Jupiter’s Metastable Companions

Jovian co-orbitals share Jupiter’s orbit and exhibit 1:1 mean-motion resonance with the planet. This includes >10,000 so-called Trojan asteroids surrounding the leading (L4) and trailing (L5) Lagrange points, viewed as stable groups dating back to planet formation. A small number of extremely transient horseshoe and quasi-satellite co-orbitals have been identified, which only briefly (<1,000 yr) exhibit co-orbital motions. Via an extensive numerical study, we identify for the first time some Trojans that are certainly only “metastable”; instead of being primordial, they are recent captures from heliocentric orbits into moderately long-lived (10 kyr–100 Myr) metastable states that will escape back to the scattering regime. We have also identified (1) the first two Jovian horseshoe co-orbitals that exist for many resonant libration periods and (2) eight Jovian quasi-satellites with metastable lifetimes of 4–130 kyr. Our perspective on the Trojan population is thus now more complex as Jupiter joins the other giant planets in having known metastable co-orbitals that are in steady-state equilibrium with the planet-crossing Centaur and asteroid populations; the 27 identified here are in agreement with theoretical estimates.


INTRODUCTION
The five famous Lagrange points of the circular restricted three-body problem are locations relative to the moving planet where objects have tiny relative accelerations.In particular the 'triangular' L4 and L5 Lagrange points are located 60 degrees ahead of and behind the planet along its orbit, and small bodies can oscillate for long durations back and forth around these points.The L4/L5 stability was initially a theoretical discovery, which was followed by the first Trojan detections in 1906 (Nicholson 1961;Shoemaker et al. 1988), but now include more than 10,000 cataloged members; these >10,000 Trojans are viewed as stable populations that date back to planet formation.
Twenty-five years ago, Levison et al. (1997) computed the stability of the first 270 Jupiter Trojans on their nominal orbits, showing that some Trojans may leave in the next 0.3-4 billion years; that study assumed all Trojans were primordial and that any recent departures were due to a combination of collisions and dynamical erosion, allowing some primordial Trojans to leak away at the current epoch.Here we will demonstrate the additional importance of recent temporary (metastable) captures into and out of co-orbital states on the shorter time scales of tens of kyr to Myr.
Most planets are now known to host temporary co-orbital companions (reviewed in Greenstreet et al. (2020) and Alexendersen et al. (2021)), defined as objects undergoing oscillation (libration) of their 1:1 resonant argument for time scales much shorter than the age of the Solar System before escaping the resonance; for direct orbits the resonant argument is simply the angle between the mean longitudes of the objects and planet.In addition to Trojans, co-orbital motion can be of the horseshoe type (when the small body passes through the direction 180 o away from the planet and motion encloses both the L4 and L5 points).Like Trojan motion, horseshoe orbits were predicted analytically, but are in most cases very unstable (Rabe 1961).No long-term stable horseshoe sharing a planet's solar orbit has ever been observed.Lastly, in the frame co-rotating with Jupiter, so-called 'quasi-satellites' have orbits that maintain large-distance motion encircling the planet (Wiegert et al. 2000).
Restricting our attention to the giant planets, Uranus and Saturn do not have L4 and L5 points stable for 4 Gyr (Nesvorny & Dones 2002).Nevertheless a metastable uranian L4 Trojan (Alexandersen et al. 2013) and a metastable saturnian horseshoe orbit (Alexendersen et al. 2021) are known; 'metastable' objects are here defined by undergoing many resonant argument librations before exiting the co-orbital state.Neptune's L4 and L5 points have long-term stability, but both stable and metastable Neptune Trojans are known (Horner & Lykawka 2012;Lin et al. 2021).Curiously, Jupiter has been the sole giant planet to have no known metastable co-orbitals, despite the expectation that the planet should host such a population (Greenstreet et al. 2020).
Planet-crossing small bodies can (rarely) find their way into co-orbital states, and numerical simulations can estimate both the steady-state fraction relative to the current planet-crossing population and the expected distribution of temporary-capture time scales (see Discussion).Because Jupiter is constantly being approached by objects originating in the outer Solar System (Centaurs, that become Jupiter Family comets), and given the estimated number of Jupiterencountering Centaurs, Greenstreet et al. (2020) calculated that the metastable capture fraction was high enough that metastable jovian co-orbitals should exist and trapping would generate all of Trojan, horseshoe, and quasi-satellite motions.Examples of all of these types will be illustrated in our results below (see Figure 1).
There has been a great deal of work studying the complex problem of co-orbital companions (Christou 1999;Morais & Namouni 2013a,b, 2019;Karlsson 2004;Beauge & Roig 2001;Wajer & Krolikowska 2012;Wiegert et al. 2017;DiRuzza et al. 2023); these studies have either been done in the context of a simplified problem (one planet, sometimes on a circular orbit) or for time scales that are only slightly longer than the resonant libration period (of hundreds of years) or did not explore the range of behaviors and time scales possible due to the orbital uncertainties.Our work pushes the sample size and the level of the model detail much further by using full N-body simulations, by exploring time scales covering thousands of resonant libration periods, and by utilizing large numbers of 'clones' drawn from the orbital uncertainty region for determining the robustness of the resonant states; we also study the entire population of known objects with semimajor axes near that of Jupiter (nearly 12,000 objects).As a result, we have identified not only the first such metastable (2-13 kyr) jovian horseshoe orbits, but also the first known set of jovian Trojans which are metastable on intermediate time scales of 0.01-30 Myr and must be recently captured into L4 or L5 motion, increasing the complexity of how we should view the Jupiter Trojan population.

Production of Sample Set and Dynamical Integrations
To produce the sample set for this study, we queried the JPL Horizons Small Body Database Browser1 for objects fitting the following constraints: 4.5≤a≤5.9au (semimajor axis a within twice Jupiter's Hill sphere radius), semimajor axis uncertainty, a-sigma, is defined, and the observational arclength, data-arc span, is defined and is >30 days.We then manually removed all cometary provisional designations.In August 2022 this resulted in a sample set containing 11,581 known objects in the near-Jupiter region with arc-lengths of at least 30 days to ensure the orbital uncertainty was small enough to confidently be used to determine each object's orbital stability in the 1:1 co-orbital resonance with Jupiter.
We then used the Small Body Dynamics Tool (SBDynT)2 to query the JPL Horizons Small Body Database Browser to obtain the orbit and covariance matrix of each small body in our sample set, including for the best-fit orbit and 999 clones of each object within the orbital uncertainty region.This produced a set of 1000 "clones" (best-fit orbit and 999 clones) for each of our 11,581 objects, totaling ≃ 11.6 million state vectors.For more details on how our sample set is produced, see Section A.1 below).
To date, we have numerically integrated the 1000 clones for all of the 11,581 objects for 0.5 Myr into the future using the SWIFT-RMVS4 package (Levison & Duncan 1994).In the Venus-Neptune planetary input files, we expanded Jupiter's radius by 1000x and turned on the "lclose" exit condition in SWIFT to remove particles from the integrations  Osculating semimajor axis vs eccentricity for the 11,581 objects with a ≃ aJ = 5.20 au that we classify with numerical integrations.The 11,423 "Trojans" (cyan) are objects for which ≥95% of their 1000 clones remain in 1:1 jovian resonance for 0.5 Myr.The 27 "Transients" (green) have ≥95% of their clones remain resonant for ≥1 kyr, but then leave the resonance (see Table 1).The 124 "Non-Resonant" (red) objects have ≥95% of their 1000 clones ejected from the resonance in <1 kyr (see Table 5).The 7 "Insecure" (orange) objects have 5%-95% of their 1000 clones remain in the resonance for ≥1 kyr before escaping (i.e., these objects would likely move to either "non-resonant" or "transient co-orbitals" upon further improvement of their orbital uncertainties; see Table 4).The dashed rectangle shows the a, e region that JPL Horizons and the Minor Planet Center (personal communication, Peter Veres) currently define as the 'jovian Trojan' parameter space; the 14 non-resonant objects in this box (listed in Table 5) are not Trojans, however, given that ≥95% of their 1000 numerically-integrated clones are ejected from the resonance in as little as tens or hundreds of years.The 27 metastable transients (green) have a larger range of semimajor axes, eccentricities, and inclinations (see Figure 4 for the semimajor axis vs inclination and eccentricity vs inclination projections) than the stable Trojans (cyan); objects can become temporarily bound to the resonance along its borders that stretch beyond the stable L4/L5 regions (cyan).
when they come too close to Jupiter.In this study of 1:1 co-orbital resonant behavior, any particle that comes within 1000x Jupiter's radius (≃0.48 au, or about 2 Hill spheres) of the planet is unlikely to remain stable in the resonance and we terminate its integration.We use a base time step of 3.7 days and an output interval of 1000 yrs.Particles are removed from the integrations when they get within 0.4 au or beyond 19.0 au from the Sun or too close to Jupiter as described above.We are currently continuing to integrate all ≃ 11.6 million state vectors for longer time periods with the goal of eventually reaching 4 Gyr.

RESULTS
We used the numerical integrations of the observationally-derived orbits and 999 clones within the orbital uncertainty region (≃11.6 million state vectors) to search for semimajor axis oscillation around Jupiter's value of 5.20 au as well as resonant argument libration for periods of time long enough (>1 kyr) to distinguish transient co-orbital capture or nonresonant behavior from primordial Trojan stability (Greenstreet et al. 2020;Alexandersen et al. 2013;Alexendersen et al. 2021).This calculation required approximately 20 CPU years on a Beowulf cluster at the University of British Columbia.Details of the methods used for co-orbital detection, resonant island classification, and determination of resonant-sticking time scales can be found in Sections A.2 and A.3.
We securely identify the transient co-orbitals and non-resonant objects in the sample of 11,581 objects in the 'near-Jupiter population' (i.e., semimajor axes a =4.5-5.9 au, within ≃ 2 jovian Hill sphere radii of Jupiter's a J ).We classify objects as belonging to one of the following dynamical classes based on their fraction of resonant clones and resonant time scales: "Trojans", "Transients", "Non-Resonant", or "Insecure" (see Figure 2 caption, Sections A.2 and A.3, and Table 3 for details).Figure 2 shows the semimajor axis vs eccentricity distribution of the sample of near-Jupiter objects along with our classifications.The "Trojans" (objects for which ≥95% of the 1000 clones remain in the 1:1 jovian resonance for 0.5 Myr) are deemed long-term stable and have not been integrated beyond this time scale; in the future we will extend these integrations to 4 Gyr to study the stability of these objects on Solar System time scales.All other objects ("transient", "non-resonant", and "insecure") have been integrated for time scales long enough that all 1000 clones have left the resonance; these integration time scales range from a few hundred years for the non-resonant objects to up to ∼2 Gyr for the transient co-orbitals.We note that some "transient" or "insecure" objects can become trapped in the 1:1 resonance multiple times during the integrations.We base our classifications on the start of the integrations (i.e., the current time) and do not discuss (rare) multiple resonant traps in this paper.
Among the near-Jupiter sample, we have identified 27 objects (Table 1), which we are confident are not primordial objects.Instead, they are almost certainly recently captured as Jupiter co-orbitals that remain metastable for time scales of 10 3 − 10 8 years.While each of these 27 objects share a commonality with the primordial Trojans by their presence in the 1:1 jovian mean-motion resonance, they are unique in their much shorter resonant stability time scales that can only mean that they are recent captures into the co-orbital population and are thus required to be placed in a category of jovian co-orbitals separate from the primordial Trojans.and 2015 YJ22 as a horseshoe (which we classify as a L5 Trojan), but we follow their orbital evolutions much longer and show that these objects leave the resonance and are not primordial.First, we identify 12 L4 and 4 L5 Trojans (four of which are shown in Figures 1 and 3) that are surely unstable on time scales much shorter than ever previously discussed (only ∼Gyr time scales are discussed in Levison et al. (1997)).The median time scales over which these metastable Trojans escape the resonance range from 1 kyr-23 Myr (Table 2), however, their observational uncertainties result in instability time scales that vary by an order of magnitude or more, as evidenced by the range in escape times of each object's 1000 clones (see Figure 3).This rapid departure means these 16 L4/L5 metastable Trojans cannot be members of the primordial population which are departing today, but must be recent metastable captures.
To date, no transient horseshoe co-orbitals of Jupiter have been identified to librate in the resonance on time scales of more than a couple hundred years (long enough for the object to experience several libration periods), despite the expectation that they should exist among the metastable jovian co-orbital population (Greenstreet et al. 2020).
We have here identified the first two known metastable horseshoes of Jupiter: 2015 OL106 and 2016 TE71.The latter provides the first known example of a real object that remains in horseshoe motion with Jupiter for dozens of libration periods and resembles historical predictions of jovian horseshoe behavior (Rabe 1961).2016 TE71 is shown in Figures 1 and 3.The number in () after each designation is the median resonant time scale for each object's current trap in the 1:1 resonance.For the full list of resonant sticking time scales for each of our 27 identified metastable jovian co-orbitals, see Table 2.
Altogether, our metastable identifications include 12 L4 Trojans, 4 L5 Trojans, 2 horseshoes, 8 quasi-satellites, and the retrograde jovian co-orbital (514107) Ka'epaoka'āwela 2015 BZ509.We note that a handful of these objects have been previously classified (Karlsson 2004;Wajer & Krolikowska 2012;DiRuzza et al. 2023) based on their dynamical behavior over the next few hundred to couple thousand years (see captions for Tables 1, 4, and 5); differences between previous shorter time scale classifications and the longer metastable time scale classifications presented here are discussed below.Figure 1 shows the forward-integrated motion for a single libration period for six metastable object examples.
A unique aspect of our work is to determine the time scales over which these objects (and the clones representing their orbital uncertainty) will eventually escape the resonance.To determine their metastable time scales, we extended each object's integrations until all 1000 clones were removed (most often for getting too close to Jupiter).The cumulative distributions for the resonance escape times for the 1000 clones of each of the six objects shown in Figure 1 are given in Figure 3.This figure also presents our measurement of the instability time scale for the retrograde co-orbital (514107) with median value of 3.6 Myr; Wiegert et al. (2017) estimated that the object remained in the near-Jupiter region for a lower limit of at least 1 Myr, while Namouni & Morais (2020) estimated a median lifetime of 6.5 Myr for the object to escape the Solar System or collide with the Sun.The examples shown in Figure 3 depict the range in metastable resonant sticking time scales (10 3 − 10 8 years or longer) we have identified so far.Table 2 contains the full list of resonant sticking time scales for each of our 27 identified metastable jovian co-orbitals.For more details on the determination of the resonance escape time scales, see Section A.3.

DISCUSSION
After the identification of asteroid (514107) as a retrograde jovian co-orbital (Wiegert et al. 2017), these are the first securely-identified metastable jovian co-orbitals for which the resonant sticking time scales have been established.While other groups (Beauge & Roig 2001;Karlsson 2004;Wajer & Krolikowska 2012;DiRuzza et al. 2023) have identified resonant behaviors of some of these objects, those analyses do not extend beyond the next ∼1-10 kyr nor do they utilize large numbers of clones drawn from the orbital uncertainty region for determining the certainty of a resonant classification.We confirm the current non-resonant and quasi-satellite classifications for a handful of objects (see Tables 1 & 5).However, our analysis is largely unique in identifying the transient nature of these objects by determining the time scales over which they (and the clones representing their orbital uncertainty) will eventually escape the resonance.
We find a number of resonant classifications that differ from previous studies (Beauge & Roig 2001;Karlsson 2004;Wajer & Krolikowska 2012;DiRuzza et al. 2023); these objects are noted in Tables 1, 4, & 5.Note that DiRuzza et al. ( 2023) include many objects in their analysis having arc lengths of ≤5 days, which we omit given our requirement that objects have arc lengths >30 days to ensure their orbital uncertainty regions are determined by the observations rather than dominated by orbit fitting assumptions.We additionally require resonant objects to librate in the 1:1 for at least 1 kyr in order to experience several libration periods before possible departure from the resonance (in the case of the transient captures).This is responsible for the classification differences for the objects that we classify as non-resonant that other studies find are resonant during the <1 kyr time scales they use (e.g., DiRuzza et al. (2023) provide classifications based on 600 yr integrations).In addition, we integrate each object's 1000 clones until all the clones have been removed from the integrations, which allows us to securely classify each co-orbital as transient in nature and determine the time scales over which they are stable in the resonance.This differs from the majority of the previous studies, which can only determine if an object is currently resonant but not how long it will remain resonant nor the fact that observational uncertainties can result in instability time scales that vary by an order of magnitude or more (see Figure 3).
We expect the number of transient co-orbitals and primordial Trojans among the 11,581 object sample to shift as we continue to integrate the 1000 clones for time periods longer than 0.5 Myr.Very long-lived resonant objects unstable in ≲1 Gyr (i.e., long-lived temporary captures) will become evident in longer integrations, shifting some objects from "Trojan" to "transient co-orbital" classification.This will then meld into the few long-known Jupiter Trojans unstable on Gyr time scales, which was suggested (Levison et al. 1997) to be due to a combination of long-term dynamical erosion and collisions.
Our perspective is thus now more complex.The Jupiter co-orbital population consists of a mix of objects with different resonant time scales that we very loosely divide into the following categories: extremely transient (≲1 kyr), metastable (10 kyr-100 Myr), primordial Trojan erosion (∼Gyr), and stable Trojans (longer than 5 Gyr Solar System time scales).Cases of extremely transient objects, which only last one (or a few) resonant libration periods, have been studied (for example, Beauge & Roig 2001;Karlsson 2004;Wajer & Krolikowska 2012;DiRuzza et al. 2023).Here we have shown for the first time that Jupiter joins the other giant planets by having recently-trapped co-orbitals that last for an enormous range of metastable time scales (10 kyr -100 Myr) consistent with the transient co-orbital populations of all the giant planets.At the very longest time scales, only Jupiter and Neptune harbor both stable Trojan swarms and Trojans whose current stability time scales are of order Gyr.These latter objects can be a combination of the longest-lived traps of Centaurs and the slowly eroding edges of the original primordial population.The metastable objects we identify in this paper, however, must be recently captured into the co-orbital state out of the planet-crossing Centaur population, with a possible (probably small) contribution from escaping main-belt asteroids (Greenstreet et al. 2020).
The metastable co-orbitals identified here thus represent the discovery of the first (curiously-missing) jovian members of the expected transient co-orbital population accompanying each giant planet (Alexandersen et al. 2013;Greenstreet et al. 2020;Alexendersen et al. 2021).Numerical simulations of the Centaur and escaped asteroid populations, both of which can become temporarily-trapped into 1:1 jovian resonance, allowed Greenstreet et al. (2020) to compute the steady-state fractions present in the jovian co-orbital population at any given time.Given the number of absolute magnitude H < 18 (sizes of order 1 km) near-Earth objects (NEOs) and Centaurs (Lawler et al. 2018), Greenstreet et al. (2020) estimated that there should be ∼1-100 metastable jovian co-orbitals that remain resonant on time scales of ≲10 Myr.Here we identify 27 metastable jovian co-orbitals, all of which have H < 18, that remain stable for time scales of 10 3 − 10 8 years, in agreement with the theoretical estimate.
More metastable jovian co-orbitals will certainly be telescopically detected; given the rarity of capture into co-orbital resonance these additional co-orbitals are likely to be small, which is partly the reason more have not been identified to date by current surveys.The upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), with its large aperture and magnitude depth, should increase the number of Jupiter Trojan detections by ∼25x (LSST Science Collaborations 2017).These fainter detections will also provide more objects currently in metastable traps with Jupiter; their identification as metasable, however, will require more than simple osculating element cuts in semimajor axis and eccentricity near Jupiter's values, as our massive numerical study has demonstrated (see Figure 2).
The Lucy spacecraft mission will visit five Trojans during 2027 -2033 (Levison et al. 2021).We have carefully integrated these Trojans for 50 Myr to study their stability in the 1:1 jovian resonance.We find that all 1000 clones for each of these five mission targets remain stable in the resonance over this time scale and thus are almost certainly primordial objects.
A preliminary examination of the (sparse) color data from the Sloan Digital Sky Survey (Sergeyev & Carry 2021) for the faint metastable co-orbitals identified here shows that, relative to most known Trojans (Szabo et al 2007) and the Lucy flyby targets, the objects 2016 TE71 (metastable horseshoe), (288282) 2004 AH4 (metastable L5 Trojan), and (163240) 2002 EM157 (metastable L4 Trojan) have evidence for redder photometric g − r and/or g − i optical colors than typical Trojans.This would be expected if they are recently trapped Centaurs.This work is supported by NASA Solar System Workings grant 80NSSC22K0978.The integrations used for this work's massive numerical study were run on a Beowulf cluster at the University of British Columbia.This work utilized the Small Bodies Dynamics Tool (SBDynT) (https://github.com/small-body-dynamics/SBDynT)and the Keplerian-to-cartesian element conversion tool from THOR (Tracklet-less Heliocentric Orbit Recovery; https://github.com/moeyensj/thor).We wish to thank Kat Volk for allowing us access to and helping us to use the SBDynT for this work, Mike Alexandersen for sharing his co-rotating reference frame plotting script that was adapted for producing the relevant plots in this paper, and Pedro Bernardinelli for helpful discussions that improved the quality of the paper.BG acknowledges funding support from the Canadian Space Agency and NSERC.
Lastly, objects for which 5 − 95% of their 1000 clones remain resonant for at least a single 1 kyr running window period are classified as "insecure".Upon further improvement of their orbital uncertainties, these objects would likely move from an "insecure" classification to either "non-resonant" or "transient co-orbitals".We identify 7 "insecurely" resonant objects among our sample set of 11,581 near-Jupiter objects; each of these 7 objects are classified by the MPC/JPL as asteroids (see Tables 3 & 4).

A.3. Determination of Resonant Sticking Time Scales
Any object in our 11,581-object sample set found to have at least one clone that does not remain resonant for the duration of the 0.5 Myr integrations has had their integrations extended (or are being extended) to the point where all 1000 clones have been removed from the integrations by entering one of the exit criteria described above.The 27 metastable co-orbitals, 124 non-resonant objects, and 7 "insecure" objects all fall into this category; none of 11,423 L4/L5 Trojans in our sample set had a single clone leave the 1:1 jovian resonance in the 0.5 Myr integrations.While the non-resonant objects had <5% of their 1000 clones librate in the resonance for ≥1 kyr, some non-resonant objects did have some number of clones that remained resonant for at least that length of time.The number of transient clones for each non-resonant object and the maximum trap durations of those transient clones are listed in Table 5, along with the same information for the "insecure" objects listed in Table 4.
These longer integrations have been run for tens to hundreds of Myr, or in one case ∼2 Gyr.The extension of these numerical integrations until the final clone has exited allows us, for the first time, to determine their resonant trapping time scales (see Tables 2, 4, & 5, and Figure 3).A resonant "trap" includes the duration of consecutive 1 kyr running windows for which a state vector satisfies our resonant criteria described above.Some "transient" or "insecure" objects can become trapped multiple times during the integrations.We base our classifications on the start of the integrations (i.e., the current time) and do not discuss (rare) multiple resonant traps in this paper.Table 2. Resonant island configuration and resonance escape time scales for our 27 identified metastable (10 3 − 10 8 yr) jovian co-orbitals (i.e., objects we classify as "transient" that have ≥95% of their 1000 clones librate in the 1:1 jovian resonance for at least 1 kyr and are then ejected from the resonance (green points in Figures 2 & 4).Current resonant island configurations are classified as L4 Trojan, L5 Trojan, Horseshoe (HS), Quasi-satellite (QS), or Retrograde (R) motion.Min, median, and max trap durations refer to the amount of time the 1000 clones for each of these objects remain trapped in the 1:1 jovian resonance before being ejected.Objects in bold are shown in Figures 1 and/  Table 4. Objects we classify as "insecure", i.e., 5-95% of their 1000 clones remain resonant for ≥ 1 kyr and then leave the resonance (these objects would likely move to either "non-resonant" or "transient co-orbitals" upon further improvement of their orbital uncertainties; orange points in Figures 2 & 4).The number of transient clones that remain trapped in the 1:1 jovian resonance for ≥1 kyr and then leave the resonance are provided along with the maximum resonant trap durations.(497619) 2006QL39, (497786) 2006SA387, 2002GE195, 2016CE150, 2017WJ30, and 2021PM66 as horseshoes and DiRuzza et al. (2023) classify 2007 EV40 as a quasi-satellite, 2009 SV412 as "compound", and 2017 QO100 as "transient", all based on their short-term orbital behavior over the next ≲1000 years.We require objects to remain stable in the 1:1 jovian resonance for ≥1 kyr in order to experience several libration periods before possible departure from the resonance (in the case of the transient captures); this is responsible for the classification differences for the objects that we classify as non-resonant that other studies find are resonant during the ≤1 kyr time scales they use.

Figure 2 .
Figure2.Osculating semimajor axis vs eccentricity for the 11,581 objects with a ≃ aJ = 5.20 au that we classify with numerical integrations.The 11,423 "Trojans" (cyan) are objects for which ≥95% of their 1000 clones remain in 1:1 jovian resonance for 0.5 Myr.The 27 "Transients" (green) have ≥95% of their clones remain resonant for ≥1 kyr, but then leave the resonance (see Table1).The 124 "Non-Resonant" (red) objects have ≥95% of their 1000 clones ejected from the resonance in <1 kyr (see Table5).The 7 "Insecure" (orange) objects have 5%-95% of their 1000 clones remain in the resonance for ≥1 kyr before escaping (i.e., these objects would likely move to either "non-resonant" or "transient co-orbitals" upon further improvement of their orbital uncertainties; see Table4).The dashed rectangle shows the a, e region that JPL Horizons and the Minor Planet Center (personal communication, Peter Veres) currently define as the 'jovian Trojan' parameter space; the 14 non-resonant objects in this box (listed in Table5) are not Trojans, however, given that ≥95% of their 1000 numerically-integrated clones are ejected from the resonance in as little as tens or hundreds of years.The 27 metastable transients (green) have a larger range of semimajor axes, eccentricities, and inclinations (see Figure4for the semimajor axis vs inclination and eccentricity vs inclination projections) than the stable Trojans (cyan); objects can become temporarily bound to the resonance along its borders that stretch beyond the stable L4/L5 regions (cyan).

Figure 3 .
Figure 3. Cumulative distribution for the resonance escape times for the 1000 clones of 7 selected transient jovian co-orbitals.The number in () after each designation is the median resonant time scale for each object's current trap in the 1:1 resonance.For the full list of resonant sticking time scales for each of our 27 identified metastable jovian co-orbitals, see Table2.

Table 1 .
Classifications of metastable jovian co-orbitals.Objects in bold are shown in Figures 1 and/or 3. Table 2 provides the resonance escape time scales for these 27 objects.

Table 3 .
Number of objects in our 11,581 near-Jupiter object sample given each resonant classification.

Table 5 .
Objects we classify as "non-resonant", i.e., <5% of their 1000 clones librate in the jovian 1:1 resonance for at least 1 kyr (red points in Figures2 & 4).If an object had any clones that librate in the resonance for ≥1 kyr, the number of transient clones and their maximum resonant trap duration are provided.The 14 objects classified by the MPC/JPL as Trojans are shown in bold.