitude λ. The simulated orbital elements yielded a good match to the728
measurements by CMOR and CAMS, even though the contribution of asteroid729
2003 EH1has been omitted here. The fit of our simulations to the observations,730
suggest that the wings of the QUA can be explained by a continuous cometary731
26
1.6
2.4
3.2
4.0
a, (AU)
0.5
0.6
0.7
0.8
0.9
1.0
e
60
64
68
72
76
80
i, (deg)
160
168
176
184
192
ω, (deg)
264 272 280 288 296 304
λ, (deg)
0.94
0.96
0.98
1.00
1.02
1.04
q, (AU)
264 272 280 288 296 304
λ, (deg)
34
36
38
40
42
44
Vg, (km/s)
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
Figure 10: Simulated distribution of the orbital elements of the QUA (color dots) for assumed
meteoroid ejection onset epoch in 10000 BC from comet 96P. The color coding is in terms
of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed are the observed
distributions by CAMS (open squares) and CMOR (grey triangles).
activity of 96P over the last 12000 years, which renders the current age estimate732
significantly higher than previous estimates of 2200 - 8000 years (Gonczi et al.,733
1992; Jones and Jones, 1993; Williams and Wu, 1993; Nesluˇsan et al., 2013b).734
4.1.2. The Southern δ-Aquariids (SDA)735
The simulated activity profile of the SDAs originating from 96P and assum-736
ing a meteoroid ejection onset time in 17000 BC, is presented in Fig. 11 and737
compared to the observed activity profiles by CMOR and IMO. We recall that738
we show the simulated resulting shower characteristics only for meteoroid ejec-739
tion epoch, that produces the best match (see Sec.4). Older or earlier ejecta740
produce poorer fits to the observations. Figure 12 shows the nodal longitude741
of meteoroids, presently approaching the Earth’s orbit within 0.01 AU, as a742
function of their ejection epoch and perihelion distance at the time of ejection.743
It is evident that meteoroids, primarily contributing to the peak of the profile744
are those ejected circa 2000 BC and 6000 BC. Particles, older than 10000 BC745
27
contribute mainly to the wings of the profile.746
Overall, the peak location and the width of the wings of the activity profile747
yielded a good match to the observation. The FWHM is somewhat narrower748
than observed but significantly improves when the contribution of comet P/1999749
J6 is added (Sec. 4.2.1). The sum of the residuals begin to deteriorate for parti-750
cles released after 17000 BC, resulting in a too narrow profile, inconsistent with751
the observations. Conversely, ejections older than 17000 BC produce activity of752
longer duration than found from observations.753
100 110 120 130 140 150 160 170
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
17000BC
r= 0.751
Figure 11: Simulated, weighted and normalized activity profile (red histogram) of the SDA,
originating from 96P/Machholz with meteoroid ejection onset in 17000 BC. Superimposed are
the observed normalized relative activity profiles by CMOR (grey histogram) and IMO visual
observations (black circles). Details similar to Fig. 7.
28
100 120 140 160
λ, (deg)
−2.0
−1.5
−1.0
−0.5
0.0
0.5
Ejection epoch (- = BC, + = AD)
×104
0.15
0.30
0.45
0.60
0.75
0.90
1.05
q, (AU)
Figure 12: Solar longitude distribution of SDA as a function of meteoroid ejection epoch from
comet 96P/Machholz assuming meteoroid ejection onset in 17000 BC. Individual meteoroids
are color coded in terms of their perihelion distance at time of ejection.
The predicted mean radiant position of the SDA at the simulated peak754
activity λ= 125◦was λ−λ= 208.8◦±0.5◦and b=−6.9◦±0.6◦. That results755
in a mean radiant difference of 1.2 degrees compared to CMOR observations.756
It is worth noting that the CMOR observed radiant has a significant spread as757
well (of order 2-3 degrees) due to measurement uncertainties.758
The simulated radiant drift is presented in Fig. 13. It shows a significant759
spread of ∆(λ−λ)≈15◦, along the ecliptic, but only a moderate dispersal760
in ecliptic latitude b. In contrast, the CMOR observations measure a nearly761
constant bfor 140◦< λ<165◦, which was not reproduced by our simulations.762
A possible reason for that may be that there is another body (or bodies) that763
may be contributing to the SDAs that has not been accounted for in the current764
study. In fact, beside comet 96P and P/1999 J6, Nesluˇsan et al. (2013a) showed765
that asteroid 2003 EH1also contributes to the SDAs. Nevertheless, meteoroid766
ejections from 96P, circa, 17000 BC produce a good match to the observed767
characteristics of the SDAs, in particular the duration of the shower activity.768
29
Figure 13: Simulated sun-centered radiant drift of SDA, with assumed meteoroid ejection onset
in 17000 BC from comet 96P. The color coding is in terms of meteoroid size. Superimposed
is the observed radiant drift by CMOR (grey squares).
Figure 14 shows the simulated distribution of the orbital elements of the769
SDAs as a function of solar longitude, for meteoroid ejection onset in 17000 BC.770
30
The theoretical values are compared against the observations by the CMOR771
and CAMS meteor surveys. There has been a long-standing discrepancy of the772
meteoroids’ calculated orbital semi-major axis and geocentric speeds derived773
from optical and radar surveys (Jenniskens et al., 2012). It is evident that the774
meteoroids’ semi-major axes deduced from radar measurements are systemat-775
ically lower than the optical measurements. Sometimes, these differences are776
larger than the scatter of individual meteoroids. Jenniskens et al. (2012) sug-777
gested that the discrepancy is likely due to improper account for atmospheric778
deceleration of radar size particles. Apart from these discrepancies, the rest of779
the simulated orbital elements produced a relatively good match to both radar780
and optical measurements.781
1.6
2.4
3.2
4.0
a, (AU)
0.88
0.92
0.96
1.00
e
0
10
20
30
40
50
i, (deg)
130
140
150
160
170
ω, (deg)
105 120 135 150 165 180
λ, (deg)
0.00
0.05
0.10
0.15
0.20
0.25
q, (AU)
105 120 135 150 165 180
λ, (deg)
32.5
35.0
37.5
40.0
42.5
45.0
Vg, (km/s)
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
Figure 14: Simulated distribution of the orbital elements of the SDAs (color dots) for assumed
meteoroid ejection onset epoch in 17000 BC, from comet 96P. The color coding is in terms
of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed are the observed
mean values of the orbital elements in each bin, respectively by CAMS (open squares) and
CMOR (grey triangles). The error bars correspond to 1σuncertainty.
4.1.3. The Northern δ-Aquariids (NDA)782
The NDAs are the northern branch of the SDAs and are also found in the783
anti-hellion sporadic source. The simulated activity profile of the NDAs is pre-784
31
sented in Fig. 15 for meteoroid ejection onset time in 16000 BC, and compared785
to observed ones by CMOR and IMO. Figure 16 shows which particles have been786
ejected at lower perihelion distances and at what epoch, so those meteoroids will787
receive a larger weights (Sec 3.4.5 and Sec. 3.4.6). Our simulations show that788
the bulk of the meteoroids contributing to the NDAs have been released prior789
to 10000 BC and the resulting FWHM of the activity profile is wider, compared790
to the SDAs for example, mainly due to the ejections between 10000 BC and791
14000 BC.792
Figure 15 shows that the IMO visual observations are rather scattered, with-793
out a clear peak. That is mainly due to the weak nature of the NDAs and794
preferential detection of only the larger meteoroids by visual observations. In795
contrast, the radar measurements yielded a better defined overall profile, though796
also without a clearly distinct peak. Instead, the CMOR profile shows an al-797
most constant activity in the range 130◦< λ<145◦with a local maximum798
around λ=137◦. In comparison, our simulated profile yielded a slightly better799
defined shape and peak, though the latter seems to occur near λ=140◦. Over-800
all, the simulated width of the activity profile produced a good fit to the CMOR801
data. There may be other bodies (not included in this study) also contributing802
to the NDAs. Nonetheless, our analysis of the fit between the theoretical and803
observed activity profiles suggest that the shower is much older than the 2000804
years previously suggested by Sekanina and Chodas (2005).805
32
120 130 140 150 160 170
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
16000BC
r= 0.951
Figure 15: Simulated, weighted and normalized activity profile (red histogram) of the NDA,
originating from 96P/Machholz with meteoroid ejection onset in 16000 BC. Superimposed are
the observed normalized relative activity profiles by CMOR (grey histogram) and IMO visual
observations (black circles). Details similar to Fig. 7.
33
120 130 140 150 160 170
λ, (deg)
−1.8
−1.6
−1.4
−1.2
−1.0
−0.8
−0.6
−0.4
−0.2
Ejection epoch (- = BC, + = AD)
×104
0.15
0.30
0.45
0.60
0.75
0.90
1.05
q, (AU)
Figure 16: Solar longitude distribution of NDA as a function of meteoroid ejection epoch,
from comet 96P/Machholz. Individual meteoroids are color coded in terms of their perihelion
distance at time of ejection.
The simulated mean radiant location at λ= 140◦is λ−λ= 206.0◦±1.4◦
806
and b= 6.7◦±0.4◦, with a difference of 2.5 degrees from the CMOR measured807
mean radiant (see Tab. 1 in Sec. 2 for details). The simulated radiant drift is808
presented in Fig. 17 and is compared to the CMOR observations. The simulation809
yielded satisfactory results, given the uncertainties and the assumptions used810
in the radiant computation. CMOR measures a substantial drift of almost811
∆(λ−λ) = 10◦along the ecliptic but almost none along the ecliptic latitude812
b. Our simulations produced a poorer fit to the drift along b(see Fig. 17).813
34
Figure 17: Simulated sun-centered radiant drift of NDA, with assumed meteoroid ejection on-
set in 16000 BC from comet 96P. The color coding is in terms of meteoroid size. Superimposed
is the observed radiant drift by CMOR (grey squares).
The simulated distribution of the orbital elements of the meteoroids, ap-814
proaching the Earth within 0.01 AU, is presented in Fig. 18 and compared with815
optical and radar observations by CAMS and CMOR, respectively. Similar816
to previous cases, there is an obvious discrepancy between the simulated and817
measured semi-major axes and meteoroids’ geocentric speeds. Our simulations818
predict a mean semi-major axis of a≈3 AU, whereas the radar and CAMS has819
35
measured a systematically lower values of a≈1.8 AU. For other showers that820
we have examined, the optical measurements show larger values for a, though821
in this case they seem to be in a good agreement with radar data. However,822
the semi-major axes measured by CAMS show a significant scatter prior to the823
peak activity , a dispersion comparable to the error bars due to small num-824
ber statistics. Furthermore, the CAMS measurements are consistent with the825
semi-major axes calculated by CMOR near and after the peak. We note that,826
similar to visual observations, video and TV observations are biased towards827
larger (millimeter) and faster meteoroids, though the sensitivity threshold is828
much higher than visual observations. In contrast, aside from the capability of829
detecting smaller and slower meteors, the radar detections are not limited by830
the weather conditions and daylight. Thus, it is not unreasonable to expected831
the CMOR data to be more uniform timewise than the CAMS data.832
1.6
2.4
3.2
4.0
a, (AU)
0.88
0.92
0.96
1.00
e
0
8
16
24
32
40
i, (deg)
260
280
300
320
340
360
ω, (deg)
120 135 150 165
λ, (deg)
0.0
0.2
0.4
0.6
q, (AU)
120 135 150 165
λ, (deg)
24
28
32
36
40
44
Vg, (km/s)
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
Figure 18: Simulated distribution of the orbital elements of the NDAs (color dots) for assumed
meteoroid ejection onset epoch in 16000 BC, from comet 96P. The color coding is in terms
of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed are the observed
distributions by CAMS (open squares) and CMOR (black triangles).
36
4.1.4. Filament 1833
Our numerical simulations from 96P predicted a meteor shower in the north834
toroidal source with radiant location between 210◦<(λ−λ)<270◦and 55◦<835
b < 70◦with activity period between 220◦< λ<270◦. Using a 3D-Wavelet836
search, described in Sec. 2 we have identified two weak showers in the CMOR837
data, that overlap in time (Fig. 6) and also simultaneously matched, within838
the uncertainty, the QUA shower. These showers are the November ι-Draconids839
(NID) and the December α-Draconids (DAD), being identified as separate in the840
IAU MDC. The simulated activity profile of this filament is presented in Fig. 19,841
and compared to the CMOR observations. Our simulations suggest that if this842
filament is considered as a single shower, then its activity steadily increases843
reaching a maximum activity near λ= 260◦and then suddenly decreases844
to the sporadic background activity and merges with QUAs. However, if the845
filament indeed consists of two weak nearby showers, their separation is not846
resolved by the wavelet search, similar to the result reported by Nesluˇsan et al.847
(2013b). According to Brown et al. (2010), the NIDs are active from 221◦<848
λ<267◦with maximum activity near λ= 241◦, whereas the CAMS data849
sets the activity period 239◦< λ<267◦with a peak activity at λ= 242◦
850
(Jenniskens et al., 2016). In contrast, the CAMS measured activity period851
of the DADs is 239◦< λ<262◦with a maximum activity at λ= 256◦
852
(Jenniskens et al., 2016). Evidently, the NID and DAD peak at the same time,853
both eventually merging with early QUA activity. We call these two showers854
- filament 1. The best match between the CMOR-derived activity profile of855
filament 1 and our simulations was obtained assuming meteoroid ejection onset856
time circa 19000 BC, from comet 96P. Earlier ejections resulted in a too narrow857
profile and low activity, inconsistent with the CMOR-derived profile. In fact858
the youngest particles that presently reach the Earth must have been released859
around 3000 BC (see Fig. 20).860
37
210 220 230 240 250 260 270 280
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
19000BC
r= 1.051
Figure 19: Simulated, weighted and normalized activity profile (red histogram) of filament 1,
originating from 96P/Machholz with meteoroid ejection onset in 19000 BC. Superimposed is
the observed normalized relative activity profiles by CMOR (grey histogram). See Fig. 7 for
details.
38
210 225 240 255 270
λ, (deg)
−2.0
−1.8
−1.6
−1.4
−1.2
−1.0
−0.8
−0.6
−0.4
−0.2
Ejection epoch (- = BC, + = AD)
×104
0.15
0.30
0.45
0.60
0.75
0.90
1.05
1.20
q, (AU)
Figure 20: Solar longitude distribution of filament 1 as a function of meteoroid ejection epoch,
from comet 96P/Machholz. Individual meteoroids are color coded in terms of their perihelion
distance at time of ejection.
Our calculated mean radiant location at the peak activity of λ= 256◦was861
λ−λ= 259.2◦±18.9◦and b= 66.7◦±3.1◦. That peak location corresponds to862
the maximum activity time of the DAD (Jenniskens et al., 2016), and the com-863
parison with the CAMS radiant results in a mean difference of about 11 degrees864
(Sec. 2, Tab. 1). That is clearly a poor match with the observations. However,865
if we calculate the radiant at the peak time of the NID (λ= 242◦), then the866
resulting mean radiant is λ−λ= 267.2◦±8.2◦and b= 64.1◦±0.3◦, with867
a mean difference with the CMOR-derived radiant of 2.6 degrees. The overall868
NID simulated radiant position yielded a better fit to the observations, while869
the DAD demonstrated a large radiant dispersion which results in a difference870
of almost 20 degrees with the mean CAMS radiant. However, given the simu-871
lation uncertainties and the observational resolution the NID and DAD appear872
as a single weak and diffuse shower. In fact, these radiants are quite diffuse in873
the radar measurements as well. However, we note that the 3D wavelet search874
applies a speed and radiant probe size, as well as an activity threshold (3σabove875
the median sporadic background), used to isolate the radiants. That, along with876
the weak nature are possible reasons of the inseparability of the two showers,877
or the NID and DAD are indeed a single continuous shower.878
The simulated radiant drift match (Fig. 21) was also poor, where observa-879
39
tions show almost no drift while our simulations predicted a drift of almost880
∆(λ−λ)≈80◦and ∆ b≈15◦. If our simulations represent the past evolu-881
tion of the complex, its nature is even more complicated than initially thought,882
where 96P maybe contributes to a few weak nearby showers as well, essentially883
rendering them as a continuous complex of meteoroids whose radiant separation884
is virtually impossible.885
Figure 21: Simulated sun-centered radiant drift of filament 1, with assumed meteoroid ejec-
tion onset in 19000 BC from comet 96P. The color coding is in terms of meteoroid size.
Superimposed is the observed radiant drift by CMOR (grey squares).
Figure 22 shows the simulated distribution of the orbital elements of mete-886
oroids, presently reaching the Earth, as a function of the solar longitude. In887
40
addition to the recurring issue whereby CMOR measured speeds tend to pro-888
duce smaller semi-major axis than the simulations predict, the overall fit to the889
measured orbital elements was poor. Our simulations predicted a greater scat-890
ter in the geocentric speeds and most of the orbital elements between individual891
meteoroids. The inclination and the argument of perihelion showed a disper-892
sion of almost 20 and 15 degrees, respectively while the theoretical eccentricity893
was overestimated by approximately 0.15. The poor match of our simulations894
with the observations may be suggests that there is another more dominant par-895
ent/parents contributing to filament 1 which was not considered in this work.896
Conversely, if our simulations represent the past evolution of the 96P complex,897
that may imply that 96P contributes to a few other meteor showers in the north898
toroidal source.899
1.6
2.4
3.2
4.0
a, (AU)
0.30
0.45
0.60
0.75
0.90
e
40
48
56
64
72
80
i, (deg)
165
180
195
210
ω, (deg)
210 225 240 255 270 285
λ, (deg)
0.92
0.96
1.00
1.04
q, (AU)
210 225 240 255 270 285
λ, (deg)
28
32
36
40
44
48
Vg, (km/s)
β=FR/FG
0.4
0.8
1.2
1.6
β=FR/FG
×10−3
β=FR/FG
0.4
0.8
1.2
1.6
β=FR/FG
×10−3
β=FR/FG
0.4
0.8
1.2
1.6
β=FR/FG
×10−3
Figure 22: Simulated distribution of the orbital elements of the filament 1 (color dots) for
assumed meteoroid ejection onset epoch in 19000 BC from comet 96P. The color coding is
in terms of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed are the
observed distributions by CAMS (open squares) and CMOR (grey triangles).
4.1.5. Filament 2900
Filament 2 in our simulations is predicted to be a meteor shower with radiant901
location between 325◦<(λ−λ)<340◦and −10◦<b<−4◦(see Fig. 6),902
located south of the well known ARI. Using a 3D wavelet search in the CMOR903
41
database, we established that filament 2 exists and has an activity profile and904
radiant position resembling the daytime λ-Taurids (DLTs) (Brown et al., 2008,905
2010). Unlike filament 1, the DLTs appear to be stronger and well defined.906
Figure 23 shows the simulated activity profile, compared to radar observations907
by CMOR. The simulated maximum activity occurs at λ= 82.5◦, while CMOR908
observations measure a peak activity at λ= 82.5◦. We note that, to our best909
knowledge at the time of preparation of this work, there were no reported or910
available optical observations of the DLT, most likely due to their daytime911
nature and significantly lower activity compared to the ARI.912
Investigation of various meteoroid ejection onset times yielded a best match913
between the theoretical and observed shapes of the activity profiles, assuming914
96P has been captured in a short period orbit circa 20000 BC. However, our915
residual analysis of the shape of the profiles did not converge to a minimum916
value, due to our limited simulations time window of 22000 years. That might917
indicate that the DLTs are even older, or that another body contributes to918
some portion of the activity profile. We note that there are a few degrees919
discrepancy between the observed and simulated extent of the wings of the920
activity profile, likely due to the activity level cutoff threshold of 3σimposed by921
our 3D wavelet search (see Sec. 2). Furthermore, the FWHM of the simulated922
profile was somewhat narrower compared to the CMOR profile, which leads to923
hypothesize that perhaps there may be another body or bodies that may be924
contributing to the stream, though 96P seems to be the dominant parent.925
42
60 65 70 75 80 85 90 95 100 105
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
20000BC
r= 1.045
Figure 23: Simulated, weighted and normalized activity profile (red histogram) of filament 2,
originating from 96P/Machholz with meteoroid ejection onset in 20000 BC. Superimposed are
the observed normalized relative activity profiles by CMOR (grey histogram).
43
60 75 90 105
λ, (deg)
−2.5
−2.0
−1.5
−1.0
−0.5
0.0
0.5
Ejection epoch (- = BC, + = AD)
×104
0.15
0.30
0.45
0.60
0.75
0.90
1.05
1.20
1.35
q, (AU)
Figure 24: Solar longitude distribution of filament 2 as a function of meteoroid ejection epoch,
from comet 96P/Machholz. Individual meteoroids are color coded in terms of their perihelion
distance at time of ejection.
The simulated mean radiant location at λ= 82.5◦was λ−λ= 333.4◦±926
1.3◦and b=−6.5◦±0.7◦. That corresponds to a mean difference of 2.8 degrees927
with the CMOR measured mean radiant (see Tab. 1 in Sec. 2 for details). Likely,928
the reason for the small difference is a result of the slightly different CMOR-929
derived peak location, as well as the uncertainties in our simulations.930
Figure 25 shows the simulated radiant drift of the DLTs, compared to the931
CMOR observations. The latter suggests a drift along the ecliptic of ∆(λ−λ)≈932
5◦whereas the simulations yielded ∆(λ−λ)≈12◦with slightly larger disper-933
sion. The drift along the ecliptic latitude produced a better match, though the934
individual radiants also demonstrated a moderate scatter. However, these fits935
are relatively good given the long integration timescales and the chaos involved936
in the dynamics.937
44
Figure 25: Simulated sun-centered radiant drift of filament 2, with assumed meteoroid ejec-
tion onset in 20000 BC from comet 96P. The color coding is in terms of meteoroid size.
Superimposed is the observed radiant drift by CMOR (grey squares).
The distribution of the orbital elements of the resulting simulated stream938
are presented in Fig. 26. As in the previous cases, there was a substantial sys-939
45
tematic offset between the simulated and the observed meteoroids’ geocentric940
speeds, orbital semi-major axes and eccentricity. We recall that, unlike the ARI,941
there are no optical detections of the DLTs, and hence no orbital elements for942
comparison. However, apart from the poor fit in semi-major axis and eccentric-943
ity, the match in the angular orbital elements and the perihelion distance yield944
satisfactory results. Figure 26 shows that the simulated width of the shower945
is somewhat wider compared to radar observations. The reason may be that946
within the frames of our simulations, we do not impose an activity level thresh-947
old, whereas in the case of CMOR a shower is defined as activity level greater948
that 3σabove the median value of the sporadic background activity (see Sec. 2).949
The distributions of the orbital elements seem to change linearly during the ac-950
tivity period of the DLTs, where the simulated slope yields a good match to the951
observations.952
1.6
2.4
3.2
4.0
a, (AU)
0.88
0.92
0.96
1.00
e
0
8
16
24
32
40
i, (deg)
192
200
208
216
224
232
ω, (deg)
45 60 75 90 105 120
λ, (deg)
0.00
0.05
0.10
0.15
0.20
0.25
q, (AU)
45 60 75 90 105 120
λ, (deg)
32.5
35.0
37.5
40.0
42.5
45.0
Vg, (km/s)
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
Figure 26: Simulated distribution of the orbital elements of the filament 2 (color dots) for
assumed meteoroid ejection onset epoch in 20000 BC from comet 96P. The color coding is
in terms of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed is the
observed distributions by CMOR (black circles).
46
4.1.6. Filament 3953
Filament 3 (see Fig. 6) is located deep in the southern hemisphere with a954
mean sun-centered radiant location (λ−λ) = 279.3◦±3.1◦and b=−63.3◦±955
1.7◦. Similar to previous filaments, a 3D wavelet search in the SAAMER956
database (Pokorn´y et al., 2017) indicated a radiant location resembling the θ-957
Carinids. The simulated activity profile of the shower is presented in Fig. 27 and958
compared to the SAAMER-derived profile. While the timing of the maximum959
activity was well reproduced, the overall width of the shower profile was not.960
The simulations predict an activity extending 272◦< λ<283◦with the main961
peak activity at λ= 276◦and a secondary maximum near λ= 281◦, the as-962
sociation of which with a separate shower is uncertain. However, we note that963
the available SAAMER observations spans only 3 years and hence the shower964
might not be well defined due to small number statistics. Moreover, likely the965
shower is weak as well, as implied by the simulations (see Fig. 28). However, if966
the activity of the TCD is indeed only 5 days, that may well imply an extended967
activity of a few overlapping showers, a case similar to QUA and filament 1.968
The best match between the predicted and observed activity profiles is ob-969
tained assuming initial meteoroid ejection onset from comet 96P circa 20000 BC.970
However, that epoch is the furthest we went back in our backward simulations.971
In fact, the residuals of the profile fit did not converge and perhaps the TCDs972
may be older than 22000 years. Figure 28 shows that meteoroids ejected after973
15000 BC would result in a weak and scattered activity.974
47
270 272 274 276 278 280 282 284
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
20000BC
r= 1.880
Figure 27: Simulated, weighted and normalized activity profile of filament 3, originating from
96P/Machholz (red histogram) with meteoroid ejection onset in 20000 BC. The black circles
corresponds to the observed normalized activity profile by SAAMER.
48
268 272 276 280 284
λ, (deg)
−2.5
−2.0
−1.5
−1.0
−0.5
0.0
0.5
Ejection epoch (- = BC, + = AD)
×104
0.15
0.30
0.45
0.60
0.75
0.90
1.05
1.20
1.35
q, (AU)
Figure 28: Solar longitude distribution of filament 3 as a function of meteoroid ejection epoch,
from comet 96P/Machholz. Individual meteoroids are color coded in terms of their perihelion
distance at time of ejection.
The simulated mean radiant location at λ= 276◦is λ−λ= 279.1◦±3.0◦
975
and b=−61.6◦±1.9◦. That corresponds to a mean difference of 4 degrees976
with the SAAMER-derived mean radiant (see Tab. 1 in Sec. 2 for compari-977
son with SAAMER radiant), a difference also evident in the simulated radiant978
drift (Fig. 29). Interestingly, the simulated radiant drift shows a large scatter979
between individual meteoroids (∆(λ−λ)≈15◦), while SAAMER measures980
a drift of roughly 4 degrees along the ecliptic and almost none in the ecliptic981
latitude. That large scatter may suggest that 96P contributes to other nearby982
shower/showers, though we did not find a candidate in the SAAMER database.983
Furthermore, the shower consists mainly of old ejecta, a result that is also984
clear from Fig. 28. There is no obvious mass segregation along the radiant,985
though the stream seems to be dominated by relatively larger particles (mil-986
limeter size). Perhaps, similar to the QUA there is a mechanism such as a987
mean-motion resonance with Jupiter which preferentially scatters away smaller988
particles or the action of PR drag has decreased the orbits of small particles, so989
that they do not presently intersect the Earth.990
49
Figure 29: Simulated sun-centered radiant drift of filament 3, with assumed meteoroid ejec-
tion onset in 20000 BC from comet 96P. The color coding is in terms of meteoroid size.
Superimposed is the observed radiant drift by CMOR (grey squares).
The fit to the observed distribution of the orbital elements of TCD is pre-991
sented in Fig. 30. Our simulations predict systematically higher values of the992
orbital semi-major axis a≈3 AU, whereas SAAMER measures a mean value993
of about 2 AU. We note that we did not find optical observations of the TCD,994
50
in the literature, so we can not determine the reliability of our estimations and995
the degree of discrepancy with optical surveys. The simulated orbital eccentric-996
ity is also somewhat higher, though within the measurement uncertainties. A997
close inspection of Fig. 30 reveals a steep drop in all orbital elements except the998
inclination, beyond λ= 276◦, which if real (not due to low meteor number999
statistics) likely suggest of existence of another nearby shower.1000
1.6
2.4
3.2
4.0
a, (AU)
0.3
0.4
0.5
0.6
0.7
0.8
e
65
70
75
80
85
i, (deg)
320
328
336
344
352
360
ω, (deg)
272 276 280 284 288
λ, (deg)
0.925
0.950
0.975
1.000
1.025
1.050
q, (AU)
272 276 280 284 288
λ, (deg)
38
40
42
44
46
48
Vg, (km/s)
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
Figure 30: Simulated distribution of the orbital elements of the filament 3 (color dots) for
assumed meteoroid ejection onset epoch in 20000 BC from comet 96P. The color coding is
in terms of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed is the
observed distributions SAAMER (grey triangles).
4.1.7. Filament 41001
Filament 4, according to our simulation, corresponds to a meteor shower1002
from a mean radiant position (λ−λ) = 260.3◦±2.8◦and b=−62.6◦±1003
1.9◦. A 3D wavelet search (see Sec. 2) in the SAAMER database indicated a1004
radiant location resembling the KVE shower that is found the southern toroidal1005
source. Figure 31 shows the simulated and weighted activity profile of the KVE,1006
compared to SAAMER observations. Interestingly, this activity range is similar1007
to that of filament 3, that was identified as the TCD. In fact, both filaments1008
seem to have approximately the same duration and peak at the same time (see1009
Fig. 27 for comparison), though their mean radiant positions are separated by1010
51
about 20 degrees (see Tab. 1 in Sec. 2).1011
265 270 275 280 285 290 295
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
19000BC
r= 0.719
Figure 31: Simulated, weighted and normalized activity profile (red histogram) of filament
4, originating from 96P/Machholz with meteoroid ejection onset in 19000 BC. Superimposed
are the observed normalized relative activity profiles by SAAMER (grey histogram). The
quantity rdenotes the sum of the residuals of the fit between the theoretical and SAAMER
profile.
The best match between the theoretical and observed profiles is obtained1012
assuming meteoroid ejection onset time circa 19000 BC. The fit is relatively1013
good, though the simulations predict a slightly longer activity of ∆λ≈4 days.1014
Our modelling did not yield a clear peak, though an average maximum seems1015
to be found near λ≈277◦or roughly 1 day later than the observed one.1016
This small discrepancy may be due to uncertainties in our simulations or also1017
may be indicate an older age. Generally, the orbital nodes regress with time1018
for prograde orbits, so an older age may account for the difference in timing1019
between the simulated and observed shower profile. However, the stream can1020
not be younger than 20000 years, as meteoroids ejected prior to 19000 BC result1021
in narrow profile and low activity, inconsistent with the observations (see on-1022
line SM). Furthermore, as seen from Fig. 32, filament 4 seems to be mainly1023
dominated by old ejecta. In fact, the bulk of the particles are released prior to1024
15000 BC, with only a small fraction of recent ejecta (2000 BC). Moreover, old1025
52
particles released circa 13000 BC and 17000 BC, have been ejected from orbits1026
of low perihelion distance, so these particles are weighted more, which results1027
in a relatively wide profile.1028
270 275 280 285 290 295
λ, (deg)
−2.0
−1.5
−1.0
−0.5
0.0
0.5
Ejection epoch (- = BC, + = AD)
×104
0.15
0.30
0.45
0.60
0.75
0.90
1.05
1.20
1.35
q, (AU)
Figure 32: Solar longitude distribution of filament 4 as a function of meteoroid ejection epoch,
from comet 96P/Machholz. Individual meteoroids are color coded in terms of their perihelion
distance at time of ejection.
The simulated radiant drift (Fig. 33) results in a good fit to the SAAMER1029
observations. However, as with previous showers, we do not observe a strong1030
mass segregation along the radiant, though it is evident that the showers is1031
mostly dominated by old ejecta and large particles.1032
53
Figure 33: Simulated sun-centered radiant drift of KVE, with assumed meteoroid ejection on-
set in 19000 BC from comet 96P. The color coding is in terms of meteoroid size. Superimposed
is the observed radiant drift by CMOR (grey squares).
Figure 34 shows the simulated distribution of the orbital elements of the1033
KVE, assuming meteoroid ejection onset time circa 19000 BC. As with the1034
previous showers, there is an obvious systematic shift in the predicted and mea-1035
sured geocentric speeds and thus the orbital semi-major axis and eccentricity,1036
though the angular orbital elements produced a relatively good match. It is also1037
noteworthy the systematic difference in the perihelion distance between the sim-1038
54
ulations and observations, a discrepancy also seen for the filament 3 (TCD) in1039
Sec. 4.1.6 and whose nature is not clearly understood.1040
1.6
2.4
3.2
4.0
a, (AU)
0.30
0.45
0.60
0.75
0.90
e
64
68
72
76
80
84
i, (deg)
0
6
12
18
24
30
ω, (deg)
270 275 280 285 290 295
λ, (deg)
0.94
0.96
0.98
1.00
1.02
1.04
q, (AU)
270 275 280 285 290 295
λ, (deg)
38
40
42
44
46
48
Vg, (km/s)
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
Figure 34: Simulated distribution of the orbital elements of the KVE (color dots) for assumed
meteoroid ejection onset epoch in 19000 BC, from comet 96P. The color coding is in terms
of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed are the observed
distributions SAAMER (black circles).
4.2. The simulated meteor showers of parent candidate - P/1999 J61041
In this section, we present our results of the meteoroid stream simulations,1042
associated with the Marsden group of comets, assuming that P/1999 J6 can1043
be taken as a representative parent body for the group as a whole. Following1044
the scenario suggested by Sekanina and Chodas (2005), wherein a single large1045
comet broke up between 100 AD and 950 AD, and formed the Marsden group1046
of comets and the ARI, SDA, and NDA, we investigate the individual showers1047
that comet P/1999 J6 may produce during its secular evolution. The resulting1048
simulated showers are presented in Fig 35, where the individual showers are1049
investigated below.1050
55
−60◦
−30◦
0◦
+30◦
+60◦
ARI
SDA
fil.1
fil.3 fil.4
−60◦
−30◦
0◦
+30◦
+60◦
ARI
SDA
fil.1
fil.4
fil.3
90◦0◦270◦180◦90◦
λ−λ, (deg)
0.15
0.30
0.45
0.60
0.75
0.90
q, (AU)
250
500
750
1000
1250
1500
1750
Eject. Epoch, (AD)
Figure 35: Resulting radiant distribution of meteoroids ejected from a single clone of comet
P/1999 J6 with meteoroid ejection onset time 100 AD. The radiants in top panel are color
coded in terms of meteoroids’ present perihelion distance, and as a function of meteoroid
ejection speed (lower panel).
56
4.2.1. The Southern δ-Aquariids1051
Figure 36 shows the simulated activity profile of the SDAs, assuming a me-1052
teoroid ejection onset time circa 100 AD, from comet P/1999 J6. The predicted1053
pre- peak portion of the profile and the timing of the peak activity (λ= 123.5)1054
produced a good fit to the observations, though the overall width was too nar-1055
row compared to radar and visual observations. It is evident from Fig. 38 that1056
mostly particles ejected between 700 AD and 1500 AD dominate the peak of the1057
SDAs. However, if the contribution of 96P, assuming meteoroid ejection onset1058
in 17000 BC, is added to the activity profile then the fit to the radar observation1059
is significantly improved (see Fig. 37).1060
100 110 120 130 140 150 160 170
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
100AD
r= 0.824
Figure 36: Simulated, weighted and normalized activity profile (red histogram) of the SDA,
originating from comet P/1999 J6 with meteoroid ejection onset in 100 AD. Superimposed
are the observed normalized relative activity profiles by CMOR (grey histogram) and IMO
visual observations (black circles). The quantity rdenotes the sum of the residuals of the fit
between the theoretical and CMOR profile.
57
100 110 120 130 140 150 160 170
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
r= 0.080
Figure 37: The combined simulated activity profile of the SDA (red histogram), assuming
meteoroid contribution from both, 96P and P/1999 J6. The assumed meteoroid ejection
onset of 96P/Machholz is 17000 BC, and meteoroid ejection onset of P/1999 J6 in 100 AD.
The grey histogram corresponds to the observed activity profile by CMOR, while the circles
are activity measured from visual observations of the IMO.
58
120 135 150 165
λ, (deg)
0
200
400
600
800
1000
1200
1400
1600
Ejection epoch (yr, 0 = 0 BC)
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
q, (AU)
Figure 38: Solar longitude distribution of SDA as a function of meteoroid ejection epoch, from
comet P/1999 J6. Individual meteoroids are color coded in terms of their perihelion distance
at time of ejection.
The simulated mean radiant location at λ= 123.5◦was λ−λ= 209.2◦±1061
0.4◦and b=−4.8◦±0.3◦. Although the simulated radiant was very narrow,1062
overall it was systematically shifted by 3.5 degrees from the CMOR-derived1063
mean radiant (see Tab. 1 in Sec. 2 for comparison). The simulated geocentric1064
radiant drift of the SDA, originating from P/1999 J6 only, is presented in Fig. 39.1065
The fit to the observations was good before λ= 125◦, though beyond that1066
point the simulated drift was higher than the measured one.1067
59
Figure 39: Simulated sun-centered radiant drift of SDA, with assumed meteoroid ejection
onset in 100 AD from comet P/1999 J6. The color coding is in terms of meteoroid size.
Superimposed is the observed radiant drift by CMOR (grey squares).
Figure 40 shows the simulated distribution of the orbital elements of the SDA1068
originating from comet P/1999 J6, assuming meteoroid ejection onset time in1069
100 AD. As with previous showers, there was a systematic difference between1070
60
the theoretical and the radar-derived geocentric speeds of the meteoroids, re-1071
sulting in systematic discrepancy in the semi-major axis. More specifically, in1072
the range 115◦< λ<125◦, where the best match between our simulated and1073
the observed activity profile was observed, our predicted meteoroids’ geocentric1074
speeds were overestimated by ∆Vg≈1.5 km s−1compared to both CMOR1075
and CAMS. However, the theoretical values of the meteoroids’ semi-major axis1076
were within the statistical uncertainty of the values measured by CAMS, though1077
CMOR’s values were underestimated by approximately 1 AU.1078
1.6
2.4
3.2
4.0
a, (AU)
0.88
0.92
0.96
1.00
e
8
16
24
32
40
48
i, (deg)
130
140
150
160
170
ω, (deg)
105 120 135 150 165 180
λ, (deg)
0.00
0.06
0.12
0.18
0.24
0.30
q, (AU)
105 120 135 150 165 180
λ, (deg)
32.5
35.0
37.5
40.0
42.5
45.0
Vg, (km/s)
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
Figure 40: Simulated distribution of the orbital elements of the SDA (color dots) for assumed
meteoroid ejection onset epoch in 100 AD from comet P/1999 J6. The color coding is in terms
of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed are the observed
distributions by CAMS (open squares) and CMOR (grey triangles).
Finally, considering the fit of our simulated activity profile to the observed1079
one, the origin of the SDA as being solely due to ejections from P/1999 J6,1080
between 100 AD and 950 AD, is not supported by our simulations. The resulting1081
shower duration from P/1999 J6 is too short. Hence, we conclude the Marsden1082
group of comets can not alone reproduce the observed profile features of the1083
SDAs. The longer activity of the shower requires inclusion of older particles,1084
consistent with much of the dust being related by 96P. In fact, the most plausible1085
scenario according to our simulations, is that comet 96P was captured into a1086
61
short period orbit circa 17000 BC, and suffered a major breakup in 100 AD,1087
which resulted in the formation of the Marsden group of comets. Comet 96P is1088
the dominant parent of the SDAs, where the Marsden group of comets contribute1089
mainly to the pre- peak portion of the stream.1090
4.2.2. Filament 1 and 31091
According to our simulations, there is a negligible contribution by P/1999 J61092
to filament 1 and filament 3, in the northern and southern toroidal sources re-1093
spectively. Using a 3D wavelet search, filament 1 seems to resemble the NID or1094
DADs as described in Sec. 4.1.4. In contrast, the radiant location of filament 31095
was in the proximity of the TCD (see Sec. 4.1.6). We omit the visual representa-1096
tion of these filaments here due to their low number of particles, in each of these1097
radiants. The radiant of filament 1 consists of 2 particles, whereas 5 meteoroids1098
contributed to filament 3. Perhaps, if our initial meteoroid ejection was earlier1099
than 100 AD, the abundance of the particles in those filaments would be higher1100
but we did not investigate this.1101
4.2.3. Filament 41102
Our numerical simulations indicate that comet P/1999 J6 contributes to the1103
KVE (filament 4 from Sec .4.1.7). The simulated activity profile is presented1104
in Fig. 41. Similar to the SDA, the timing of the shower is reproduced well,1105
while the overall width of the profile is not. The resulting FWHM of the profile1106
corresponds to approximately 2 days, whereas SAAMER measures FWHM ≈1107
10◦. The bulk of the meteoroids are old, in the sense they have been ejected1108
between 100 AD and 1000 AD, but they did not have enough time to spread1109
across the width of the stream (see Fig. 43). It is also evident that meteoroids1110
released after 1000 AD do not presently reach the Earth.1111
Clearly, there is a need for older meteoroid supply or for an additional parent.1112
In Sec. 4.1.7 we showed that the most of the observed characteristics of the KVE1113
can be explained by meteoroid ejection onset time, from 96P after 19000 BC.1114
Indeed, if the latter contribution is added, the overall simulated activity profile1115
produces a better fit to the observations (see Fig. 42). Thus, the observed1116
activity profile is consistent with a capture of 96P into a short period orbit1117
circa 20000 BC, followed by a major fragmentation of the comet near 100 AD,1118
resulting in the formation of the Marsden group of comets. The subsequent1119
independent evolution of the Marsden group of comets have supplied meteoroids1120
mainly to the core of the KVE. We recall that a similar scenario was proposed1121
by Sekanina and Chodas (2005), except that observed features of the activity1122
profile of the KVE can not be explained by a cometary activity of the Marsden1123
group of comets alone over only 2000 years.1124
62
265 270 275 280 285 290 295
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
100AD
r= 1.109
Figure 41: Simulated, weighted and normalized activity profile (red histogram) of filament 4,
originating from comet P/1999 J6 with meteoroid ejection onset in 100 AD. Superimposed is
the observed normalized relative activity profiles by SAAMER (grey histogram). The quantity
rdenotes the sum of the residuals of the fit between the theoretical and SAAMER profile.
63
265 270 275 280 285 290 295
λ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N
r= 0.399
Figure 42: The combined simulated activity profile of the filament 4 (red histogram). The
assumed meteoroid ejection onset of 96P/Machholz is 20000 BC, and meteoroid ejection onset
of P/1999 J6 in 100 AD. The grey histogram corresponds to the activity profile as measured
by SAAMER. The number ”r” is sum of the residuals from the fit.
64
274 275 276 277 278
λ, (deg)
0
200
400
600
800
1000
1200
Ejection epoch (yr), 0 = 0 BC
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
q, (AU)
Figure 43: Solar longitude distribution of filament 4 as a function of meteoroid ejection epoch,
from comet P/1999 J6. Individual meteoroids are color coded in terms of their perihelion
distance at time of ejection.
The simulated sun-centered radiant (Fig. 44) drift yields a poor match to1125
the SAAMER observations. The latter measures only a moderate drift, while1126
the simulations predict a large motion in each dimension, (λ−λ) and b, in1127
the range of the simulated activity. Since, both the predicted and measured1128
drifts intersect, they are only consistent over a short time, corresponding to the1129
narrow peak of the activity profile. That clearly indicates that the Marsden1130
group of comets are not the sole parent of the shower, where our simulations1131
show that the dominant contributor to the shower is comet 96P (see Sec. 4.1.7).1132
65
Figure 44: Simulated sun-centered radiant drift of KVE, with assumed meteoroid ejection
onset in 100 AD from comet P/1999 J6. The color coding is in terms of meteoroid size.
Superimposed is the observed radiant drift by CMOR (grey squares).
Figure 45 shows the predicted distribution of the orbital elements of the KVE1133
across the simulated activity period. Apart from the poor fit to the measured1134
semi-major axis and eccentricity, the simulated angular orbital elements seem1135
to be consistent with observations within a narrow time interval, corresponding1136
to the predicted activity period of the shower, resulting from P/1999 J6. An1137
interesting feature is that the simulated orbital elements split into two groups,1138
a difference that is most noticeable in the (i, λ), (ω, λ), (q, λ) and (Vg, λ)1139
space. The simulations predict meteoroid with orbits that span a wide range1140
66
of orbital elements values within a few days, a feature not supported by the1141
SAAMER observations. The measured orbital elements by SAAMER do predict1142
a drift as a function of the solar longitude, though moderate and more gradual.1143
Due to the poor match of the simulations to the observed shower characteristics1144
of the KVE, the Marsden group of sunskirters do not seem to be the dominant1145
parent of the shower, but may contribute to the core of stream.1146
1.6
2.4
3.2
4.0
a, (AU)
0.30
0.45
0.60
0.75
0.90
e
64
68
72
76
80
84
i, (deg)
−8
0
8
16
24
32
ω, (deg)
272 276 280 284 288
λ, (deg)
0.94
0.96
0.98
1.00
1.02
1.04
q, (AU)
272 276 280 284 288
λ, (deg)
39.0
40.5
42.0
43.5
45.0
46.5
Vg, (km/s)
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
β=FR/FG
0.5
1.0
1.5
2.0
β=FR/FG
×10−3
Figure 45: Simulated distribution of the orbital elements of the KVE (color dots) for assumed
meteoroid ejection onset epoch in 100 AD from comet P/1999 J6. The color coding is in terms
of meteoroids’ β-parameter (or equivalent to meteoroid size). Superimposed is the observed
distributions by SAAMER (black circles).
5. Discussion and Conclusions1147
We performed numerical simulations to investigate the individual meteoroid1148
streams of comets 96P/Machholz and the most prominent member of the Mars-1149
den group of comets, P/1999 J6. Our goal was to obtain a self-consistent sce-1150
nario of the past dynamical evolution of the interplanetary bodies associated1151
with comet 96P, and to determine the parent producing most of the mete-1152
oroids from the associated streams now visible at the Earth. In addition, we1153
also aimed to establish a possible past fragmentation chronology of a single1154
67
large first precursor, presumably giving rise to the Marsden group of sunskirt-1155
ing comets (Sekanina and Chodas, 2005). The relative contribution of each1156
parent to the complex is determined, by simultaneous matching and investiga-1157
tion of the observed characteristics of their resulting showers. As observational1158
shower constraints we used radar, optical and visual activity measurements from1159
CMOR, SAAMER, CAMS and IMO.1160
Our simulations confirm the results of Babadzhanov and Obrubov (1992)1161
and Nesluˇsan et al. (2013b) that within one full Kozai circulation cycle, the as-1162
cending and descending nodes of comet 96P intersect the Earth’s orbit in eight1163
different locations, and thus result in eight different meteor showers. Four of1164
these showers are found in the ecliptic sporadic meteoroid sources and four be-1165
long to the Northern and Southern toroidal sources, respectively. Furthermore,1166
four of these showers are well known, the Quadrantids (QUA), the daytime Ari-1167
etids (ARI), the Southern and Northern δ-Aquariids (SDA and NDA), whereas1168
the remainder four showers are weak and have less well determined characteris-1169
tics. We call these weak showers “filaments”:1170
Filament 1, which was previously identified by Babadzhanov and Obrubov1171
(1992) as the Ursids, is found in the north toroidal source and is likely associated1172
with the “November ι-Draconids (NID)” or with the “December α-Draconids1173
(DAD)”. The two showers peak at the same time and have radiants partially1174
overlapping, so their separation as individual showers was not possible in this1175
work, a similar result initially suggested by Nesluˇsan et al. (2013b). Filament1176
2 resembles the “daytime λ-Taurids (DLT)” that appears to be consistent with1177
the long-sought southern branch of the daytime Arietids. Filament 3 and 41178
likely corresponds to the θ-Carinids (TCD) and κ-Velids (KVE) respectively,1179
found in the southern toroidal source. Similar to filament 1, the TCD and KVE1180
appear to peak at the same time, though their radiant locations are separated1181
by 20 degrees. However, the separation of filaments 3 and 4 is more obvious1182
and they appear to be two distinct showers. We note that the DLT, TCD and1183
the DAD (or NID) were identified by Babadzhanov and Obrubov (1992) as the1184
α-Cetids, Carinids and Ursids, respectively. Among these showers, the most1185
active are the QUA, followed in order of apparent strength by the ARI, SDA,1186
NDA, DLT, KVE, NID or DAD and the TCD.1187
We use the width of the wings and shape of the observed activity profile as a1188
strong proxy as to the age of individual showers to fit to our simulated meteoroid1189
streams. We find that ages of the eight showers, assumed to originate solely from1190
96P, range between 10000 BC and 20000 BC.1191
The best match between the duration of the simulated and observed activity1192
profiles for the QUA is obtained assuming initial meteoroid ejection onset from1193
96P in 10000 BC. We did not attempt to match the narrow or core portion of1194
the shower, which we showed in a previous work (Abedin et al., 2015) to be1195
associated with asteroid 2003 EH1.1196
The simulated width of the ARI requires a meteoroid ejection onset time1197
at least 12000 years ago (Abedin et al., 2017), whereas the bulk of the activity1198
profile of the SDA is reproduced, assuming that 96P has been captured in a1199
short period orbit circa 17000 BC. A similar result is obtained for the NDA,1200
68
with a best fit between the simulated and observed duration of the shower for1201
meteoroid ejection onset time in 17000 BC. The observed widths of the profiles1202
of filament 1, 2, 3 and 4 can only be explained if the comet became active circa1203
19000 BC.1204
Assuming the scenario proposed by Sekanina and Chodas (2005) of formation1205
of the Marsden group of comets, the ARI, SDA and NDA, in a major comet1206
break-up event, between 100 AD and 950 AD, we simulated the possible showers1207
associated with comet P/1999 J6, taking this to be a substitute of the Marsden1208
group of comets as a whole. Our simulations confirm that the Marsden group of1209
comets contribute to the ARI, SDA and three weak filaments (filament 1, 3 and1210
4 associated with 96P), though we find that P/1999 J6 is not the parent of the1211
NDA, in contradiction to previous suggestions (Ohtsuka et al., 2003; Sekanina1212
and Chodas, 2005; Jenniskens, 2006). Furthermore, using a 3D wavelet search1213
in the CMOR and SAAMER database, the three weak filaments are identified1214
as part of the NID or DAD, the TCD and KVE showers, respectively. However,1215
the contribution of the comet to filaments 1 and 3 is extremely low, with only1216
a few particles in our simulations approaching the Earth. Finally, assuming1217
even the earliest fragmentation epoch, 100 AD, as suggested by Sekanina and1218
Chodas (2005), our simulations indicate the Marsden group of comets can not1219
alone explain the observed wide activity profiles of the showers associated with it1220
(ARI, SDA, NDA, KVE, TCD and NID or DAD). There is a need for meteoroids1221
ejection at least a few tens of millenia, in order for the observed width of the1222
activity profiles to be explained.1223
In summary, the bulk of the observed characteristics of the meteor showers,1224
associated with comet 96P, can be explained if the comet has been captured into1225
a short period orbit circa 20000 BC and has been active until the present. Then1226
there is a sufficient time for it to produce most of the features the QUA, ARI,1227
SDA, NDA, DLT, KVE, TCD and the NID or DAD. However, a better match1228
to the activity profiles is produced if we also add the scenario by Sekanina and1229
Chodas (2005), namely brake-up of 96P after 100 AD, which has formed the1230
Marsden group of comets, and perhaps other sungrazing comets. The meteoroid1231
supply from the Marsden group of comets complement the observed features of1232
these showers, though mainly contribute to their peak activity.1233
6. Acknowledgements1234
Funding provided by the Canada Research Chair program, the Natural1235
Sciences and Engineering research council and NASA co-operative agreement1236
NNX15AC94A.1237
The deployment of SAAMER and its remote receiving stations were sup-1238
ported by NSF awards AGS-0634650, AGS-0944104, and AST-0908118 and1239
currently by NASA-Solar System Observation Program. DJ’s participation is1240
currently supported through NASA awards 12-PAST12-0007 and 12-PATM12-1241
0006 and SSO. The authors wish to give special thanks to the EARG personnel1242
for their invaluable assistance with the operation and day-to-day oversight of1243
69
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