11institutetext: Institut de Mécanique Céleste et de Calcul des Éphemerides,
Observatoire de Paris, PSL, 75014, Paris, France 22institutetext: Departmento
de Astronomía, Facultad de Ciencias, Iguá 4225, 11400 Montevideo, Uruguay
33institutetext: Space Science and Technology Centre, Curtin University, GPO
Box U1987, Perth WA 6845, Australia 44institutetext: International Centre for
Radio Astronomy Research, Curtin University, GPO Box U1987, Perth WA 6845,
Australia 55institutetext: Astronomical Institute of the Romanian Academy,
Cutitul de Argint 5, 040557 Bucharest, Romania

# Comparing the dynamics of Jupiter-family Comets and comet-like fireballs
††thanks: The data used in this study is available at
https://doi.org/10.5281/zenodo.10671333

P.M. Shober, E-mail<EMAIL_ADDRESS>G. Tancredi 22 J. Vaubaillon 11
H.A.R. Devillepoix 3344 S. Deam 33 S. Anghel 1155 E.K. Sansom 3344 F. Colas 11
S. Martino 22

(Received February 17, 2024; accepted April 16, 2024)

###### Abstract

Context. Jupiter-family comets (JFCs), which originate from the Kuiper belt
and scattered disk, exhibit low-inclination and chaotic trajectories due to
close encounters with Jupiter. Despite their typically short incursions into
the inner solar system, a notable number of them are on Earth-crossing orbits,
with fireball networks detecting many objects on “JFC-like” ($2<T_{J}<3$)
orbits.

Aims. This investigation aims to examine the orbital dynamics of JFCs and
comet-like fireballs over $10^{4}$ yr timescales, focusing on the trajectories
and stability of these objects in the context of gravitational interactions
within the solar system.

Methods. We employed an extensive fireball dataset from Desert Fireball
Network (DFN), European Fireball Network (EFN), Fireball Recovery and
InterPlanetary Observation Network (FRIPON), and Meteorite Observation and
Recovery Project (MORP), alongside telescopically observed cometary ephemeris
from the NASA HORIZONS database. The study integrates 646 fireball orbits with
661 JFC orbits for a comparative analysis of their orbital stability and
evolution.

Results. The analysis confirms frequent Jupiter encounters among most JFCs,
inducing chaotic orbital behavior with limited predictability and short
Lyapunov lifetimes ($\sim$120 years), underscoring Jupiter’s significant
dynamical influence. In contrast, ”JFC-like” meteoroids detected by fireball
networks largely exhibit dynamics divergent from genuine JFCs, with 79-92% on
“JFC-like” orbits shown not to be prone to frequent Jupiter encounters; in
particular, only 1-5% of all fireballs detected by the four networks exhibit
dynamics similar to that of actual JFCs. In addition, 22% (16 of 72) of near-
Earth JFCs are on highly stable orbits, suggesting a potential main belt
origin for some of the bodies.

Conclusions. This extensive study delineates the stark dynamical contrast
between JFCs and JFC-like meteoroids detected by global fireball networks. The
majority of centimeter- and meter-scale meteoroids on JFC-like orbits exhibit
remarkably stable trajectories, which starkly differ from the chaotic paths of
their km-scale counterparts. Our findings suggest that the JFC-like objects
observed by fireball networks predominantly originate from the outer main
belt, with only a minor fraction being directly attributable to traditional
JFCs.

###### Key Words.:

Comets: general – Meteoroids – Celestial mechanics – Methods: data analysis

##  1 Introduction

Jupiter-family comets (JFCs) are a distinct group of low-inclination
($\lesssim$30∘) comets predominantly originating from the Kuiper belt and
scattered disk, a vast region of icy bodies extending beyond Neptune’s orbit,
where volatile components are retained (Fernández 1980; Boehnhardt 2004;
Duncan & Levison 1997; Duncan et al. 2004). The transformation of these trans-
Neptunian objects into the inner solar system is driven and controlled
completely by a series of chaotic close encounters with Neptune and then
Jupiter, as reflected in the name of the population (Tancredi & Rickman 1992;
Levison & Duncan 1997; Di Sisto et al. 2009; Nesvorný et al. 2017). However,
in the inner solar system, JFCs exhibit short orbital periods, typically less
than 20 years. Previously defined by these shorter orbital periods, it has
since become standard to classify these bodies by their Tisserand’s parameter,
which stays predominantly within the range $2<T_{J}<3$ (Carusi et al. 1985;
Levison & Duncan 1994).

The incursions of JFCs into the inner solar system are infrequent and short-
lived, with only $\sim 30$% of JFCs becoming active and part of the ”visible”
population (i.e., q$<$2.5 au) during their lifetimes (Levison & Duncan 1997).
This specific distance is used as a threshold because it is at this point that
the heating by the Sun becomes significant enough to cause sublimation of
water ice, resulting in observable cometary activity such as the development
of a coma or tail (Duncan et al. 1988; Levison & Duncan 1994). Significantly
fewer make it all the way to a near-Earth orbit, and those that do only spend
a few thousand years normally in the region (Fernández et al. 2002). This is
because the frequent close encounters with Jupiter will quickly remove the
JFCs. As a result, the Lyapunov lifetimes (the inverse of the Lyapunov
characteristic exponent) for these bodies tend to concentrate between 50-150
years, as the encounters with Jupiter make predicting their orbital evolution
impossible on very short timescales (Tancredi 1995, 1998, 2014). The dynamical
lifetime of JFCs is found to be around $1.5\text{\times}{10}^{5}$ yrs,
however, they only typically spend $\sim 10^{3}$ yrs in near-Earth space
(q$<$1.3 au). This implies that of the JFCs that serendipitously end up in
near-Earth space at some point during their lifetime, this phase only accounts
for about 1% of their total dynamical lifetime.

Based on telescopic observations and dynamical modeling, there is a paucity of
JFCs at sub-kilometer scales (Meech et al. 2004; Fernández & Morbidelli 2006;
Nesvorný et al. 2017). This lack of objects at smaller sizes is thought to be
related to the inferred brief physical lifetimes ($10^{3}-10^{4}$ yrs) of JFCs
in the inner solar system (Levison & Duncan 1997; Fernández et al. 2002; Di
Sisto et al. 2009). Due to their low bulk density and high volatile content,
JFCs should fade away more quickly when they are within 2.5 au of the Sun.
Typically, the JFCs lose mass through volatile sublimation and dust
entrainment, with rates of $\sim 10^{1-3}$ kg/s near perihelion, depending on
the active surface area (A’Hearn et al. 1995). However, towards the end of
their physical lifetime, these objects are believed to either go dormant as
they have built up an insulating outer layer of devolatilized material or
(much more likely) fragment and disintegrate (Rickman et al. 1990; Di Sisto et
al. 2009). This fragmentation process is likely why there is a paucity of JFCs
at smaller sizes. However, this material does not simply disappear. Large
amounts of debris are generated from these cometary fracturing and splitting
and are left behind. For example, the Andromedid meteor shower, a currently
weaker shower with outbursts of meteoroids of $\sim 10^{-7}$ kg, is linked to
the short-period comet 3D/Biela. This parent comet is believed to have
completely disintegrated due to a catastrophic splitting event after being
observed to fragment in 1845/1846 and a final observation in 1852 (Wiegert et
al. 2013). Several years later, on November 27, 1872, the debris from this
catastrophic splitting event manifested in a spectacular meteor display
labeled the ”Bielids,” with reports of several thousand meteors per hours
(Hoffleit 1988). The prevalence of JFC fracturing and splitting has been
demonstrated with numerous observations of cometary splitting and fracturing
(Chen & Jewitt 1994; Boehnhardt 2004; Fernández et al. 2005; Fuse et al. 2007;
Fernández 2009; Dones et al. 2015; Li & Jewitt 2015; Graykowski & Jewitt
2019). The debris from the destruction of these JFCs should produce ample
numbers of micron to sub-millimeter meteors on Earth.

The zodiacal cloud (ZC) is a faint, diffuse population of small (a few
micrometers to a few millimeters) interplanetary dust particles, primarily
consisting of material released by comets and asteroid collisions (Gustafson
1994; Nesvorný et al. 2010). The thermal emission and scattered light from the
ZC, aptly called ”zodiacal light,” has been observed for centuries as a faint,
diffuse glow extending around the ecliptic plane of the solar system.
Cassini’s 17th-century study was the first to attribute the zodiacal light to
sunlight reflecting off a disk-shaped interplanetary dust cloud, challenging
the notion of it as an atmospheric phenomenon (Cassini 1685). The structure of
the dust within the ZC was first mapped by the Infrared Astronomical Satellite
(IRAS) (Hauser et al. 1984; Sykes 1988), and has also been detected and
characterized by other interplanetary space missions such as the Cosmic
Background Explorer (COBE), Pioneer 10, AKARI, the Parker Solar Probe (PSP),
and Juno missions (Kelsall et al. 1998; Matsumoto et al. 2018; Szalay et al.
2021; Jorgensen et al. 2021). Dust within the ZC has been linked to both
asteroids and comets based on concentrations in the ecliptic latitudes, which
have been linked to asteroid families (Kehoe et al. 2015) and from narrow
trails of dust associated with comets (Sykes & Walker 1992). However, research
suggests that JFCs contribute significantly more to the ZC, with more than 90%
of the mid-infrared emission in the ZC attributed to dust grains released by
JFCs (Nesvorný et al. 2010). This abundance of mass being contributed to the
ZC from JFCs suggests that 85% of the total mass flux hitting the Earth’s
atmosphere annually ($3\text{\times}{10}^{7}$ kg yr-1) originates from JFCs
(Nesvorný et al. 2010; Plane 2012). However, the mass input required to
maintain the ZC is several times larger than the mass loss from JFCs due to
regular activity due to volatile sublimation. This implies spontaneous
disruptions and splittings of JFCs are contributing the bulk of the mass
within the ZC (Nesvorný et al. 2010; Nesvornỳ et al. 2011; Rigley & Wyatt
2022). This fragmentation and splitting process should occur relatively
frequently (lower limit of 0.01 yr-1), producing enough dust to support the
observed population (Chen & Jewitt 1994).

The Rosetta mission’s observations using its OSIRIS cameras at comet
67P/Churyumov-Gerasimenko revealed the ejection of boulders, alongside smaller
dust particles, challenging our understanding of cometary ejecta (Agarwal et
al. 2016; Ott et al. 2017). The observation and detection of cm to m particles
or aggregates in the inner coma of 67P/Churyumov-Gerasimenko have confirmed
the fact that comets can eject boulders in addition to small dust particles.
However, there is limited information about the nature of these objects,
leaving the question open as to whether they are fluffy aggregates or more
cohesive bodies. This intermediate-size cometary debris being produced could
have significantly short physical lifetimes (Beech & Nikolova 2001; Boehnhardt
2004; Fernández 2009; Jewitt et al. 2016).

The steady-state debiased near-Earth object (NEO) model by Granvik et al.
(2018) predicted that $\sim$10% of the meter-scale NEO population below
diameters of 100 m originate from the JFC population; however, this estimate
decreases to only a maximum of 1.7% if cometary splitting is considered a more
likely end-state (Bottke Jr et al. 2002; Nesvorný et al. 2010, 2023). This
prediction would seem reasonable based on the proportion of fireballs with
JFC-like pre-impact orbits ($2<T_{J}<3$) (Brown et al. 2000; Borovička et al.
2013; Spurny et al. 2013; Madiedo et al. 2014; Trigo-Rodriguez et al. 2019;
Peña-Asensio et al. 2022; Hughes et al. 2022). While cometary fragmentation is
believed to contribute substantial amounts of dust to the ZC (Nesvorný et al.
2010; Rigley & Wyatt 2022), the contribution of more substantial debris,
ranging from centimeters to meters (observable by fireball networks), remains
an open question. In recent studies, alternative approaches to determining the
origins of these meteoroids have also been explored. Notably, Borovička et al.
(2022a) conducted a fragmentation analysis, concluding that the evidence
supports an abundance of weaker cometary debris on JFC-like ($2<T_{J}<3$)
orbits. However, the fragmentation characteristics and meteoroids’ strengths
are difficult to compare as many factors influence the observed atmospheric
fragmentations. While cometary debris are statistically weaker and more
friable, it has also been shown that asteroidal debris can be extremely weak
due to macro-scale features of the sample (cracks, porosity, etc.; Popova et
al. 2011).

The dynamics of the fireball orbits offer a much clearer picture of the
meteoroid source regions because the dominant forces acting on centimeter-to-
meter debris and the kilometer-scale JFCs do not differ significantly on
10,000 yr timescales. Over periods of thousands of years in the inner solar
system, the orbits for both size ranges of objects are primarily perturbed
through close encounters and mean-motion resonances (MMRs); whereas Poynting-
Robertson drag needs to be considered for smaller sub-millimeter debris
(Nesvornỳ et al. 2011). Solar radiation pressure and Yarkovsky-induced drift
are also considerable at these size ranges, however, they are insignificant on
the concerned timescales of $10^{3}-10^{4}$ years. The JFC population has many
close encounters with Jupiter, causing the orbits to rapidly and chaotically
jump in and out of the inner solar system every few thousand years (Tancredi
1995, 1998, 2014). This is in stark contrast with the orbital evolution of
nearly all near-Earth asteroids, which behave predictably on similar periods.
However, there is a tiny fraction of the near-Earth asteroid population that
does exist on similarly chaotic orbits. This group of bodies has been referred
to as the ”asteroid cometary orbit” (ACO) population previously, making up
$<$0.05% of the entire asteroid population and $<$0.1% of the near-Earth
asteroid population (Tancredi 2014). The work of Fernández et al. (2002) and
Fernández et al. (2014) suggests that these ACOs could originate from the
main-belt asteroid population, which has diffused out due to perturbations
from the terrestrial planets. However, further dynamical evolution analysis
needs to be done on this population to discern the prevalence of dormant,
inactive comets.

Thus, to accurately gauge the source of fireballs on JFC-like orbits, whether
it is the MB or the JFC population, an in-depth analysis of the orbital
stability is necessary. Shober et al. (2021) studied the orbital stability of
50 sporadic fireballs detected by the Desert Fireball Network, originating
from JFC-like orbits. The dynamical analysis showed that almost none ($<$6 %)
of the sporadic JFC-like fireballs are dynamically linked to Jupiter. Entirely
all of the sporadic fireballs were interlopers from the main belt. In this
study, we aim to build upon the foundational work established in Shober et al.
(2021) by examining the orbital stability of fireballs and the JFC comet
population more extensively. This direct comparison of the orbital dynamics is
pivotal for a conclusive source region analysis. Our expanded work includes
the examination of 646 fireball orbits and 661 JFC orbits. This massive
comparison of fireball data and the JFC population and their orbital
stabilities on 10,000 yr timescales will provide a clear picture of what is
happening at the centimeter- and meter-size range in this region of the solar
system.

##  2 Materials and methods

###  2.1 Overview

We employed a multifaceted approach to identify the sources of meteoroids and
comets on orbits with Tisserand’s parameters of $2<T_{J}<3$ in near-Earth
space. This research is characterized by its extensive collection of fireball
data from four separate continental-scale fireball observation networks,
combined with the ephemeris data of JFCs. This methodology is notable for its
direct comparison of the dynamics of meteoroid and comet populations within a
single study, which has not been explored in previous research.

Our methods encompass a range of techniques that focus on determining the
source populations of these objects based on their orbits and dynamics. The
scale of data analysis and the direct comparison of meteoroid and comet orbit
dynamics are key aspects that distinguish this study. These elements
contribute to a more comprehensive understanding of these objects in near-
Earth space and provide valuable insights. The methodology comprises the
following steps: 1\. Collection and processing of data on fireballs and
comets. 2\. Identification of fireballs that qualify as asteroids in cometary
orbits (ACOs), using the criterion defined by Tancredi (2014). 3\. Monte Carlo
integration of meteoroid and comet orbits over a span of 10,000 years. 4\.
Estimation of Lyapunov lifetimes for meteoroids and comets. 5\. Calculation of
debiased source regions for Near-Earth Objects (NEOs) of meteoroids and
comets. 6\. Identification of meteorite falls. 7\. Identification of meteor
showers. These enumerated steps underscore our comprehensive approach and
provide a clear summary of our methodologies, contributing to a deeper
understanding of the dynamics of these objects in near-Earth space.

The dynamics of the comets and meteoroids in this study are characterized
based on the 10 kyr simulations, Lyapunov lifetimes, and source region
likelihood based on a debiased NEO model. On the other hand, the meteorite
fall and meteor shower analysis helps us better understand how the dynamics
relate to the populations and what they can tell us about the meteorites we
find on Earth.

###  2.2 Data collection and processing

This study has collected the largest fireball dataset of objects originating
from orbits with a Tisserand’s parameter of $2.0<T_{J}-3\sigma$ and
$3.0>T_{J}+3\sigma$, and has completed a detailed analysis of the stability
and dynamics of this population. The data used here comes from four
continental-scale fireball networks: Desert Fireball Network (DFN), European
Fireball Network (EFN), Fireball Recovery and InterPlanetary Observation
Network (FRIPON), and Meteorite Observation and Recovery Project (MORP). The
data for the DFN and FRIPON were accessed as the authors of this study are
collaborators on the projects. Given the reduced quality of data for less
observed events, only FRIPON fireballs with at least four observations were
considered. In contrast, the data used within this study from the EFN and MORP
were taken from previously published datasets. Except for the MORP network,
all the networks are still active and continually making fireball
observations.

Slight variations existing between the fireball datasets are noted and
discussed within the study (orbits, velocity uncertainties, etc.), however,
the source of these variations is beyond the scope of this individual study.
Ongoing work is being conducted on comparing the data reduction pipelines and
methodologies used by several of the largest meteor physics research groups in
order to ensure accurate interpretations of meteor and fireball data (Shober
et al. 2023).

Figure 1: Semi-major axis (au) versus eccentricity distribution of fireballs
on JFC-like orbits (i.e., $2<T_{J}<3$), where the plot on the right is the
dashed-zone on the left plot. The fireball observations for the DFN (blue
dots), EFN (red diamonds), FRIPON (green triangle), and MORP (black squares)
are shown. The horizontal and vertical bars of the fireball data indicate the
1-$\sigma$ uncertainties in the semi-major axis and eccentricity. In addition,
the 661 JFCs used in this study taken from NASA’s HORIZONS database are also
shown as black crosses. Figure 2: Semi-major axis (au) versus inclination
distribution of fireballs on JFC-like orbits (i.e., $2<T_{J}<3$). The fireball
observations for the DFN (blue), EFN (red), FRIPON (green), and MORP (black)
are shown. In addition, the 661 JFCs used in this study taken from NASA’s
HORIZONS database are also shown as black crosses.

####  2.2.1 DFN

Desert Fireball Network (DFN) is a massive network of cameras covering around
2.5 million km2 of the Australian outback (Bland et al. 2012; Howie et al.
2017a). This is over one-third of the Australian landmass, making the DFN the
largest contiguous photographic fireball network globally. Initiated with a
robust focus on reliability and autonomy, the DFN began assembling its first
digital prototypes in 2013, leading to a final design rolled out in 2014–2015
(Howie et al. 2017a). This expansion resulted in the establishment of
approximately 50 digital fireball stations. Technologically advanced, the DFN
utilizes high-resolution digital single-lens reflex (DSLR) cameras paired with
all-sky fish-eye lenses. This combination allows for long exposure captures,
enhanced by GNSS synchronized liquid crystal shutters, a method proven
instrumental for accurate meteorite fall position determinations (Howie et al.
2017b; Devillepoix et al. 2019). The observatories exhibit a limiting
magnitude of zero, allowing the capture of meteoroids as small as
approximately 5 centimeters while they are still at higher altitudes before
significant atmospheric deceleration occurs. This sensitivity also enables the
observation of the brightest ablation phases of larger, half-meter-sized
meteoroids despite some sensor saturation challenges.

Strategically situated in desert locales, the DFN optimizes the likelihood of
meteorite recovery by being positioned in favorable regions for meteorite
searching. Since its inception, the network and its team have helped lead to
the recovery of 15 meteorites ($\sim$30% of total recovered with orbit
information) (King et al. 2022; Shober et al. 2022; Devillepoix et al. 2022;
Anderson et al. 2022). The DFN has since expanded globally, forming the Global
Fireball Observatory (GFO) (Devillepoix et al. 2020). The
GFO111https://gfo.rocks/ consists of ten partner networks and 18 collaborating
institutions spread over nine countries globally, all using observatories
originally developed by the DFN.

Atmospheric trajectories of fireball events captured by the DFN are determined
by employing a refined straight-line least squares (SLLS) approach and a
velocity profile is extracted using an extended Kalman smoother (Borovicka
1990; Sansom et al. 2015). This methodology accounts for the uncertainties in
both the trajectory and the velocity data, stemming from the observational
errors and the fitting process. The Kalman filter plays a critical role in
managing these uncertainties and helping the uncertainties be realistic. For
calculating pre-entry orbits, the meteoroids’ states are numerically
integrated beyond Earth’s gravitational influence, considering all significant
perturbative effects (Jansen-Sturgeon et al. 2019). A Monte Carlo technique is
applied to estimate the associated orbital uncertainties, which integrates
various initial state samples within the uncertainty bounds at the entry point
of the Earth’s atmosphere (Shober et al. 2019, 2020b).

####  2.2.2 FRIPON

FRIPON222https://www.fripon.org/ is a ground-breaking international initiative
aimed at the meticulous monitoring and recovery of meteoroids and meteorites,
enhancing our understanding of interplanetary matter and the evolution of the
solar system. The FRIPON consortium started in 2015 in France by deploying
fully automated cameras and radio receivers (Colas et al. 2020). In the years
that followed, many neighboring nations joined the consortium, combining the
data from over 15 countries on 4 continents, covering an area of $\sim$2
million km2 with over 250 cameras and 40 radio receivers. The cameras are
wide-angle CCDs recording at 30 frames per second, producing high-time-
resolution data. The detections and underlying data are openly available on
the consortium webpage 333https://fireball.fripon.org. The limiting magnitude
of any single frame is about zero, but longer exposures are taken every 10
minutes to acquire better astrometry and photometry, resulting in a good
signal-to-noise ratio (S/N) up to a stellar magnitude of 6 for dark sites
(Anghel et al. 2019; Jeanne et al. 2019; jeanne2020methode; Colas et al.
2020). FRIPON’s automation facilitates rapid response for meteorite recovery
campaigns, aiming to recover meteorites with final masses estimated at 500
grams or more. Its international expansion and collaboration have further
bolstered the network’s coverage and capabilities, heralding a new era of
meteorite recovery and interplanetary observation. The network and team have
assisted in the tracking and recovery of seven meteorites to date.

The standard data reduction process of FRIPON observations is described in
Jeanne et al. (2019), jeanne2020methode, and Colas et al. (2020). However,
within this study, we decided to process the FRIPON observations using the
Monte Carlo triangulation approach described by Vida et al. (2020). The method
begins with an initial trajectory estimation using intersection points (IP)
and lines of sight (LoS) methods to fit observed meteor paths, using the
angular residuals as a direct measure of uncertainty (Gural 2012; Weryk &
Brown 2012). These residuals inform the generation of Monte Carlo simulations,
wherein Gaussian noise is added to the observations, and the trajectory is
recalculated to produce a variety of geometrically plausible solutions within
the bounds of measurement uncertainty. A key advancement of this method is the
selection of the best solution based on the consistency of observed meteor
dynamics across different stations, rather than relying solely on a geometric
fit. The open-source Python code444https://github.com/wmpg/WesternMeteorPyLib
for the simulation and solver is available for public use, which increases the
transparency and reproducibility of the method.

####  2.2.3 EFN

Established in 1963, EFN has since evolved tremendously over the decades,
adapting various technological advancements to improve its meteor detection
capabilities (Borovička et al. 2022b). Over the several decades of operation,
the network and team have aided in the recovery of at least 13 meteorites
(Spurnỳ et al. 2003; Spurny et al. 2013; Spurný et al. 2017; Spurnỳ et al.
2020). The network primarily utilizes digital autonomous fireball observers
(DAFOs), which are weather-proof, fully autonomous systems, to capture images
of the entire sky continuously during favorable weather conditions. Each DAFO
employs DSLR cameras equipped with fisheye lenses, similar to the DFN,
providing images with remarkable clarity and detail. Regarding sensitivity and
detection capabilities, EFN’s cameras are configured to collect digital images
of meteors brighter than an absolute magnitude of about -2, and they can
perform high-temporal-resolution radiometric measurements of those brighter
than a magnitude of approximately -4 (Borovička et al. 2022b). The EFN is
proficient in detecting meteoroids larger than 5 grams and can capture high-
velocity meteoroids down to masses of about 0.1 grams. The EFN comprises 26
stations equipped with DAFOs spread across central Europe, covering about one
million km2.

The EFN data used within this study was published and described in Borovička
et al. (2022b) and Borovička et al. (2022a). The fireball’s atmospheric
trajectory is deduced using the SLLS method, assuming a straight-line
trajectory in space (Borovicka 1990), similar to the DFN. However, the
velocity method differs from the DFN. Time data are projected onto a computed
SLLS trajectory and fitted with a physical four-parameter function that
accounts for atmospheric drag and ablation (Pecina & Ceplecha 1983). This
function includes the preatmospheric velocity, ablation coefficient, and mass-
related parameters, and it is fine-tuned using atmospheric density models like
CIRA72 or NRLMSISE-00. When deceleration is significant, manual adjustments or
alternative models may be employed. Outliers are carefully weighed or excluded
to ensure accuracy, and systematic discrepancies between cameras are resolved
before finalizing the data. The heliocentric orbits are then calculated with a
slightly modified version of the method described in Ceplecha (1987),
correcting for Earth’s rotation and gravity.

####  2.2.4 MORP

MORP was an operational fireball network in Western Canada from 1971 to 1985
(Halliday et al. 1996). It was a landmark initiative to observe bright meteors
and recover meteorites to discern their pre-collision orbits. MORP utilized a
network of 60 cameras distributed across 12 stations, enabling near-
comprehensive sky coverage. MORP successfully recorded over 1000 fireballs
throughout its operational years, contributing significantly to meteoroid
orbit research. However, only a small fraction (285 in total) of these
fireballs had orbits reduced and published (Campbell-Brown & Hildebrand 2004).
A milestone achievement was the recovery and analysis of the Innisfree
meteorite, marking a pivotal success in linking meteorites to their original
orbits (Halliday et al. 1978). However, the project faced several challenges,
such as lost original measurements and uncertainties in time determinations,
which somewhat affected the precision and comprehensiveness of the data.
Despite these hurdles, MORP’s legacy remains important in the meteor science
research landscape. The MORP orbital data used within this study was taken
from Halliday et al. (1996).

####  2.2.5 Case studies

In addition to the fireballs observed by DFN, EFN, FRIPON, and MORP, we also
completed a stability analysis of three individual fireballs claimed to have
originated from the JFC population. The first two of these fireballs were
recorded by another fireball network: Spanish Meteor Network (SPMN). The first
SPMN event was described in (Madiedo et al. 2014), where they observed a
$-13.0\pm 0.5$ fireball over the center of Spain. The second event, also
observed by the SPMN in 2008, similarly reached an absolute magnitude of
$-18\pm 1$ and the authors claimed the fireball could have produced meteorites
(Trigo-Rodríguez et al. 2009). The third event was described in the study of
Hughes et al. (2022), where a very bright fireball of peak magnitude of -19
was detected to impact over the eastern coast of Florida.

####  2.2.6 Jupiter-family comets

In addition to the fireball data, we also performed the same exact analysis on
661 JFCs, extracted from the NASA
HORIZONS555https://ssd.jpl.nasa.gov/horizons/ database, excluding only the
cometary fragments from the study. Each object has been given a comet
designation and fulfills the Carusi et al. (1985) Tisserand parameter JFC
definition. If the JFC population is producing the debris we observe with
fireball networks around the globe, the dynamics of their orbits should be
extremely similar. All ephemeris information of JFCs available through the
HORIZONS databases were used, excluding cometary fragments.

All fireball and JFC data used in this study is openly
available666https://doi.org/10.5281/zenodo.10671333.

###  2.3 Orbital analysis

Asteroidal and cometary orbits are traditionally classified based on
Tisserand’s parameter ($T_{J}$), a widely used criterion introduced by Kresak
(1979) and further supported by subsequent studies (Carusi et al. 1985;
Levison & Duncan 1994; Levison 1996). According to this classification, minor
bodies are categorized based on their $T_{J}$ values. Asteroids are defined as
having $T_{J}>3$. On the other hand, comets are classified as having
$T_{J}\leq 3$, with further subdivisions into Jupiter-family comets (JFCs) if
$2<T_{J}\leq 3$ and Halley-type comets if $T_{J}\leq 2$. This classification
helps in understanding the dynamic properties and evolutionary trajectories of
these minor celestial bodies.

However, there are problems with this simple method to classify objects, since
there are some border cases: objects that behave dynamically as comets but
have not shown any type of activity (asteroids in cometary orbits, ACOs), and
objects in asteroidal orbits that present evidence of gas and/or dust
ejections (main belt comets, MBCs; or active asteroids). Tancredi (2014)
(hereafter, T14) considered it necessary to develop a more adequate orbital
criterion for the distinction between asteroids and comets, and to determine
the border cases. The criterion is based on Tisserand’s parameter and the
minimum orbital intersection distance (MOID); it also considers information on
perihelic and aphelic distances of the objects and the location of the
resonances. A summarized version of the criterion is presented here. We
recommend reading the original article to understand the classification
scheme’s details. According to this scheme, there are four classes of periodic
comets: Halley-type comets, Jupiter-family comets, “Comets” in asteroidal
orbits (ACOs), and centaur comets. On the other hand, ACOs are grouped into
three categories: ACO-Jupiter family types (AJFs), Centaur asteroids (CAs),
and ACO-Halley types (AHTs). Moreover, ACOs in the Jupiter Family have
$2<T_{J}<3.05$, $q<Q_{J}$, are not in resonances, and have low MOID respect to
the giant planets; Centaur asteroids have $T_{J}>2$ and $Q_{J}<q<a_{Ura}$; and
Halley-type ACOs have $T_{J}<2$; where $q$ is the object perihelion, $Q_{J}$
is the Jupiter aphelion, and $a_{Ura}$ is the Uranus semi-major axis. We will
use the traditional simple criterion and this other one and compare the
results for the population of fireballs.

###  2.4 Dynamic analysis

The diagnostic feature of an object originating from the JFC population is its
frequency of chaotic close encounters with the gas giant Jupiter, on
timescales of centuries to millennia (Tancredi & Rickman 1992; Fernández &
Sosa 2015). These encounters characterize the JFCs and lead to extremely short
predictability of the orbits (typically less than 50-150 yrs; Tancredi 1995,
1998, 2014). Conversely, small bodies originating from the main asteroid belt
on similar orbits rarely have close encounters with Jupiter, giving them
fairly predictable orbits on the same 10,000 yr timescales (Tancredi 2014).

Within this study, we replicated the orbital analysis of Shober et al. (2021)
and expanded upon the work of Fernández & Sosa (2015). Using the IAS15
integrator implemented by the REBOUND python module (Rein & Liu 2012; Rein &
Spiegel 2015), each fireball orbit and JFC from the HORIZONS database had
their trajectory integrated backward 10,000 yrs. The IAS15, a high-order,
adaptive timestep algorithm, ensures exceptional accuracy, a crucial attribute
for modeling the intricate and sensitive dynamics of JFC-like debris. This
high accuracy is imperative given that minor deviations in initial conditions
or perturbative forces can yield substantial divergences in orbital evolution
over time. Crucially, the IAS15’s proficiency in handling close planetary
encounters is of paramount importance. JFCs frequently undergo close
approaches with Jupiter and the terrestrial planets, necessitating an
integrator capable of accurately resolving these encounters without
significant loss of precision. The adaptive timestep mechanism of IAS15
dynamically adjusts time steps in response to varying dynamical conditions, a
feature that is particularly beneficial in the simulation of planet-
encountering objects where rapid changes in gravitational forces are common.

We generated 1000 clones within the published orbital uncertainties of the
EFN, FRIPON, and DFN fireball events. Covariance matrices were not used to
generate the clones within the simulations as the DFN, EFN, and MORP did not
output matrices. The diagonal elements were used to initialize the Monte Carlo
simulations, giving an overall uncertainty volume slightly larger than and
enclosing, the actual one. The same was done for the JFCs taken from the NASA
HORIZONS service, with 1000 clones generated within the given observational
uncertainties. The MORP fireballs dataset had no listed uncertainties;
therefore, an assumption had to be made about the uncertainties of the orbital
data of the historical dataset. The MORP orbital simulations were initiated
with 1-sigma uncertainties corresponding to 0.01 au, 0.001, 0.1∘, 0.01∘, 0.01∘
for the semi-major axis, eccentricity, inclination, longitude of ascending
node, and argument of perihelion. Each simulation included the gravitational
influence of the Sun, the planets (Mercury through Neptune), and the Moon. The
planetary ephemeris was obtained from online solar system data and ephemeris
computation service NASA HORIZONS, and the simulations were initiated at the
beginning of the fireball observation. The results of the integrations can be
accessed through the supplementary materials.

The 10,000 yr orbital simulations performed using REBOUND recorded the
positions and osculating heliocentric orbital elements at each time step. In
addition, the minimum orbital intersection distance (MOID) with Jupiter and
Saturn were also calculated at each timestep using the technique described in
Baluev & Mikryukov (2019). The MOID value indicates the minimum distance
between the two Keplerian orbits, but it is important to remember that the
bodies may never reach this distance in reality due to MMRs and perturbations.
The methodology of Baluev & Mikryukov (2019) produces accurate and fast
results with its algebraic approach, solving a 16th-order polynomial to
determine all the critical points of the distance function. The speed and
accuracy of the MOID algorithm was necessary to process all 1000 timesteps of
the 646,000 particles integrated within the simulations.

####  2.4.1 Assessing orbital instability

JFC orbits can be analyzed through a mean dynamical path derived from a set of
outcomes for a specific comet and its multiple clones. To quantify the
instability of these orbits, certain metrics are utilized:

Initially proposed by Fernández et al. (2014), the $f_{q}$ index quantifies
the instability by measuring the duration, in the preceding 10,000 years, that
the clones generated within the observational uncertainties of a JFC have a
perihelion distance greater than 2.5 au. This distance is significant because
comets predominantly remain beyond this limit under Jupiter’s gravitational
influence, rarely approaching the Sun, in agreement with many previous studies
(Fernández & Morbidelli 2006; Fernández et al. 2014; Fernández & Sosa 2015).
The metric is mathematically represented as:

$f_{q}=\frac{\sum_{j=1}^{N}\Delta t_{j}}{N\times 10^{4}},$ (1)

where $\Delta t_{j}$ signifies the time duration (in years) with the specified
orbital conditions among the $N$ clones (here, $N=1000$).

The fa index, also formulated by Fernández et al. (2014), reflects the
fraction of the past 10,000 years during which a JFC or its clones maintain a
semi-major axis exceeding 7.37 au. Expressed mathematically:

$f_{a}=\frac{\sum_{j=1}^{N}\Delta t^{\prime}_{j}}{N\times 10^{4}}.$ (2)

An observed correlation between $f_{q}$ and $f_{a}$ indices indicates that
comets with higher values of these indices typically follow unstable orbits,
spending significant time outside the defined thresholds.

Another metric we introduce here is the percentage of the particle clones that
reach at least a perihelion value of 2.5 au. This criterion is useful and
meaningful in addition to the $f_{q}$ statistic introduced by Fernández et al.
(2014). Instead of being weighted by the proportion of time spent with $q>$
2.5 au, this metric is only concerned with the likelihood that any event
reaches $q>$ 2.5 au within the 10,000 year integration.

In Shober et al. (2021), the variation in the orbital elements and close
encounters with Jupiter during the orbital integrations were manually
assessed. This is an intensive process of evaluating the orbital histories of
every particle and is only effective if the distinction between the dynamics
is extremely drastic. For the 50 events analyzed, which were mostly confined
to smaller semi-major axis values, this was true. However, for larger
datasets, and those with more data well beyond 3 au, the dynamic differences
become less and less obvious. Therefore, in this study, a manual reduction of
the data was performed, as described in Shober et al. (2021), to demonstrate
how the $f_{q}$, $f_{a}$, and the likelihood of $q>$ 2.5 au metrics produce
similar results but are more informative and scale-able in comparison.

####  2.4.2 Calculation of Lyapunov lifetimes

In addition to the 10,000 yr orbital simulations to characterize the
prevalence of close encounters with Jupiter, a separate set of simulations was
done to estimate the Lyapunov characteristic exponents of the orbits. These
simulations were also conducted using the REBOUND architecture. However, using
the WHfast integrator with a 0.01 yr timestep (Rein & Tamayo 2015) for 20,000
yrs. This timescale is consistent with previous studies Tancredi (1995, 1998),
and was also found here to be a good duration that produced reproducible
results based on our testing of integrations between 1000 and 25,000 yrs.

The REBOUND integration module employs a symplectic integrator tailored for
gravitational dynamics to calculate the Lyapunov Characteristic Exponent
(LCE), a quantitative measure of chaos in dynamical systems. The methodology
involves integrating the equations of motion for the system alongside a
variational equation representing a small deviation from the initial
conditions. REBOUND tracks the divergence of this deviation over time,
providing a direct measure of the system’s sensitivity to initial conditions.
The LCE is then computed by averaging the exponential growth rate of this
divergence. The accuracy and reliability of the LCE as computed by REBOUND
have been validated against established benchmarks in the field, confirming
its efficacy in characterizing the dynamical stability of celestial
configurations (Rein & Spiegel 2015; Rein & Tamayo 2015).

####  2.4.3 Debiased NEO model source region estimate

The fireball pre-encounter orbits were also compared to the debiased
NEOMOD777https://www.boulder.swri.edu/~davidn/NEOMOD_Simulator/ model to
compare the $10^{4}$ yr dynamics of these objects to the long-term dynamics of
NEOs on similar orbits. Nesvorný et al. (2023) developed a novel orbital model
for NEOs, integrating asteroid orbits from the main belt and aligning these
with NEO observations from the Catalina Sky Survey (CSS). This model
represents NEOs as a transitional population originating from the main
asteroid belt and trans-Neptunian scattered disk. Their lifecycle concludes
either via planetary impact, solar disintegration, or ejection from the solar
system. The study utilized the
astorb.dat888https://asteroid.lowell.edu/main/astorb/ catalog from the Lowell
Observatory for initial orbit setup of main-belt asteroids, which, as of early
2022, contained nearly 1.2 million entries. The main-belt asteroids evolved
into resonances by the Yarkovsky thermal effect, although the exact mechanism
of their entry into these resonances was deemed less significant for the NEO
orbital distribution. Orbital elements for the eight planets (Mercury to
Neptune) were obtained from NASA/JPL Horizons database. Using the Swift rmvs4
N-body integrator, the orbital evolution of planets and 105 test bodies per
source was followed. The integrations utilized 2000 Ivy Bridge cores of NASA’s
Pleiades Supercomputer, each core handling eight planets and 50 test bodies.
The initial integrations ran for 100 Myr, with NEO orbits extended to 500 Myr.
The study found the contribution of long-lived NEOs beyond 500 Myr to be
insignificant.

The CSS data, comprising nearly 22,000 NEO detections from 2005-2012, provided
a basis for calibration. The survey’s pointing history and detection
efficiency were crucial for understanding the observational bias. The
detection probability of an object in a CSS Field of View (FOV) was broken
down into geometric probability, photometric probability, and trailing loss.
The study employed MultiNest for model selection, parameter estimation, and
error analysis. This Bayesian evidence-based approach helped in dealing with
high-dimensional parameter spaces and multiple posterior modes. The log-
likelihood definition in MultiNest was used to compute the joint probability
over all bins, considering detection probability and the number of objects
detected by CSS. The model considered bin sizes and ranges as follows: semi-
major axis (a) from 0 to 4.2 au in 42 bins of 0.1 au each, eccentricity (e)
from 0 to 1 in 20 bins of 0.05 each, inclination (i) from 0 to 88∘ in 22 bins
of 4∘ each, and absolute magnitude (H) from 15 to 25 in 40 bins of 0.25 each
(Nesvorný et al. 2023).

For our study, we found the corresponding bin within the NEOMOD model for each
of the JFC-like fireballs considered here to estimate the source region
likelihood. The H value of 25.0 was used in the model for the fireball data as
it was the highest absolute magnitude (smallest object) defined in the model.
For an object with a geometric albedo of 0.25, this roughly translates to an
object of $\sim$27 m in diameter, i.e., at least one order of magnitude or
more larger than any of the meteoroids analyzed in this study. This caveat may
prove to be significant as the source region variations between $>$100 m
asteroids/comets used to calibrate the model and the cm-m meteoroid
populations differ, a concern that can be tested here by comparing the JFC
source region prediction of the model to ours based on the dynamics of the
objects during a 10 kyr simulation.

###  2.5 Meteorite fall determination

In this study, the determination of meteorite falls is crucial for discerning
the nature of meteoroids on comet-like orbits, particularly those with
Tisserand’s parameters between 2 and 3. This analysis helps ascertain whether
meteoroids from stable or dynamically active orbits are more likely to
contribute to meteorite falls on Earth. Given that our data appears to
predominantly feature objects from stable orbits (Shober et al. 2021), finding
meteorite falls among these provides insight into the source regions of the
meteoroids and aids in understanding the compositional diversity of this
population.

The alpha-beta ($\alpha-\beta$) methodology is a pivotal approach in the
analysis of fireball dynamics and their potential to result in meteorite
falls. This methodology, which calculates the ballistic coefficient ($\alpha$)
and the mass-loss parameter ($\beta$), was notably developed and refined in
several studies (Gritsevich & Stulov 2006; Gritsevich 2007; Lyytinen &
Gritsevich 2016; Sansom et al. 2019). Sansom et al. (2019) then applied these
theoretical constructs, demonstrating the practical utility of the
$\alpha-\beta$ parameters in quickly identifying potential meteorite-dropping
events.

While a theoretical construct, the $\alpha-\beta$ methodology gains its
significance in practical applications, as demonstrated by Sansom et al.
(2019). They not only elucidated the theoretical underpinnings of these
parameters but also applied them in real-world scenarios to identify potential
meteorite-dropping events. This application involved analyzing the trajectory
and physical properties of observed fireballs to calculate their $\alpha$
(ballistic coefficient) and $\beta$ (mass-loss parameter). By doing so, Sansom
et al. (2019) effectively bridged the gap between theoretical meteor dynamics
and empirical observations, offering a methodological framework that enhances
the predictive accuracy of meteorite fall determinations.

The limiting lines for a 50 g final mass are based on the methodology of
Sansom et al. (2019) using the following equations for meteoroids of different
densities (Consolmagno et al. 2008). The boundary lines denote the regions
below where, given a shape change coefficient ($\mu$), a meteorite of at least
50 g would survive:

For meteoroids with an ordinary-chondrite density of 3500 kg/m3:

$\ln(\alpha)-\ln(\beta)=\ln(13.2)-3\ln(\sin(\gamma)),\mu=0,$ (3)
$\ln(\alpha)-\ln(\beta)=\ln(4.4)-2\ln(\sin(\gamma)),\mu=2/3.$ (4)

For meteoroids with a carbonaceous density (2240 kg/m3):

$\ln(\alpha)-\ln(\beta)=\ln(14.09)-3\ln(\sin(\gamma)),\mu=0,$ (5)
$\ln(\alpha)-\ln(\beta)=\ln(4.7)-2\ln(\sin(\gamma)),\mu=2/3.$ (6)

Here, $\gamma$ is the entry angle of the meteoroid, and $\mu$ is the shape
change coefficient representing the rotation of a meteoroid body
($0\leq\mu\leq 2/3$). For more comprehensive insights into the development and
applications of the $\alpha-\beta$ methodology, we refer to the following
works: Gritsevich & Stulov (2006); Gritsevich (2007); Lyytinen & Gritsevich
(2016); Sansom et al. (2019); Shober et al. (2021). The $\alpha-\beta$
parameters can be calculated from any event with velocity and height data and
determine if a meteorite is on the
ground999https://github.com/desertfireballnetwork/alpha_beta_modules.

###  2.6 Meteor shower identification

Identifying meteor showers in our dataset serves as a key method for tracing
the origin of meteoroids observed entering Earth’s atmosphere, thus providing
a window into the dynamic processes shaping their source regions. By
correlating atmospheric trajectories and orbital characteristics with known
meteor showers and their parent bodies, we can ascertain whether these
meteoroids stem from the main asteroid belt, are part of an evolved comet
population, or directly originate from the JFCs. This comparative analysis
between identified showers and the sporadic background allows us to unravel
these meteoroids’ dynamical history and potential evolutionary paths, offering
profound insights into the mechanisms that govern their delivery to near-Earth
space.

Several established methods exist to identify meteor showers or orbital
similarity. The conventional approach has been the use of an orbital
similarity criterion. The first of these was introduced by Southworth &
Hawkins (1963); however, other improved orbital criteria have since been
proposed (Drummond 1981; Jopek 1993; Jopek et al. 2008).

The criterion chosen to be used in this study is based on a distance function
($D_{N}$) involving four geocentric quantities directly linked to observations
proposed by Valsecchi et al. (1999). This method, defined in a space with as
many dimensions as the number of independently measured physical quantities,
differs from the conventional orbital similarity criteria. It is based on the
components of the geocentric velocity at the encounter, essential for Öpik’s
theory of close encounters, and two of the new variables are near-invariant
with respect to the principal secular perturbation affecting meteoroid orbits
(Valsecchi et al. 1999). The approach aims to overcome the limitations of
previous methods by focusing on quantities that can be computed directly from
observed data without relying solely on the derivation of conventional orbital
elements.

##  3 Results

###  3.1 Orbital distribution

The incursion of a JFC onto an Earth-crossing orbit is a rare event. Only a
small portion of the JFC population exists on Earth-crossing orbits (Fig. 1).
In the NASA HORIZONS database, 72 of the 661 JFCs (excluding fragments) are
also NEOs – and we note that this is an overestimation as there is a
significant bias towards the discovery of near-Earth JFCs. Also, the
contribution from the main asteroid belt is much more significant, long-lived,
and easier to produce. According to Granvik et al. (2018), the JFC component
of the near-Earth population is at most 10% depending on the H-value and
assuming that dormancy is a more likely outcome than disintegration. This
implies that if the dormancy assumption is incorrect, the JFC component is
even less than predicted.

Moreover, only $\sim$30% of JFCs are predicted to become active bodies, with
an orbit below 2.5 au where the water begins to sublimate (Levison & Duncan
1997). Additionally, of the bodies that encroach even closer to the sun to
near-Earth space (q$<$1.3 au), they typically only do so for a few thousand
years (Fernández et al. 2002). As seen in Fig. 1, only a small portion of the
JFCs overlap in orbital space with the fireballs detected around the globe.
Most of the known JFCs exist on orbits well beyond the orbit of the Earth,
mostly concentrated with aphelion values crossing the orbit of Jupiter. The
inclination distribution tends to stay $<$30∘, expected for short-period
comets originating from the scattered disk (Fig. 2). A majority of the
fireball orbits overlap with the inclination distribution of the JFC
population, but this does not signify any link as the JFC distribution is low-
inclination. The asteroid population also has low inclinations, typically more
concentrated toward the ecliptic plane. Surprisingly, the EFN also seems to
contain more events beyond 3 au compared to the other networks in this study,
with a concentration around 3.2-3.5 au. This concentration could be indicative
of the larger proportions of fireballs originating from the 2:1 MMR within the
EFN dataset or some observational bias. The 2:1 MMR is a wide, powerful
resonance centered at 3.28 au (Tancredi 2014).

There are some inconsistencies in the fireball and JFC populations as we
concentrate on the longitude of perihelion. The longitude of perihelion
($\varpi$) is defined as the sum of the argument of perihelion ($\omega$) and
the longitude of the ascending node ($\Omega$). For low inclination orbits, it
can be thought of as the orientation of the perihelion of an orbit relative to
other solar system bodies. The perihelion longitudes of JFCs have long been
known to cluster near the $\varpi$ of Jupiter (Opik 1971), as the encounters
are more likely at perihelion and aphelion. In Fig. 3, we have plotted a polar
histogram of the $\varpi$ values of the sporadic fireballs found within the
datasets. The fireball orbits that belonged to a meteor cluster and had a
D${}_{N}<0.15$ (Valsecchi et al. 1999) were removed from the plot to better
compare the general population. A broad concentration of JFCs exists near the
value of Jupiter (Fig. 3(a)). The fireball data, however, mostly shows no
correlation except for the DFN, which seems to strongly concentrate towards
the planet. Despite this, given the significant variation between the network
$\varpi$ distributions, it is difficult to ascertain the significance of this
association.

(a) JFCs

(b) DFN

(c) EFN

(d) FRIPON

(e) MORP

Figure 3: Polar representation of the longitudes of perihelion $\varpi$ for
fireballs versus JFCs. The datasets are represented by histograms in unique
colors: JFCs (light gray), DFN (blue), EFN (red), FRIPON (green), and MORP
(dark gray). A prominent gold line marks Jupiter’s longitude of perihelion to
demonstrate the concentration of JFC $\varpi$ values towards that of the
planet.

The JFC arguments of perihelion ($\omega$) are also known to concentrate
towards 0∘ and 180∘ (Dones et al. 2015) and the inclinations tend to stay
$<$30∘ (Fig. 4). The 646 fireballs studied here do not show a significant
concentration of $\omega$ towards 0∘, and only the northern hemisphere
networks show concentrations toward 180∘ (Fig. 4). This concentration towards
180∘ is tempting to link to the JFC population distribution, but as can be
seen in Fig. 4, there is a clear trend toward higher inclinations ($>$30∘)
within the fireball dataset when $\omega\sim$ 180∘. Despite the lack of data,
there is also a similar trend with only the southern hemisphere fireballs
(primarily from the DFN) that trend towards higher inclinations near 0∘.
Conversely, the eccentricities tend to decrease for these high-inc portions of
the fireball population (as indicated by the color bar in Fig. 4). This likely
implies that these objects were in a Kozai resonance, and our orbital
integrations confirm this. Some showers in the dataset, particularly the high-
inc Quandrantid meteor shower (inc$\sim$72∘), support this as other studies
have already identified that the meteoroids were moving in a “Kozai
circulation” (Wiegert & Brown 2005). Otherwise, the high inclinations of these
bodies may also be a filtering effect, as the higher inclinations will reduce
the amount of time near the equatorial plane and, thus, the chances of a close
encounter with Jupiter. This relationship between the probability of an
encounter and the inclination is confirmed by our orbital simulations, which
(as seen in Fig. 4(b)) is higher for the low-inclination meteoroids clustered
toward $\omega$ values of 0∘ and 180∘.

(a)

(b)

Figure 4: Argument of perihelion ($\omega$) versus the inclination ($\iota$)
of the JFC-like ($2<T_{J}<3$) meteoroid population (cm-m size range) observed
by the DFN (circle), EFN (diamond), MORP (square), and FRIPON (triangle).
Black crosses denote the 661 JFCs taken from the NASA HORIZONS database. The
coloration of subplot (a) is based on the eccentricity of the object, while
subplot (b) corresponds to the percentage of particle clones generated within
the observational uncertainties of the object that achieved at least a
perihelion value of 2.5 au during a 10 kyr orbital integration.

###  3.2 Applying the criteria of Tancredi (2014)

For the following analysis, we group all the fireballs detected by the DFN,
EFN, FRIPON, and MORP networks. In this section, our focus shifts towards
evaluating the efficacy of the simplistic Tisserand’s parameter ($T_{J}$)
criterion for JFC identification against the more elaborate classification
system proposed by T14. This comparison aims to scrutinize how each criterion
fares in discerning cometary from asteroidal origins, especially in light of
the orbital integration analyses detailed in subsequent sections.

Figure 5: Distribution of fireball and comet orbits in the semi-major axis
versus eccentricity space, highlighting the classification according to
Tancredi (2014) criteria. The data points are: black dots - meteoroids in
orbits not similar to cometary orbits, green dots: meteoroids inside
resonances, blue dots: meteoroids in Jupiter family orbits, magenta squares:
comets in Centaur-type orbits, and red squares: Jupiter family comets. Several
relevant lines are drawn.

Our initial dataset comprised 646 fireballs and 661 comets, as defined by
having $2<T_{J}<3$. Implementing T14’s criteria resulted in the identification
of 640 comets within the Jupiter Family and 21 with Centaur-type orbits from
the original comet set. Conversely, of the 646 fireballs, 322 were excluded
from the ACO classification, and an additional 95 were set aside due to their
resonant orbits. Consequently, a substantial 65% (417 out of 646) of the
fireball dataset was deemed non-cometary according to T14’s criteria, leaving
230 (35%) as plausible candidates within the Jupiter family ACO orbits.

Figure 5 depicts the semi-major axis ($a$) versus eccentricity ($e$)
distribution for these groups, accentuated by various markers and lines to
delineate the different classifications and relevant dynamical thresholds. The
fireballs excluded as cometary candidates (represented by black dots)
predominantly occupy regions with $T_{J}$ values marginally below 3 and
feature orbits that do not intersect with Jupiter’s path, as indicated by
their aphelion distances not surpassing Jupiter’s perihelion ($Q\lessapprox
q_{J}$), a delineation refined through the use of minimum orbital intersection
distance (MOID) in T14’s criteria.

A clear demarcation between the different object groups emerges within the
$a-e-\sin(i/2)$ phase space (Fig. 6), showcasing the nuanced separation
achieved by T14’s classification scheme. Notably, the boundary for $T_{J}=3$
curves inward for orbits with significant inclinations, excluding them from
Jupiter’s orbital domain.

The refined analysis provided by T14’s criteria markedly narrows down the list
of fireball candidates with potential cometary affinities. This subset of
fireballs, filtered through the lens of T14’s comprehensive classification
system, presents a more targeted group for further investigation into their
dynamical stability and potential cometary lineage. The ensuing sections will
delve into a comparative analysis of these candidates’ orbital stability,
juxtaposing them with the broader dataset to draw conclusions about their
origins and dynamical evolution.

Figure 6: Three-dimensional representation in the $a-e-\sin(i/2)$ space,
illustrating the separation between cometary and asteroidal/meteoroidal orbits
as per Tancredi (2014) criteria. Same symbols as in Fig. 5.

###  3.3 Orbital stability

Simply based on the pre-impact orbital distribution of the DFN, EFN, FRIPON
and MORP data, the JFC-like ($2<T_{J}<3$) meteoroids being detected by
fireball networks overall do not align well with JFCs. This is further
supported by the 10 kyr orbital integrations of the 661 JFCs and the 646
fireball orbits.

####  3.3.1 Orbital Integrations

A manual data reduction approach was followed in the study summarized by
Shober et al. (2021). When analyzing the simulations of a handful of objects,
the 10 kyr simulation results were manually examined and the number of JFC-
like histories was counted. When we say “JFC-like histories”, we are
describing objects that have several close encounters with Jupiter over a
10,000 yr timescale, which produce large and unpredictable jumps in the
orbital elements (see Fig. 1 from Shober et al. (2021)). This procedure was
also undertaken for this study, requiring the analysis and manual
interpretation of 646,000 particle histories. For meteoroids with a semi-major
axis still within range of the main belt, the difference between the orbital
evolution of an asteroid and a JFC is very clear, and it has been used in
several past studies (Tancredi 2014; Fernández et al. 2014; Fernández & Sosa
2015). However, as the orbits grow beyond 3 au, the histories can often begin
to defy the simplistic binary classification (“asteroid-like” vs. “JFC-like”)
due to the gradually increasing chaotic nature of the orbits. The analysis of
the dynamics in this study had to evolve from the methodology of Shober et al.
(2021) to be more comprehensive, unbiased, and scalable.

The term ”active” is used to describe comets that fall within 2.5 au of the
Sun, as this is approximately when water ice begins to sublimate (Levison &
Duncan 1997). Thus, the rarity of having JFCs $<$2.5 au is somewhat of a self-
fulfilling prophecy because if too many JFCs were below this limit for too
long, there would likely not be a steady-state population of active JFCs.
After all, the physical lifetimes of these objects are estimated to be only a
few thousand years in the inner solar system (Fernández et al. 2002). Only a
very small portion of the JFC population is ”active” at any given time, and
only $\sim$30% of the population ever reaches an active phase. Thus, this 2.5
au criterion was also selected as a metric to compare the fireball population
to the JFC population.

The manual identification and analysis of the 646,000 particle histories in
this study revealed a consistent story with that found by Shober et al.
(2021), with a large majority of the fireballs originating from very stable
orbits compared to JFCs. When these manual counts were then compared to the
q$>$2.5 au metric for the same fireball events (Fig. 7), the two methods
varied very linearly with a Pearson’s correlations coefficient of 0.86. This
is especially true when the manual counts and the percentage of particle
clones that reached q$>$2.5 au were below 50%, where the values are nearly
identical. Otherwise, for percentages $>$50%, the manual analysis results seem
to be normally over-counting the proportion of ”JFC-like” histories. The
counting deviates from a 1:1 relationship and only produces a correlation
coefficient of 0.31. These over-counts (bottom right quadrant of Fig. 7)
result from the particles having many distant encounters with Jupiter over the
10 kyr simulation while never having a close enough encounter to drive them
out of the active region. On the other hand, some events have nearly all the
particle clones reach 2.5 au, but were marked as very stable during the manual
reduction (top-left quadrant of Fig. 7). These, conversely, have very
predictable trajectories during the 10 kyr simulations but can reach higher
perihelion orbits through a large q-variation due to a Kozai resonance.

Figure 7: Scatter plot comparing the manual counting method of reviewing
integration particle clones histories versus the more simplistic method of
identifying the percentage of particle clones that reach a minimum perihelion
value of 2.5 au at least once during the 10 kyr integrations. The
uncertainties of the manual counting method correspond to the standard
deviations of the sample means. For each meteoroid, 10 samples of 100
particles were independently counted to gauge the variation in the manual
reduction. The line depicts a perfectly 1:1 relationship. Figure 8: Normalized
histogram representing the percentage of particle clones for each object that
reach a minimum perihelion value of 2.5 au at least once during the 10 kyr
integrations for the JFC-like fireballs and the 661 NASA HORIZONS JFCs. The
JFCs that have orbits at the observation epoch with q$>$2.5 au were not
included in the histogram.

As seen in Fig. 8, the q$>$2.5 au metric is also clearly a very good limit,
given that nearly the entire JFC population reaches it on 10 kyr timescales.
Over 90% of the 661 JFCs included in this study have a $>$50% chance of
reaching q$>$2.5 au at least once within that time. Given that this minimum
perihelion metric is very predicting for JFCs, is much more objective, and
prevents the over-counting of some events with only rare events in a Kozai
resonance being mischaracterized, this likelihood of q$>$2.5 au will be used
from here forward instead of the manual analysis. This does not change the
results in any way, but it does make them more repeatable.

As seen in Fig. 8, the fireball distribution drastically differs from the JFC
population. The proportion of the JFC-like meteoroids observed by the fireball
networks that originate from orbits with $<$50% chance over reaching q$>$2.5
au at least once within 10 kyr is $\sim$90%. Almost none of the fireballs in
JFC-like orbits witnessed by the DFN, EFN, MORP, and FRIPON originate from
orbits capable of having close encounters with Jupiter like the JFC
population. The N-body modeling confirms the difference between the orbital
distributions, demonstrating that these are two distinct populations
dynamically.

However, there are some notable variations and nuances present between the
datasets. These differences are likely due to the slightly varied hardware
used by each network, resulting in a different limiting magnitude range. These
minute differences in the magnitude ranges of the networks here also somewhat
modify the size range of objects being detected. Understanding these
differences could be the key to better characterizing the physical breakdown
of cometary debris and understanding the size-frequency distribution of the
results remnants.

For example, in Fig. LABEL:fig:all_networks_orbits_q25 we have plotted the a-e
and a-i orbital distribution for all of the fireball networks and modified the
coloration to indicate the percentage of particle clones that reach a minimum
perihelion value of 2.5 au. For comparison, the 661 JFCs are also plotted as
large crosses. The fireball data technically satisfies the Tisserand’s
parameter definition of JFC membership ($2<T_{J}<3$; Carusi et al. 1985);
however, a large proportion of the fireballs lie on orbits hovering just below
the perihelion distance of Jupiter. These meteoroids have a dark blue
coloration in Fig. LABEL:fig:all_networks_orbits_q25, indicating that they
likely have no chance of having a close encounter with Jupiter on 10 kyr
timescales. The further Jupiter-crossing the orbits become, generally the
higher percentage of clones have encounters. However, not many fireballs are
detected by the FRIPON and DFN networks to originate on orbits larger than 3
au. On the other hand, the EFN has reported having witnessed many events in
comparison coming from $>$ 3 au (around 30% more than the DFN or FRIPON),
particularly concentrated between 3.2 and 3.5 au. This abundance of objects
originating from beyond 3 au was claimed by Borovička et al. (2022b) to
indicate the abundance of cometary material on these orbits; however, no trend
in dynamics or longitude of perihelion supports this claim based on our
results. Given the lack of close encounters with Jupiter and some semi-major
axis values clustering towards 3.2-3.4 au, we interpret this as likely
indicating an origin within the 2:1 MMR. To verify this, we created a
dynamical map where we calculated the Lyapunov exponent of a grid of over
400,000 orbits with $2<T_{J}<3$. The methodology used to calculate the
Lyapunov exponents was the same as used for the fireball and JFC data. The
orbits were randomly generated within the desired a-e range ([2.9 au,3 au],
[0.35, 0.99]) and had discrete inclinations of either 0∘, 10∘, 20∘, or 30∘.
The results of this chaos mapping can be seen in Fig. 9, where the coloration
is indicative of the mean Lyapunov lifetimes and the points are the EFN
fireball datapoints. The white regions in Fig. 9 contain no points due to not
being in range or a lack of convergence. The fireball data points also have
the 1-sigma uncertainties plotted, and the pink points indicate that the
fireball is within 3-sigma of the 2:1 MMR. In total, 62 events in the EFN
$2<T_{J}<3$ dataset are within 3-sigma of the 2:1 MMR, which is the maximum
limit. This high value, and correspondence with the location of the 2:1 MMR,
is the most likely explanation for the higher number of fireballs with
$2<T_{J}<3$ beyond 3 au. However, exactly why the EFN contains more meteoroids
from the 2:1 MMR is still up for debate. One possible cause of these
variations between the fireball networks is the deviation in the fireball
absolute magnitude range being observed.

Figure 9: Chaos heat map in a-e space using Lyapunov lifetimes (the inverse of
the Lyapunov exponent) calculated from 435,000 randomized orbits. The
coloration indicated the mean Lyapunov lifetime at that point in space, while
the individual black points are fireball data points from the EFN network, and
the pink points are the fireballs that lie within 3$\sigma$ of the 2:1 MMR.
The 2:1 MMR is clearly visible in the plot centered at around 3.27 au.

####  3.3.2 Chaos indicators

(a) JFC

(b) DFN

(c) EFN

(d) MORP

(e) FRIPON

Figure 10: Minimum orbital intersection distances with Jupiter (MOIDJupiter;
au) for the osculating orbits versus the Lyapunov lifetimes (yrs) for the 661
known JFCs listed in the NASA HORIZONS database compared to the JFC-like
fireball datasets of the DFN (blue), EFN (red), MORP (black), and FRIPON
(green).

The use of chaos indicators to characterize the JFC population is not new. The
work of Tancredi (1995) and Tancredi (1998) found that the JFC population
exhibited a stronger concentration of shorter Lyapunov lifetimes (50-150 yr),
whereas NEOs exhibited a more diffuse distribution. These results showed that
the dynamical “memory” of JFCs is extremely short due to their frequent close
encounters with Jupiter. These encounters produce chaotic scattering and
macroscopic changes to the object’s orbit. This pattern found in Tancredi
(1995) suggests a common dynamical memory and indicates a connected region of
chaos within the JFC population.

We also calculated the Lyapunov lifetime for the 661 JFCs and compared them to
the Lyapunov lifetimes of 646 fireballs from JFC-like ($2<T_{J}<3$) orbits
instead. As shown in Fig. 10, we have plotted the Lyapunov lifetimes for each
fireball network dataset versus the MOIDJupiter for the pre-impact orbit,
along with the 661 JFCs. The Lyapunov lifetimes of the JFCs are found to be
generally consistent with the results of Tancredi (1995) and Tancredi (1998).
The lifetimes for JFCs concentrate just above 100 yrs and show minimal spread
in values (Fig. 10(a)). Also, $\sim$90% of the known JFC population has
MOIDJupiter values below 1 au, consistent with being dynamically linked to
Jupiter. Contrarily, the fireball network data show moderately longer
lifetimes and larger MOIDJupiter values. A fractional component of the JFC-
like fireballs matches the concentration in MOIDJupiter and Lyapunov lifetime,
but nowhere to the degree of the JFCs. The fireball data is consistent with
the NEO data from Tancredi (1998), displaying a more diffuse, wider lifetime
and MOID distribution. This further supports the theory that the fireball data
is mostly indicative of meteoroids originating from the main asteroid belt.

####  3.3.3 Jupiter-family comets

The 10 kyr numerical simulations of the 661 known JFCs clearly show most of
the JFC population has frequent close encounters with Jupiter, and these
encounters tend to keep excursions to the inner solar system to a minimum.
This is consistent with the many previous studies of this population, which
find that even when JFCs venture onto active (q$<$2.5 au) orbits, they only do
so for $\sim 10^{3}$ yrs (Lindgren 1992; Fernández et al. 2002). This is
likely a result of two main coordinating mechanisms: the close encounters with
Jupiter which cause chaotic jumps in the orbit, and the physical lifetimes of
JFCs in this region which are also thought to be $\sim 10^{3}$ yrs (Levison &
Duncan 1997; Fernández et al. 2002).

Employing the $f_{q}$ \- $f_{a}$ indices as defined by Fernández et al. (2014)
(refer to Methods), we statistically evaluate the duration for which these
bodies typically remain within q$<$2.5 au and a$>$7.37 au during the
integration period. These indices are crucial for examining this group’s
overall traits and drawing parallels with the meteoroid population. As
depicted in Fig. 11, JFCs, denoted by crosses, predominantly occupy high-q and
high-a orbits for most of the 10 kyrs. This observation aligns with the
findings of Fernández et al. (2014) and Fernández & Sosa (2015) on the near-
Earth subset of 139 NEAs and 58 JFCs. Our study expands this analysis to
include over 600 more JFCs. Also, unlike past studies that concentrated on the
near-Earth segment, where a nearly linear correlation was noted, our findings
reveal a deviation from linearity for $f_{q}>0.9$, indicative of many JFCs
spending most of their existence beyond the terrestrial planets’ orbits. This
trend is likely rooted in the fact that the majority of these objects often
possess a semi-major axis exceeding 7.37 au and spend minimal time in active
orbits (Levison & Duncan 1997; Fernández et al. 2002). Of the 661 JFCs
analyzed, approximately 78% have $f_{q}$ values over 0.5, suggesting
infrequent presence in the active zone ($<$2.5,au). This observation is
reinforced by the discovery bias against non-active and high-inclination JFCs
(Di Sisto et al. 2009), hinting at a probable overestimation of their near-
Earth residency time.

Another interesting nuance to this population is that there have been several
members of the JFC population previously identified by Fernández & Sosa (2015)
to have higher than expected $f_{q}$ values given the lack of close encounters
witnessed in the N-body simulations conducted. It was found that this
q-variation was caused by the coupling of $\omega$ and q, in a Kozai cycle.
The Kozai mechanism plays a pivotal role in decreasing the perihelion distance
(q) observed in numerical simulations. This dynamical process is understood
through the Kozai energy level curves of a celestial body, influenced by its
semi-major axis and the parameter $H=\sqrt{1-e^{2}}\cos i$, where $H$ is the
Kozai energy, $e$ is the eccentricity and $i$ is the inclination. These curves
(see Figure 10 in Fernández et al. 2014) ensure a long-term orbital evolution
that maintains high perihelia for asteroids, both inside and outside the 2:1
MMR with Jupiter, as long as $H\gtrsim 0.85$. Most asteroids meet this
condition in the main belt and nearly all JFCs (Fig. 11). However, a notable
shift in these curves occurs when $H$ falls below approximately 0.7,
dramatically altering their topology. This change allows for transitions
between high and low-q values, paired with oscillations in the semi-major axis
and inclination over a few thousand years. The curves are also influenced by
whether the asteroid’s orbit is resonant or non-resonant, particularly
regarding the amplitude and center of libration (Gomes et al. 2005; Gallardo
et al. 2012). The amplitude of these curves is broader for non-resonant
bodies, linking large and very low-q values, whereas it is more constrained
for resonant bodies with similar $H$ values. In essence, non-resonant bodies
experience a stronger Kozai effect. For instance, a resonant asteroid with
$H=0.6$ and $q=2$ au shows negligible q variation while in resonance but can
drop to 0.7 au once it leaves the resonance. The Kozai mechanism can also lead
some comets and asteroids to sungrazing orbits. Notable examples from our
sample include 321P/SOHO and 322P/SOHO, both of which are argued to be
asteroids that evolved into sungrazing orbits due to the Kozai-Lidov
mechanism. Another notable example not examined in this sample, as the $T_{J}$
is in excess of 3, is asteroid 2003 EH1 one of the proposed parents of the
Quadrantid meteor shower. The asteroid has also been shown to be in a strong
Kozai resonance, driving the q values to extremely small values in the past
(Wiegert & Brown 2005; Granvik et al. 2016).

Of the 661 JFCs in this study, $\sim$20% of them have a $H<0.7$. Many of these
are beyond the orbits of Jupiter; however, 38 are within near-Earth space. Of
the JFCs with $H<0.7$, that are also not beyond Jupiter’s orbit ($a<7.37$ au),
94% are within the ”active” region and about 50% are in near-Earth space. Half
of the near-Earth JFCs are in a Kozai resonance to some degree. When this is
compared to the fireball datasets, this trend becomes overwhelming. Over 90%
of the fireball data have H values less than 0.7, and 100% are less than 0.75.
This indicates that nearly all the meteoroid population on JFC-like
($2<T_{J}<3$) orbits are in some level of Kozai resonance. This is not
surprising as the objects that are on Earth-crossing orbits on JFC-like orbits
already have high eccentricities (e$>$0.6). This interplay of MMRs and secular
oscillations due to the Lidov-Kozai effect have been shown in numerous other
studies to be effective together to drive down q-values creating Sun-grazing
objects (Toliou & Granvik 2023).

Similar to Fernández & Sosa (2015), a subset of very ”stable” JFCs have also
been identified. The particle clones of these JFCs evade the close encounters
with Jupiter during the 10 kyr simulations, resulting in more or less
predictable trajectories. The proportion of stable interlopers in the dataset
tends to also increase as the initial perihelion decreases. Of the near-Earth
JFCs, excluding fragments, (75 in total), 22 ($\sim$30%) move on extremely
stable orbits over the 10 kyrs timescales according to the histories of 1000
particle clones. These extremely stable JFCs all have $f_{q}$ values less than
0.02 and $f_{a}$ less than 0.005 (Table 1), and most of these were also
previously identified by Fernández & Sosa (2015) for their stability. Of these
22, 16 of the JFCs had zero particles meet either q$>$2.5 au or the a$>$7.37
au limits, implying there is a very low probability of close encounters with
Jupiter. Moreover, of the 22, 6 are lost comets. Comets 3D/Biela, 5D/Brorsen,
and 34D/Gale are thought to have suffered major splitting events and were lost
due to their disintegration (Fernández 2009). Notably, comet 3D/Biela, was one
of the first well-observed cometary-splitting events in the observation
record, and the debris from this event can still be seen in the Andromedid
meteor shower. The other three ”defunct” comets are D/1766 G1 (Helfenzrieder),
D/1770 L1 (Lexell), and D/1895 Q1 (Swift); these are all only observed for the
one perihelion passage, so they were likely lost due to the orbital
uncertainty. A breakup of D/1895 Q1 (Swift) was speculated to be the source of
the intense meteor storm experienced by Mariner 4 on September 15, 1967;
however, the uncertain orbits cast doubt on this explanation (Beech et al.
1999).

Compared with most JFCs, these highly stable objects almost all have small
semi-major axis values, with 18 of the 22 within the range of major main-belt
resonances (a$<$3.2 au) and lower Kozai energies. In addition to the three
defunct comets with high orbital uncertainties, six others within this
extremely stable subset were not previously studied. These include
294P/LINEAR, 321P/SOHO, 322P/SOHO, 384P/Kowalski, 414P/STEREO, and
463P/NEOWISE. Of these newly analyzed comets, only 294P/LINEAR has a semi-
major axis beyond 3 au, however, it is within the range of the 2:1 MMR and was
identified as being within the region with the highest concentration of
Themis-family asteroids Hsieh et al. (2020). The others all have a$<$3 au, and
except for 384P/Kowalski, are well below the Kozai critical energy of 0.7.
Comets 321P and 322P are both in extremely low-q orbits, within 0.06 au of the
Sun at closest approach. Such a close encounter with the Sun should produce
devastating results for most JFCs; however, these objects are much more likely
to be asteroidal in origin. The orbits of these objects were also found to be
consistent with those of small NEAs and their rates of observation correlate
with expected rates of small asteroid injection into the near-Sun region
(Wiegert et al. 2020). Furthermore, 322P was observed without a coma,
bolstering its classification as an asteroid (Knight et al. 2016). The
evidence presented in Wiegert et al. (2020) indicates that objects 321P and
322P, traditionally labeled as comets, might be better classified as asteroids
undergoing “supercatastrophic disruption”. Granvik et al. (2016) found that
there exists a paucity of objects expected at extremely low-perihelion values
(below around 0.074 au), due to some form of “supercatastrophic disruption” as
objects approach the Sun. These objects are also found to oscillate in
q-value, going in and out of sungrazing states due to a strong Kozai
resonance, with q oscillating between 0.4 and $<$0.1 au and the inclination
correspondingly varying between 3∘ and 45∘ for 321P and between 9∘ and 70∘ for
322P. This is unsurprising as the Kozai energies for 321P and 322P are both
below 0.2. The inclinations also reach a maximum as their $\omega$ values
start to align with Jupiter (0∘ and 180∘), producing a distribution identical
to the fireball distribution seen in Fig. 4(a), as nearly all the fireballs
are in a secular Kozai resonance cycle. This period of high-inclination, low-
aphelion, and high-perihelion when the $\omega$ values are at 0∘ and 180∘
decreases the chance of frequent close encounters with Jupiter, as the objects
sit significantly above the ecliptic plane and aphelion distance decreases at
the encounter point. These meteoroids are crossing the orbit of Jupiter,
however, the evolution inside a typical secular Kozai mechanism creates less
ideal conditions for a very close encounter due to pushing the orbit out of
Jupiter’s orbital plane when the orientation is optimal. This ability to
protect certain bodies from close encounters with planets was first shown by
Kozai (1979), where it was found that (1373) Cincinnati avoids close
encounters with Jupiter. Meanwhile, (1866) Sisyphus and Midas (1981) avoid
close encounters with Mars due to the effect.

Additionally, there are two non-NEOs with extremely stable orbits as well,
meeting the same criteria as the 22 comets in Tab.1. Comets 247P/LINEAR and
421P/McNaught both have moved very predictably over 10 kyr timescales with 0%
and 1.9% of the particle clones respectively reaching a q$>$2.5 au. Both
comets are within the active region and have H values between 0.7-0.75,
displaying some Kozai cycling. However, both have significantly larger semi-
major axis values, 3.96 au and 5.08 au, respectively. They are also both stuck
in MMRs with Jupiter: 247P/LINEAR is in the 3:2 MMR (a quasi-Hilda orbit) and
421P/McNaught is in 1:1 MMR. Considering these regions of space are dominated
by D- and P-type asteroids, making a distinction between the main belt and JFC
populations is even more difficult.

Figure 11: Correlation between the indices $f{q}$ and $f_{a}$ for the 661 JFCs (crosses), and the JFC-like fireball data from the four networks included (DFN, EFN, MORP, FRIPON). The color bar indicates the Kozai energy of JFC or meteoroid, where yellow-red color corresponds to objects that are capable of large cyclic q variation, and blue ones cannot. Figure 12: Semi-major axis (au) versus the $f_{q}$ index for 661 JFCs (large square) and 646 JFC-like ($2<T_{J}<3$) fireballs collected by the DFN (hollow circle), EFN (hollow diamond), MORP (hollow square), and FRIPON (hollow triangle) networks. The coloration is indicative of the Kozai energy of the comet or meteoroid orbit at the observed epoch, where 0.7 is the critical limit where Kozai cycling of q - $\omega$ begins (Fernández et al. 2014). Name | a (au) | i (${}^{\circ})$ | TJ |  $MOID_{Jupiter}$ (au) | H | $f_{q}$ | $f_{a}$
---|---|---|---|---|---|---|---
3D/Biela | 3.53 | 13.22 | 2.531 | - | 0.642 | 0.0 | 0.0
5D/Brorsen | 3.1 | 29.38 | 2.467 | - | 0.511 | 0.0 | 0.0
34D/Gale | 4.94 | 11.73 | 2.291 | - | 0.636 | 0.0 | 0.0
66P/du Toit | 6.02 | 18.67 | 2.123 | 0.864 | 0.585 | 0.0 | 0.0
141P/Machholz 2 | 3.05 | 13.98 | 2.709 | 0.56 | 0.656 | 0.015 | 0.004
162P/Siding Spring | 3.05 | 27.82 | 2.792 | 0.587 | 0.71 | 0.001 | 0.0
169P/NEAT | 2.61 | 11.3 | 2.888 | 0.978 | 0.629 | 0.0 | 0.0
182P/LONEOS | 2.93 | 16.91 | 2.846 | 1.007 | 0.713 | 0.0 | 0.0
189P/NEAT | 2.92 | 20.4 | 2.909 | 0.666 | 0.751 | 0.0 | 0.0
209P/LINEAR | 2.94 | 20.98 | 2.789 | 0.458 | 0.677 | 0.018 | 0.003
249P/LINEAR | 2.77 | 8.4 | 2.707 | 0.746 | 0.568 | 0.002 | 0.0
294P/LINEAR | 3.19 | 18.54 | 2.819 | 0.97 | 0.759 | 0.0 | 0.0
300P/Catalina | 2.7 | 5.68 | 2.963 | 0.813 | 0.719 | 0.003 | 0.001
321P/SOHO | 2.43 | 19.74 | 2.396 | 0.678 | 0.184 | 0.0 | 0.0
322P/SOHO | 2.52 | 12.59 | 2.347 | 1.044 | 0.2 | 0.0 | 0.0
384P/Kowalski | 2.91 | 7.29 | 2.958 | 0.894 | 0.782 | 0.0 | 0.0
414P/STEREO | 2.8 | 23.38 | 2.647 | 0.838 | 0.536 | 0.0 | 0.0
463P/NEOWISE | 2.98 | 29.5 | 2.492 | 0.997 | 0.492 | 0.0 | 0.0
D/1766 G1 (Helfenzrieder) | 2.66 | 7.87 | 2.705 | - | 0.526 | 0.0 | 0.0
D/1770 L1 (Lexell) | 3.15 | 1.55 | 2.612 | - | 0.618 | 0.0 | 0.0
D/1895 Q1 (Swift) | 3.73 | 2.99 | 2.677 | - | 0.757 | 0.0 | 0.0
P/2003 T12 (SOHO) | 2.57 | 11.48 | 2.894 | 1.019 | 0.618 | 0.0 | 0.0
Table 1: Near-Earth (q$<$1.3 au) JFCs that move on extremely stable orbits
over $10^{4}$ yr timescales.

####  3.3.4 Source region analysis

Another method to determine source regions of meteoroids from fireball data is
the use of debiased near-Earth steady-state models. These models are a
mathematical representation of the population of NEOs that accounts for the
observational biases inherent in the data collected by various telescopic
surveys. Such biases can occur due to factors like the limited sensitivity of
telescopes, which can preferentially detect larger or brighter objects, or the
positioning and timing of observations, which might miss objects with certain
orbits or are visible only at certain times. By accounting for these biases,
the model aims to represent the true distribution of NEOs as they exist in
space, independent of the limitations of our observations. By comparing the
back-tracked orbit calculated from fireball observations with the distribution
of orbits in the debiased model, it is possible to identify the most likely
source region from which the object originated. This has been used in many
studies previously to understand meteorite source regions (Bottke Jr et al.
2002; Granvik et al. 2018; Nesvorný et al. 2023).

Here, we have used the NEO model described in Nesvorný et al. (2023) as
another method to determine the source regions of these JFC-like fireballs.
However, the problem of size dependence of source regions, which has been
identified before, is particularly important to keep in consideration as the
model does not consider objects down to the meteoroid cm-m size range. So,
when applied to centimeter-meter-sized meteoroid datasets, we had to use the
maximum absolute magnitude in the model of H=25.

Based on the NEOMOD model, the JFC population is a more significant source of
the JFC-like fireball observations (Fig. 13) relative to the predictions based
on the 10 kyr dynamics. However, the NEOMOD model still also predicts that a
large majority of the fireballs (66-82%) come from main-belt sources for all
the networks. The DFN had the smallest JFC contribution according to the model
(18%), while the MORP and FRIPON networks both had the highest ($\sim$34%)
according to the model. Most surprisingly, it also predicts that only 43% of
the near-Earth JFC population is likely to be sourced from the JFC population,
with large proportions coming from the 11:5 (18%), 5:2 (15%), and 2:1 (11%)
MMRs. When this is compared to the orbital simulations (Fig. 14), the NEOMOD
seems to be overpredicting the contribution of the JFC population to the
fireball observations while simultaneously underpredicting for the near-Earth
JFC population.

As seen in Fig. 14, NEOMOD predicts very broadly that a large portion of the
fireballs beyond 3.5 au or at higher eccentricities are more likely to come
from the JFC source region in the model, a prediction that does not match the
stability of these objects during our 10 kyr simulations. As seen in Fig. 14
(c,e), all of the high-eccentricity fireballs originate from very stable
orbits during the 10 kyr simulations, which is a strong indicator that these
are not directly from the JFC population. The most likely regions to be JFC
population in origin tend to concentrate towards the intersection of the line
of equal perihelia equal to the Earth’s aphelion and the line of equal aphelia
corresponding to the perihelion of Jupiter.

Conversely, the NEOMOD model also does not clearly identify some of the most
unstable near-Earth JFCs within our dataset that overlap with the model (69
objects), and underpredicts greatly the instability of the population.
However, this is not a mistake of the model. A debiased NEO model works by
propagating fictitious particles from several source regions until they leave
the simulation, and their period of time in near-Earth space is weighted based
on considering the objects discovered by telescopic surveys and their inherent
biases. In this way, the model then organizes near-Earth space into bins of
a-e-i, and by checking the particles within each bin (weighted by
observations), the source region likelihoods can be estimated. It is crucially
important though to keep in mind that this model considers all objects, not
just JFCs. The JFC population is a small minority population within near-Earth
space. Thus, even though they are often constrained and defined by having an
orbit with a $2<T_{J}<3$, the asteroid population is much more numerous in
this region, and thus even a small level of diffusion by outer main belt
resonances significantly decreases the overall JFC source region likelihood on
these orbits. When only considering the near-Earth JFCs in the Horizons
database that are within the bounds of NEOMOD (69 objects), on average, it
only predicts a 29-43% JFC source region contribution (depending on absolute
magnitude estimate). To obtain a better estimate, one must include all of the
objects, including asteroids, on similar orbits. When the source regions for
all 1,860 NEOs on $2<T_{J}<3$ orbits were estimated using the NEOMOD model, we
found a much more reasonable estimate of 6-14%, which corresponds more nicely
to our estimate of 8-21% of the JFC-like fireball population being genetically
cometary based on our 10 kyr simulation results. This demonstrates clearly
that although the JFC population is characteristically constrained to these
orbits, even a minor diffusion of asteroids from the outer main belt can
overwhelm the a-e-i statistics.

Figure 13: Source region for JFC-like fireballs detected by the DFN, EFN,
MORP, and FRIPON determined by the NEOMOD debiased NEO model Nesvorný et al.
(2023). The source region probabilities were also determined for the near-
Earth portion of the JFC population; the low JFC source region likelihood for
these comets is due to the significantly higher number of asteroids from the
MB in the same a-e-i region.

(a) JFC-like Fireballs

(b) Near-Earth JFCs

(c) JFC-like Fireballs

(d) Near-Earth JFCs

(e) JFC-like Fireballs

(f) Near-Earth JFCs

Figure 14: Comparison of JFC contribution estimated using the NEOMOD model,
the $f_{q}$ index, and the percentage of clones that reach q$>$2.5 au during a
10 kyr simulation. Subplots (a,c,e) show data for JFC-like ($2<T_{J}<3$)
fireball datasets of DFN (circle), EFN (diamond), MORP (square), and FRIPON
(triangle). Subplots (b,d,f) show the near-Earth subset of the 661 JFCs used
in this study.

###  3.4 Meteorite falls

Another question is whether meteorite-dropping fireballs are contained within
the dataset and what kinds of orbits they originate from. The EFN dataset,
released by Borovička et al. (2022b), only contains four fireballs from JFC-
like orbits ($2<T_{J}<3$) that have a terminal mass estimated to be greater
than a gram. Of these four, none originate from beyond 3 au and $<<$1% of
particles had a close encounter with Jupiter during the 10 kyr simulations.

Figure 15: Distribution of $\alpha–\beta$ values for JFC-like fireballs from
the DFN, MORP, and FRIPON observation networks. Here $\gamma$ is the
trajectory slope relative to the horizontal. If a macroscopic event is
considered to have a final mass of $\geq$50 g, assuming $\rho_{m}$ = [2240,
3500] kg m-3 (carbonaceous and ordinary chondrite, respectively) and cdA =
1.5, meteorite-dropping events can easily be identified given the range of
possible shape change coefficients ($\mu$). The black lines correspond to the
ordinary chondrite density, whereas the red lines denote a carbonaceous
meteorite density, described by Eq.3 \- 6. The coloration is indicative of the
percentage of particle clones within the 10 kyr simulations that reached
perihelion values $>$2.5 au, and only fireballs that also fulfilled the
meteorite-dropping criteria of Vfinal $<$ 10 km s-1 and Hfinal $<$35 km are
considered likely meteorite droppers (after Brown et al. 2013).

Otherwise, for the DFN, FRIPON, and MORP networks, we utilized the
$\alpha–\beta$ methodology of Sansom et al. (2019) to identify potential
meteorite falls within the dataset. The $\alpha–\beta$ values are easily
calculated from the velocity-height data from any fireball and correspond to
the ballistic coefficient and mass-loss parameter, respectively. As seen in
Fig. 15, a majority of the fireballs are unlikely to drop any meteorite.
Assuming an ordinary-chondrite composition, we are expected to have somewhere
between 11 and 42 meteorites $>$50 g from the three fireball networks. Whereas
when a carbonaceous chondrite density is used, the estimate grows to between
18 and 62 meteorites $>$50 g. However, in Fig. 15, only the colored data
points that also fall below the limits are considered as the most likely
meteorite-dropping events, as they also fulfill the end height/velocity
criteria (Vfinal $<$ 10 km s-1 and Hfinal $<$ 35 km; Brown et al. 2013). When
combining the end height/velocity criteria with the $\alpha–\beta$
methodology, we find 21 potential meteorite-dropping events. That’s 22
potential meteorite-dropping events in total out of the 646 JFC-like
fireballs, as only one EFN event is predicted to have a terminal mass $>$50 g
(Borovička et al. 2022b).

The coloration in Fig. 15 is weighted according to the percentage of particle
clones in the 10 kyr simulations that reach a q$>$2.5 au, indicating
indirectly the probability of a close encounter with Jupiter over the time
period. As expected, nearly all of the likely meteorite-dropping events are
very stable during the 10 kyr simulations (dark blue), comprising 20 of the
events. However, two DFN events diverge from this trend. DFN events
DN210516_02 (78.9%) and DN220825_01 (57.9%), both have a likelihood of
reaching q$>$2.5 au during the 10 kyr timescale of over 50%. However, given
that the semi-major axis values of 2.96 au and 2.85 au are still within range
of the main belt and the longitude of perihelion values of 254.6∘ and 51.0∘
are not near the concentration of JFC values, the meteoroids could have still
very easily be transferred from the main-belt to these orbits. Additionally,
several studies have demonstrated that debris can migrate out onto these
orbits from the main belt (Fernández & Sosa 2015; Shober et al. 2020b, a;
Hsieh et al. 2020). Also, none of the identified likely meteorite-droppers
have an association with a meteor shower.

###  3.5 Shower Associations

As seen in Fig. 16(a), several meteor showers are present in this dataset.
Some of these are edge cases that have drifted over the $T_{J}\sim 3$
boundary, while others have likely parent bodies that also inhabit the
Jupiter-approaching region. In total, we found nine meteor shower clusters of
at least 3 fireballs with a $D_{N}<0.1$, a limit that produces limited false
positive rates for the datasets (Shober & Vaubaillon 2024). There are more
possible shower associations beyond just these nine showers, but these nine
are the only clear clusters with several fireballs in each. In Fig. 16(a), we
have plotted the minimum $D_{N}$ for each fireball after having compared every
fireball to every established shower on the IAU Meteor Data Center’s (MDC)
database101010https://www.ta3.sk/IAUC22DB/MDC2007/Roje/roje_lista.php?corobic_roje=1&sort_roje=0.
These showers include:

####  3.5.1 Quadrantids (QUA)

The Quadrantids meteor shower was only detected by the FRIPON network within
this study, with approximately 20 events matching the shower characteristics.
The lack of detections by the other networks could be a result of
observational bias against the detection of smaller, fainter meteoroids or due
to weather (e.g. Borovička et al. 2022b) because the shower has a very short
peak window (12-14 hours; Wiegert & Brown 2005). Despite its short duration,
the Quadrantids meteor shower is a strong annual shower. Peaking around early
January, it typically displays a zenith hourly rate of approximately 110 to
130 meteors under optimal viewing conditions (Abedin et al. 2015). The parent
body of the Quadrantid stream is identified as 2003 EH1, an Amor-type asteroid
with a comet-like orbit ($T_{J}=2.06$), indicating its potential as a dormant
or extinct comet (Jenniskens 2004). Given the very high inclination of the
stream ($\sim 72^{\circ}$) and the non-corresponding $\varpi$ of 90-100∘, the
proposed parent body (2003 EH1) is currently not in good agreement with the
core distribution of JFCs. However, the object exists in a Kozai-resonance,
along with other possible related bodies, that could lower the inclination in
exchange for eccentricity and render the orbit more resembling the bulk of
JFCs. The degree of separation of 2003 EH1 and the Quadrantid stream is most
consistent with a quick release of material around 200 years ago, possibly
from a fracturing event of a comet nucleus (Wiegert & Brown 2005).

####  3.5.2 Southern $\delta$-Aquariids (SDAs)

The Southern $\delta$-Aquariids are annually observed from late May to early
July, reaching their peak activity when the solar longitude is at $\lambda$ =
126∘ (Brown et al. 2010). The northern branch, although weaker, displays
activity from late July to late August, with its maximum activity occurring at
$\lambda$ = 139∘. Previously proposed to be related to the Marsden group
comets, the SDA are now generally thought to be related to the 96P/Machholz
complex (Abedin et al. 2018). This complex is also believed to include other
major showers and bodies such as asteroid 2003 EH1 and the corresponding QUA
shower, a result of a Kozai circulation cycle causing eight intersection
points with the Earth’s orbits (Babadzhanov et al. 2008). The Marsden group of
comets was found to be incapable of producing the observed profile features of
the SDAs alone (Abedin et al. 2018). Abedin et al. (2018) found that the most
likely scenario to reproduce the principal activity features of the
Quandrantids, Arietids, Southern $\delta$-Aquariids, Northern
$\delta$-Aquariids, and several other showers would be the capture of comet
96P/Machholz into a short-period orbit -$\sim$22 kyr ago. However, they also
found that the match to the activity profile could be improved if the comet
96P/Machholz broke up after 100 CE to form the Marsden group comets, an idea
proposed by Sekanina & Chodas (2005).

For the SDA, there are also 17 fireballs in the dataset with a D${}_{N}<0.1$,
and they are also almost entirely observed by FRIPON with 16 observations.
There are also one associated with the shower observed by the EFN. This
abundance of QUA and SDA observations by the FRIPON network demonstrates
clearly that these four networks are observing slightly different size ranges.
The FRIPON network has the highest limiting magnitude (i.e., it observes the
faintest/smallest meteoroids) of the four networks analyzed here. The
meteoroids of the QUA and SDA showers are normally only millimeters or less in
size, thus limiting the detection rate by the fireball networks.

####  3.5.3 $\alpha$-Capricornids (CAP)

The EFN, MORP, and FRIPON networks all contribute to the 15 fireballs
associated with the $\alpha$-Capricornids within the dataset, with 10, 3, and
2, respectively. The CAP shower is notable for its slow (21-23 km s-1) and
often bright meteors emanating from the constellation Capricorn. Short-period
comet 169P/NEAT (2002 EX12) has been identified as the likely parent body of
this shower (Jenniskens & Vaubaillon 2010). Comet 169P, as described by Kasuga
et al. (2010), is a medium-sized (2.3$\pm$0.4 km) nearly dormant comet. The
numerical simulations of Jenniskens (2004) found the object likely had a
massive breakup 4000-5000 yrs ago, losing about half of the comet’s original
mass. The $\alpha$-Capricornids we observe today are just the outskirts of the
resulting dust complex (Jenniskens & Vaubaillon 2010). Over the centuries, a
fraction of this dust has evolved into longer orbits and is now intersecting
Earth’s orbit, giving rise to the observed meteor shower. There are also other
proposals for associated parents of the $\alpha$-Capricornids. Asteroid 2017
MB1 has been recently proposed as being associated with the stream (Ye 2018).
Another candidate is P/2003 T12 (SOHO), which, according to Fernández & Sosa
(2015), may share a common origin with comet 169P following a fragmentation
event around 2900 years ago. However, Fernández & Sosa (2015) also argued this
common origin may have originated in the main asteroid belt based on the
stability of the orbits, a result supported by the 10 kyr simulation results
of this study (Fig. 16(b)).

####  3.5.4 Taurid Complex - Northern Taurids (NTAs) and Southern Taurids
(STAs)

The Taurid meteor shower, encompassing the Northern and Southern branches, is
a complicated, puzzling shower of long duration and wide breadth. Many bodies
have been speculated to be associated with the complex based on their similar
orbital history and proximity (Egal et al. 2021). However, Comet 2P/Encke is
widely recognized as the primary parent of the shower. The Taurid complex is
characterized by its low inclination and perihelia between 0.2 and 0.5 au,
influenced by planetary perturbations, resulting in its very diffuse structure
(Matlovič et al. 2017). The entire mass of the Taurid stream, estimated to be
around $10^{14}$ kg, is thought to have been released over the last 6 to 30
kyrs, indicating a mass loss rate higher than that of typical Jupiter family
comets (Jenniskens 2006). Also, this large stream of bodies contains a
diversity of size ranges, even observed to contain meter-scale debris (Brown
et al. 2013; Spurnỳ et al. 2017; Devillepoix et al. 2021). However, based on
the spectra and fragmentation characteristics, typical break up around
0.02–0.10 MPa, the meteoroids seem to be quite weak and possibly carbonaceous-
like (Matlovič et al. 2017). Most of the bodies are detached from Jupiter
($T_{J}>3$), but some can be observed on $T_{J}<3$ orbits, as seen by 21
fireballs in the study. These fireballs were observed by MORP, EFN, and
FRIPON, consisting of 15 NTA fireballs (5 MORP, 6 EFN, 4 FRIPON) and 6 STA
fireballs (4 EFN, 2 MORP).

####  3.5.5 $\eta$-Virginids (EVI)

The $\eta$-Virginids is a minor shower that occurs annually during February
and March. It is known to have stronger meteoroids that penetrate further into
the atmosphere, similar to the Geminids (Jenniskens et al. 2016; Borovička et
al. 2022a). This study has 12 associated with the shower, 4 DFN, 3 EFN, and 4
FRIPON events. This is the only shower distinctly present within the DFN JFC-
like ($T_{J}>3$) fireball database.

####  3.5.6 August Draconids (AUD) and $\kappa$-Cygnids (KCG)

A few minor showers are often overshadowed by the Perseids, which also occur
in August. Two of these are found within the fireball datasets: the August
Draconids and the $\kappa$-Cygnids. First reported in 1877, KCG is known for
its activity between August 3 and 31, peaking around August 18 (Jenniskens
2006). The asteroid 2008 ED69 is proposed to be the parent body of the stream,
originating during a breakup event 2–3 nutation cycles ago (3600–6000 yrs ago;
Jenniskens & Vaubaillon 2008). Additionally, Jones et al. (2006) found that
asteroids 2001 MG1 and 2004 LA12 have similar orbits to the KCG. Within the
JFC-like databases examined here, we also find a diffuse cluster of 12
fireballs that may be associated with the August Draconids or
$\kappa$-Cygnids, with 6 for each respectively. Most of AUD fireballs, with
eight in total, were observed by the EFN with the rest observed by FRIPON. The
KCG fireballs were observed by the EFN (3), FRIPON (2), and MORP (1).

####  3.5.7 October Draconids (DRA)

Lastly, we have three October Draconid fireballs observed by the EFN.
Considering the low $D_{N}$ values of $\sim$0.01, and the similar dynamics of
the meteoroid orbit, these are very likely genuine despite the low numbers.
The Draconid meteor shower, associated with the JFC 21P/Giacobini-Zinner, is
known for its occurrence in early October and is notable for the low velocity
of its meteors at around 20 km/s. The Draconids are distinctive due to their
fragile composition and low density (Borovička et al. 2007). The Draconid
meteoroids show varying grain compositions; some are coarse-grained while
others are fine-grained. This variance in grain size impacts the meteoroid’s
interaction with the atmosphere, influencing the light curves and deceleration
patterns observed. Elements such as Na, Mg, and Fe are present in nearly
chondritic proportions, but the differential ablation causes a preferential
loss of sodium at the beginning of the trajectory. These findings align with
the understanding of cometary dust as a complex mixture of materials with
diverse physical and chemical properties Borovička et al. (2007).

####  3.5.8 Shower dynamics

Surprisingly, despite the evident presence of showers in Fig. 16(a) in the
dataset, it is clear that, in fact, nearly all of the showers elude close
encounters with Jupiter that send them on higher perihelion orbits. When
compared to the sporadic background, in Fig. 16(b), all the showers are dark
blue in color, signifying there was a low percentage of particle clones that
reached q$>$2.5 au during the 10 kyr simulations. However, there is one shower
that stands out as being very consistent with JFC dynamics: the October
Draconids. Although there are only three EFN Draconid events, all three have a
65-70% probability of reaching a q$>$2.5 au within a 10 kyr period. There are
multiple other showers mention here also thought to have a cometary parent
body; however, these parents tend not to be explicitly classified as JFCs.
Furthermore, often, there seem to be several associated objects on nearby
orbits or those with similar dynamics, and these bodies are asteroids, comets,
or something in between. For example, comet 2P/Encke, which is widely accepted
as the primary parent of the Taurid Complex, is detached from Jupiter
dynamically and displays a mixture of characteristics of asteroids and comets.
To be clear, all of these objects exhibit chaos at some level and timescale.
Nevertheless, the chaotic behavior of JFCs is primarily dominated by very
close encounters with Jupiter which cause macroscopic changes in the orbits on
millennium timescales, and only the three Draconids here are consistent with
that diagnostic feature of the population.

(a)

(b)

Figure 16: Meteor showers shown in longitude of perihelion (∘) versus
inclination (∘) distributions for JFC-like fireballs detected by DFN (circle),
EFN (diamond), MORP (square), and FRIPON (triangle). Meteor shower clusters of
3+ fireballs are denoted with their official abbreviations. The coloration of
subplot (a) corresponds to the minimum $D_{N}$ calculated relative to all of
members of IAU MDC’s established shower list. The coloration of sublot (b)
corresponds to the number of particle clones generated within the
observational uncertainties of each fireball that reached a perihelion of 2.5
au or greater during a 10 kyr N-body simulation.

###  3.6 Case studies

Over the previous decades, there have been a handful of large JFC-associated
fireball case studies reported by several networks across the globe. These
individual fireball observations often claim to have witnessed large, strong
material on a JFC-like orbit, indicating the presence of durable material and
the possibility of JFC meteorites. Here, we have done the same 10 kyrs
numerical simulations based on the reported orbits of three of such JFC-like
fireballs (Table 2), generating 1000 particle clones within the orbital
uncertainties provided.

Network | a (au) | e |  $\iota$ (∘) | % of clones q$>$2.5 | $f_{q}$ | $f_{a}$ | Ref.
---|---|---|---|---|---|---|---
SPMN | 4.3$\pm$0.7 | 0.79$\pm$0.04 | 7.1$\pm$0.1 | 17.3 | 0.07 | 0.08 | Madiedo et al. (2014)
SPMN | 2.89$\pm$0.27 | 0.737$\pm$0.024 | 29.9$\pm$0.6 | 18.9 | 0.05 | 0.03 | Trigo-Rodríguez et al. (2009)
SACN | 3.58$\pm$0.02 | 0.725$\pm$0.002 | 9.06$\pm$0.02 | 39.7 | 0.15 | 0.08 | Hughes et al. (2022)
Table 2: Orbital elements (a-e-i) and 10 kyr simulation results for three very
bright fireballs reported to be originating from the JFC population observed
by the Spanish Meteor Netork (SPMN) and the Spalding Allsky Camera Network
(SACN).

As seen in Table 2, all three of these events have low probabilities of their
q values reaching 2.5 au on 10 kyr timescales. This is not surprising for the
two SPMN fireballs, as both have extremely high orbital uncertainties and can
easily be argued as main belt in origin. The published semi-major axis values
for the fireball reported by Madiedo et al. (2014) is extraordinarily high,
however, the uncertainties are so high that it is within 3 $\sigma$ of the
entire main belt. Meanwhile, the very bright (19-magnitude) fireball reported
by Hughes et al. (2022) has the highest likelihood of being a genuine JFC, but
it still had $<$50% of the particle clones in the simulation reach a
perihelion above 2.5 au, which is not statistically consistent with JFCs.
Also, while the orbit reported by Hughes et al. (2022) is likely very precise
as a multi-parameter fit was used (Gural 2012), the uncertainties are likely
vastly underestimated. The uncertainties would be expected to be larger, given
that only two observations were used for the triangulation (Shober et al.
2023). Also, both observations were over both 200 km away with a convergence
angle of less than 5∘. The initial velocity uncertainty expected for such a
low convergence angle should be $>$200 $\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$
according to the work of Jansen-Sturgeon et al. (2020) (Figure. 2) – four
times greater than the $\pm$50 $\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$
uncertainty quoted in Hughes et al. (2022).

##  4 Discussion

###  4.1 Orbital stability and dynamics

The analysis of the orbital trajectories of 661 JFCs retrieved from the NASA
HORIZONS database111111https://ssd.jpl.nasa.gov/horizons/ shows a consistent
trend with previous studies, with a majority of the population characterized
by their frequent close encounters with Jupiter over 10,000 years. These close
encounters rapidly change the orbits, particularly the perihelion distance on
hundred to thousand-year timescales. In addition, we also find that the JFC
population tends to concentrate toward low Lyapunov lifetimes (50-150 yrs).
This result is also consistent with previous studies of the chaos present in
this population, which tends to reduce the dynamical memory of these objects
(Tancredi 1995, 1998). However, as we start to examine JFCs in active orbits
(q$<$2.5 au) or even in near-Earth space, this dynamical fingerprint begins to
get blurry. The study by Fernández & Sosa (2015) found many stable JFCs within
near-Earth orbits, and this result is replicated here where we find 24
extremely stable JFCs on ”active” orbits (22 of which are NEOs). These objects
could be asteroids that have diffused out from the main asteroid belt or
possibly comets that are in an anomalously longer period of orbital stability.
Contamination from the main belt would not be completely unexpected, as JFCs
seldom spend time in the inner solar system, and those periods are often only
a few thousand years (Fernández et al. 2002). Furthermore, there is only
expected to be 0.1-1% of objects transferred from the JFC region to detached
orbits (Hsieh & Haghighipour 2016), a value 4-40 times lower than the rate
described here if all the bodies in Table 1 are detached comets. This low
percentage rate of detached orbits could still be interesting as the dynamical
lifetimes are much longer on these orbits that no longer encounter Jupiter
regularly. However, we would also need to have a highly physically evolved
object with an insulating layer present in order to survive the longer
timescales in the inner solar system, where JFCs are believed to have physical
lifetimes of a few thousand years (Levison & Duncan 1997; Di Sisto et al.
2009). This is believed to possibly be the case for comet 2P/Encke, which is
the parent body of the very active and large Taurid meteor shower complex. The
study by Levison et al. (2006) found that comet 2P/Encke’s detachment from
Jupiter could have resulted from gravitational interactions with JFCs and
terrestrial planets alone, however, these transitions are significantly longer
than the typical physical lifetimes of comets ($\sim 10^{3}$ yrs). The study
suggests that 2P/Encke likely became dormant after being influenced by Jupiter
and reactivated when its perihelion distance was reduced by the $\nu_{6}$
secular resonance. The research also highlights the need for considering non-
gravitational forces in explaining 2P/Encke’s orbit, while warning against
using over-simplified constant non-gravitational forces to achieve shorter
timescales.

However, given the considerable number of JFCs in near-Earth orbits found to
move on stable trajectories by Fernández & Sosa (2015) and in this study, the
contamination of dark, hydrated outer main belt asteroids in JFC-like orbits
is also quite considerable. It has since been demonstrated that asteroids from
the outer main belt are capable of diffusing out due to eccentricity
excitation by the 2:1 MMR and subsequent terrestrial planets encounters (Hsieh
et al. 2020). The objects from the outer main belt that are primarily
dominated by D- and P-type asteroids, could diffuse onto comet-like orbits and
be very difficult to discern from pristine comets from the trans-Neptunian
regions.

In the 661 JFCs studied here, we found a significant number of objects with
stable trajectories on $10^{4}$ yr timescales. Of the JFCs in the NASA
HORIZONS database on near-Earth orbits, we find that 22 of the 75
(approximately 30%) move on extremely stable orbits, with nearly all of the
1000 particle clones per object avoiding close encounters with Jupiter. Six of
these were designated as lost comets. Comets 3D/Biela, 5D/Brorsen, and
34D/Gale suffered major splitting events and were lost due to their physical
breakdown Fernández (2009). The other three are D/1766 G1 (Helfenzrieder),
D/1770 L1 (Lexell), and D/1895 Q1 (Swift), which were all observed for only
one perihelion passage and were lost due to their orbital uncertainty. The
three comets lost to disintegration and splitting events might indicate that
the longer stability of their orbits in near-Earth space might be a
contributing factor. Their arrival into a more stable orbit, spending more
time in the ‘active’ region compared to most JFCs, could explain their
physical demise. Thus, ignoring the three comets lost to high uncertainties
and considering the comets lost to splitting events as genuine JFCs this gives
us a final estimate of approximately 22% (16 out of 72 objects) as potentially
being asteroidal interlopers. This is consistent with the findings of
Fernández & Sosa (2015), which found that between 14-33% of near-Earth JFCs
have asteroid-like trajectories on 10 kyr timescales. In addition, 15 of the
16 are found to have a$<$3.2 au, which strengthens the argument for an origin
in the main belt. The only very stable body with a considerable semi-major
axis is 66P/du Toit (a$\sim$6.02). Comet 66P/du Toit was similarly identified
by Fernández & Sosa (2015) for being highly stable, and they found the object
to be trapped in a 4:5 MMR with Jupiter with critical angle librating around
180∘. Our estimate could be slightly higher as these are just the objects on
extremely stable orbits, and there were other objects in our analysis that had
lower-than-average likelihoods of close encounters with Jupiter.

The study by Ye et al. (2016) found by analyzing 13,567,542 meteor orbits
recorded by Canadian Meteor Orbit Radar (CMOR), which captures the ionized
trails of mostly submillimeter-sized objects hitting the atmosphere, comets
likely disrupt more often than they become dormant. Their study used these
meteor observations to identify dormant comets within the near-Earth object
(NEO) population, and they identified five statistically significant meteor
showers, suggesting a dormant comet fraction of at least 2.0 $\pm$ 1.7% in the
NEO population. The findings indicate a low dormancy rate of approximately
$10^{-5}yr^{-1}$ per comet and support the hypothesis that disruption and
dynamical removal, rather than dormancy, are the prevalent end states for
near-Earth JFCs. These studies have estimated that there could be as many as
20-30 dormant comets in near-Earth space (Mommert et al. 2015; Ye et al.
2016). Other similar estimates have been made for the proportion of dormant
comets in the NEO population, assuming the number on $T_{J}>3$ orbits is
negligible, and they range between 2-14% (Bottke Jr et al. 2002; Fernández et
al. 2005; Mommert et al. 2015; Granvik et al. 2018). There are only 75 near-
Earth JFCs, of which a quarter have very asteroid-like dynamics. At the same
time, there are currently 1,875 NEAs with JFC-like orbits, according to the
NASA HORIZONS database. If this is the case, it is not surprising to find an
abundance of centimeter-to-meter debris with asteroid-like dynamics on
$2<T_{J}<3$ orbits, as there are two orders of magnitude more objects at 100 m
to km scale from the main belt compared to JFCs.

Fireball networks also often record events originating from these JFC-like
orbits, and these have been used to better understand the JFC population.
However, based on the dynamics results of Shober et al. (2021), only 3 of the
50 sporadic JFC-like fireballs detected by the DFN displayed comet-like
frequent encounters with Jupiter. Shober et al. (2021) interpreted this
finding as indicating that almost none of the sporadic JFC-like meteoroids
impacting the Earth were originating from JFCs. More recently, Borovička et
al. (2022b) examined the 824 fireballs detected by the EFN between 2017-2018
and disputed these claims. They argued that the use of dynamic masses (i.e.,
mass estimates based on deceleration profiles) in the methodology of Shober et
al. (2021) prohibited the use of low-deceleration fireballs and thus severely
biased the data. This use of dynamic masses is certainly a caveat, and the
analysis of Borovička et al. (2022a) correctly describes the inability to use
them for the PE criterion – a criterion used to describe the strengths of
meteoroids based on a fireball’s ablation characteristics. However, Borovička
et al. (2022a) assumed that low-deceleration events were removed, and this is
untrue, as can be seen in the data shared by the study where 29 of the 50
fireballs (58%) have less than 20% deceleration. In contrast, the EFN JFC-like
dataset contains 66% events with low deceleration. When a chi-squared test is
applied to see whether the EFN has statistically significantly more low-
deceleration events as claimed by Borovička et al. (2022a), a P-value of 0.373
is found, i.e., the datasets do not differ significantly as claimed.

Still, there are significant differences between the orbital datasets of the
EFN and DFN due to the hardware of the networks themselves. As explained in
Howie et al. (2017b), the absolute timing of the DFN is recorded very
differently compared to the EFN, as the timing is encoded into the image
itself in a de-Bruijn sequence using a liquid-crystal shutter. By doing this,
the DFN can achieve submillisecond precision on timing. However, the fireball
events need to be at least one second long to have enough points in the de
Bruijn sequence to get a unique solution. This one-second minimum for the DFN
was viewed as acceptable as the primary objective of the network is to recover
meteorites; an objective achieved as the team has now used observations in the
recovery of 15 meteorites around the
world121212https://dfn.gfo.rocks/meteorites.html.

Thus, a bias is present in the DFN data against short-duration fireballs. To
see how this bias would affect the data, assuming the EFN dataset is
comparable in every other way, we compared the orbital distribution of
fireballs $<$1 sec (29%) and $>$1 sec (71%) found within the EFN dataset
(Borovička et al. 2022b). As seen in Fig. 17, this bias within the EFN dataset
seems to have the greatest effect on reducing the number of fireballs
originating from between 3.0-3.5 au. This coincides nicely with the range
described as being the “comet domain” in Borovička et al. (2022a), seeming to
support their claim that the results of Shober et al. (2021) are missing the
cometary component (however, for a different reason than they claimed). This
breaks down however, as a vast majority of JFC-like EFN fireballs from
Borovička et al. (2022b) and 66% of those beyond 3 au have relatively low
probabilities ($<$50%) of close encounters with Jupiter on 10 kyrs timescales
(Fig. 11) and have more dispersed and larger Lyapunov lifetimes compared to
the JFC population (Fig. 10). Additionally, this “comet domain” indicated by
Borovička et al. (2022a) to mostly contain weak cometary material with a
subset of strong asteroidal objects, does not account for the 2:1 MMR which
can produce asteroids on comet resembling orbits (Hsieh et al. 2020). As seen
in Fig. 9, 62 of the 213 JFC-like EFN events are within 3$\sigma$ uncertainty
of the resonance, likely indicating it is a source of these weaker meteoroids
on stable orbits.

Figure 17: Semi-major axis (au) versus eccentricity heat map, marking the
differences in concentration of fireballs detected by the EFN on JFC-like
orbits (Borovička et al. 2022b) for fireballs of less than one second and
greater than one second. Blue areas indicate regions where $<$1 second
fireballs have a higher concentration of data points compared to the number of
fireballs $>$1 second, and the red is the inverse

Based on our 10 kyr numerical simulations, the DFN, EFN, FRIPON, and MORP have
9%, 21%, 8%, and 18% respectively of their JFC-like fireball population likely
($>$50%) to reach q$>$2.5 au over the integration time. This indicates that
only a minor fraction of the JFC-like fireballs are pristine cometary material
delivered from the trans-Neptunian region. The variations between the datasets
are likely due to a mixture of hardware and data processing choices which
influence the composition of the datasets. While we are still uncertain of all
the exact causes of the differences between the four datasets, based on the
dynamics and fireball observations, the EFN network’s abundance of shower and
weaker meteoroids likely indicates that the EFN JFC-like subset contains some
of the smallest, faintest objects. The FRIPON network contains much more
meteors within the dataset, but given the importance of orbital uncertainties
in analyzing the dynamics of these fireballs, the FRIPON observations were
limited to fireballs observed by four or more cameras. This likely introduces
another bias into the dataset; however, based on preliminary analysis of
FRIPON event with only two or three observations (Shober et al. 2023), this
choice is a reasonable one. Understanding these differences and accurately
characterizing the biases of the datasets is critically important to better
understand the meteoroid population as a whole. As equipment to conduct
fireball and meteor observations continues to become more affordable, we need
to start sharing our data reduction methods and hardware specifications more
openly to compare and ensure the data being collected by the community is
translatable (Shober et al. 2023).

When we compare the various criteria for classifying fireball orbits as
potential JFC-like candidates, we notice that while 646 orbits match the
simple criterion ($2<T_{J}<3$), there are only 237 fulfilling the more
stringent T14’s criteria, and 329 where at least one clone q$>$2.5 au over the
integration time. A detailed comparison between the T14’s orbital criteria and
the Fernández & Sosa (2015)’s dynamical criteria can be done by comparing the
T14’s classification of the fireballs as a function of the fraction of clones
reaching q$>$2.5 au over the integration time. A large fraction of clones
correspond to unstable orbits, typically of JFCs. A comparison of these
criteria is shown in Fig. 18: the blue bars are the number of meteoroids with
an increasing fraction of clones reaching q$>$2.5 au (e.g. there are 219
objects with a fraction of clones larger than 10%); the orange bars are among
the corresponding set, the number of meteoroids that fulfill the JFC criteria
of T14 (in the previous example there are 185). The numbers are converging for
a higher fraction of clones; for a fraction $>$50%, the numbers are almost
identical (81 and 79). We conclude that the sets selected by the orbital and
dynamical criteria converge for the events with high probabilities of reaching
q$>$2.5 au orbits during our integrations.

Figure 18: Comparison of the proportion of the 646 “JFC-like” ($2<T_{J}<3$)