Jovian Resonance Research Articles

Resonant amplitude distribution of the Hilda asteroids and the free-floating planet flyby scenario

In some recent work, we provided a quantitative explanation for the number asymmetry of Jupiter Trojans by hypothesizing a free-floating planet (FFP) flyby into the Solar System. In support of that explanation, this paper examines the influence of the same FFP flyby on the Hilda asteroids, which orbit stably in the 3:2 mean motion resonance with Jupiter. The observed Hilda population exhibits two distinct resonant patterns: (1) a lack of Hildas with resonant amplitudes <40° at eccentricities <0.1; (2) a nearly complete absence of Hildas with amplitudes <20°, regardless of eccentricity. Previous models of Jupiter migration and resonance capture could account for the eccentricity distribution of Hildas but have failed to replicate the unusual absence of those with the smallest resonant amplitudes, which theoretically should be the most stable. Here we report that the FFP flyby can trigger an extremely rapid outward migration of Jupiter, causing a sudden shift in the 3:2 Jovian resonance. Consequently, Hildas with varying eccentricities would have their resonant amplitudes changed by different degrees, leading to the observed resonant patterns. We additionally show that, in our FFP flyby scenario, these patterns are consistently present across different resonant amplitude distributions of primordial Hildas arising from various formation models. We also place constraints on the potential parameters of the FFP, suggesting it should have an eccentricity of 1-1.3 or larger, an inclination up to 30° or higher, and a minimum mass of about 50 Earth masses.

REVISITING JOVIAN-RESONANCE INDUCED CHONDRULE FORMATION

It is proposed that planetesimals perturbed by Jovian mean-motion resonances are the source of shock waves that form chondrules. It is considered that this shock-induced chondrule formation requires the velocity of the planetesimal relative to the gas disk to be on the order of > 7 km/s at 1 AU. In previous studies on planetesimal excitation, the effects of Jovian mean-motion resonance together with the gas drag were investigated, but the velocities obtained were at most 8 km/s in the asteroid belt, which is insufficient to account for the ubiquitous existence of chondrules. In this paper, we reexamine the effect of Jovian resonances and take into account the secular resonance in the asteroid belt caused by the gravity of the gas disk. We find that the velocities relative to the gas disk of planetesimals a few hundred kilometers in size exceed 12 km/s, and that this is achieved around the 3:1 mean-motion resonance. The heating region is restricted to a relatively narrow band between 1.5 AU and 3.5 AU. Our results suggest that chondrules were produced effectively in the asteroid region after Jovian formation. We also find that many planetesimals are scattered far beyond Neptune. Our findings can explain the presence of crystalline silicate in comets if the scattered planetesimals include silicate dust processed by shock heating.

Saturnian mean motion resonances in meteoroid streams

Abstract Many previous works have shown the relevance and dynamics of Jovian mean motion resonances (MMR) in various meteoroid streams. These resonant swarms are known to have produced spectacular meteor displays in the past. In this work, we investigate whether any MMR due to Saturn are feasible, and subsequently check whether such effects are strong enough to trap meteoroids so as to cause enhanced meteor phenomena on Earth. Extensive numerical simulations are done on two major meteoroid streams, which are known to exhibit exterior Jovian resonances. The roles of the 1:6 and 5:14 Jovian MMR have already been studied in the Orionids and Leonids, respectively. Now we find strong evidence of 1:3 and 8:9 Saturnian MMR in Orionids and Leonids, respectively. The presence of compact dust trails in real space due to these two Saturnian resonances is confirmed from our calculations.

Dynamical resonant structures in meteoroid stream orbits

Herein we use the Canadian Meteor Orbit Radar (CMOR) data set to search for evidence of a resonant swarm in the Taurid meteoroid stream at the 7:2 Jovian resonance. We use a numerical method to estimate the reduction in radar orbit measurement uncertainty required to detect this feature in a data set. This is highly dependent on the proportion of observed particles that are members of the resonant swarm. However, we find that a meteor radar with uncertainties a factor of 10 lower than those of the current CMOR will be sufficient for detection to be possible, if the meteor shower consists of more than 5 per cent resonant particles (considered likely given the results of visual meteor studies). Such an improvement will require accurate removal of deceleration errors from pre-atmospheric meteor velocities, and improvement to the robustness of echo inflection point identification algorithms and interferometric measurements.

Nebular shock waves generated by planetesimals passing through Jovian resonances: Possible sites for chondrule formation

Abstract— The primordial asteroid belt contained at least several hundred and possibly as many as 10,000 bodies with diameters of 1000 km or larger. Following the formation of Jupiter, nebular gas drag combined with passage of such bodies through Jovian resonances produced high eccentricities (e = 0.3‐0.5), low inclinations (i &lt; 0.5°), and, therefore, high velocities (3–10 km/s) for “resonant” bodies relative to both nebular gas and non‐resonant planetesimals. These high velocities would have produced shock waves in the nebular gas through two mechanisms. First, bow shocks would be produced by supersonic motion of resonant bodies relative to the nebula. Second, high‐velocity collisions of resonant bodies with non‐resonant bodies would have generated impact vapor plume shocks near the collision sites. Both types of shocks would be sufficient to melt chondrule precursors in the nebula, and both are consistent with isotopic evidence for a time delay of ˜1‐1.5 Myr between the formation of CAIs and most chondrules. Here, initial simulations are first reported of impact shock wave generation in the nebula and of the local nebular volumes that would be processed by these shocks as a function of impactor size and relative velocity. Second, the approximate maximum chondrule mass production is estimated for both bow shocks and impact‐generated shocks assuming a simplified planetesimal population and a rate of inward migration into resonances consistent with previous simulations. Based on these initial first‐order calculations, impact‐generated shocks can explain only a small fraction of the minimum likely mass of chondrules in the primordial asteroid belt (˜1024‐1025g). However, bow shocks are potentially a more efficient source of chondrule production and can explain up to 10–100 times the estimated minimum chondrule mass.

A record of planet migration in the main asteroid belt

The main asteroid belt lies between the orbits of Mars and Jupiter, but the region is not uniformly filled with asteroids. There are gaps, known as the Kirkwood gaps, in distinct locations that are associated with orbital resonances with the giant planets; asteroids placed in these locations will follow chaotic orbits and be removed. Here we show that the observed distribution of main belt asteroids does not fill uniformly even those regions that are dynamically stable over the age of the Solar System. We find a pattern of excess depletion of asteroids, particularly just outward of the Kirkwood gaps associated with the 5:2, the 7:3 and the 2:1 Jovian resonances. These features are not accounted for by planetary perturbations in the current structure of the Solar System, but are consistent with dynamical ejection of asteroids by the sweeping of gravitational resonances during the migration of Jupiter and Saturn approximately 4 Gyr ago.

Anomalous diffusion in the first-order Jovian resonance

A method is presented for the characterization of anomalous diffusive processes in dynamical systems. This method is applied to the analysis of the diffusion in some Hamiltonian systems with special emphasis on the orbital problems. We show that the types of diffusion processes in the borders and in the resonant regions are common for all the studied systems. In the borders the diffusion is governed by an initial exponential stage and in the resonant regions the diffusion is also represented by a power law. In the orbital problem we show that, in general, the resonant asteroids are associated with regions where diffusive processes for the semi-major axis and eccentricity are described by σ ∝ t H ,w hereσ is the standard deviation and 1 < H < 1.7. The values of exponent H were determined in grids of initial conditions in the 2:1, 3:2 and 4:3 Jovian resonances.

The population of asteroids in the 2:1 mean motion resonance with Jupiter revised

We study the population of asteroids inside the 2/1 mean motion resonance with Jupiter, in the so called Hecuba gap. Origin of these bodies is not well understood: (i) the long-lived (stable) population may be primordial, but this contradicts its steep size distribution, while (ii) the short-lived (unstable) population requires an efficient sustaining mechanism. Our working hypothesis is that the unstable asteroids are continuously resupplied from outside the resonance by the Yarkovsky effect. As a first step toward comparison of such model with observations, we report here an update of the observed population of asteroids residing in the 2/1 Jovian resonance, mainly because the number of cataloged orbits increased substantially during the last few years. We found there are 153 numbered and multi-opposition resonant asteroids in total and we classified them into the three sub-populations according to their dynamical lifetime. Our work also allowed us to derive several important parameters such as asteroid locations inside the resonance or size distribution of the sub-populations. As a particular novelty, we identified 6 asteroids located inside the high-eccentricity quasi-regular stable island, which previously seemed empty.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Observed spectral properties of near-Earth objects: results for population distribution, source regions, and space weathering processes

We present new visible and near-infrared spectroscopic measurements for 252 near-Earth (NEO) and Mars-crossing (MC) objects observed from 1994 through 2002 as a complement to the Small Main-Belt Asteroid Spectroscopic Survey (SMASS, http://smass.mit.edu/). Combined with previously published SMASS results, we have an internally consistent data set of more than 400 of these objects for investigating trends related to size, orbits, and dynamical history. These data also provide the basis for producing a bias-corrected estimate for the total NEO population (Stuart and Binzel, 2004, Icarus 170, 295–311). We find 25 of the 26 Bus (1999, PhD thesis) taxonomic types are represented, with nearly 90% of the objects falling within the broad S-, Q-, X-, and C-complexes. Rare A- and E-types are more common in the MC than NEO population (about 5% compared to <1%) and may be direct evidence of slow diffusion into MC orbits from the Flora and Hungaria regions, respectively. A possible family of MC objects (C-types) may reside at the edge of the 5:2 jovian resonance. Distinct signatures are revealed for the relative contributions of different taxonomic types to the NEO population through different source regions. E-types show an origin signature from the inner belt, C-types from the mid to outer belt, and P-types from the outer belt. S- and Q-types have effectively identical main-belt source region profiles, as would be expected if they have related origins. A lack of V-types among Mars-crossers suggests entry into NEO space via rapid transport through the ν6 and 3:1 resonances from low eccentricity main-belt orbits, consistent with a Vesta origin. D-types show the strongest signature from Jupiter family comets (JFC), with a strong JFC component also seen among the X-types. A distinct taxonomic difference is found with respect to the jovian Tisserand parameter T, where C-, D-, and X-type (most likely low albedo P-class) objects predominate for T⩽3. These objects, which may be extinct comets, comprise 4% of our observed sample, but their low albedos makes this magnitude limited fraction under-representative of the true value. With our taxonomy statistics providing a strong component to the diameter limited bias correction analysis of Stuart (2003, PhD thesis), we estimate 10–18% of the NEO population above any given diameter may be extinct comets, taking into account asteroids scattered into T<3 orbits and comets scattered into T>3 orbits. In terms of possible space weathering effects, we see a size-dependent transition from ordinary chondrite-like (Q-type) objects to S-type asteroids over the size range of 0.1 to 5 km, where the transition is effectively complete at 5 km. A match between the average surface age of 5 km asteroids and the rate of space weathering could constrain models for both processes. However, space weathering may proceed at a very rapid rate compared with collisional timescales. In this case, the presence or absence of a regolith may be the determining factor for whether or not an object appears “space weathered.” Thus 0.1 to 5 km appears to be a critical size range for understanding the processes, timescales, and conditions under which a regolith conducive to space weathering is generated, retained, and refreshed.

Stable Chaos in High-Order Jovian Resonances

In a previous publication (Tsiganis et al. 2000, Icarus 146, 240–252), we argued that the occurrence of stable chaos in the 12/7 mean motion resonance with Jupiter is related to the fact that there do not exist families of periodic orbits in the planar elliptic restricted problem and in the 3-D circular problem corresponding to this resonance. In the present paper we show that nonexistence of resonant periodic orbits, both for the planar and for the 3-D problem, also occurs in other jovian resonances—namely the 11/4, 22/9, 13/6, and 18/7—where cases of real asteroids on stable-chaotic orbits have been identified. This property may provide a “protection mechanism”, leading to semiconfinement of chaotic orbits and extremely slow migration in the space of proper elements, so that diffusion is practically unrelated to the value of the Lyapunov time, T L, of chaotic orbits. However, we show that, in more complicated dynamical models, the long-term evolution of chaotic orbits initiated in the vicinity of these resonances may also be governed by secular resonances. Finally, we find that stable-chaotic orbits have a characteristic spectrum of autocorrelation times: for the action conjugate to the critical argument the autocorrelation time is of the order of the Lyapunov time, while for the eccentricity- and inclination-related actions the autocorrelation time may be longer than 10 3 T L. This behavior is consistent with the trajectory being sticky around a manifold of lower-than-full dimensionality in phase space (e.g., a 4-D submanifold of the 5-D energy manifold in a three-degrees-of-freedom autonomus Hamiltonian system) and reflects the inability of these “flawed” resonances to modify secular motion significantly, at least for times of the order of 200 Myr.

Diffusion characters of the orbits in the asteroid motion

A symplectic mapping is studied carefully. The exponential diffusion law in developed chaotic region and algebraic law in mixed region were observed. An area was found where the diffusion follows a logarithmic law. It is shown in the vicinity of an island, the logarithm of the escape time decreases linearily as the initial position moves away from the island. But when approaching close to the island, the escape time goes up very quickly, consistent with the superexponential stability of the invariant curve. When applied to the motion of asteroid, this mapping's fixed points and their stabilities give an explanation of the distribution of asteroids. The diffusion velocities in4∶3, 3∶2 and2∶1 jovian resonances are also investigated.

Yarkovsky-Driven Leakage of Koronis Family Members: I. The Case of 2953 Vysheslavia

The orbit of the asteroid 2953 Vysheslavia is currently locked in a tiny chaotic zone very close to the 5 : 2 mean motion jovian resonance. Its dynamical lifetime is estimated to be of the order of only about 10 Myr. Since Vysheslavia is a member of the Koronis family, such a short dynamical lifetime opens a variety of interesting questions concerning its origin and evolution. A. Milani and P. Farinella (1995, Icarus 115, 209–212) considered a number of plausible scenarios and suggested that most probably Vysheslavia is an outcome of a recent secondary fragmentation event in the family. Here we propose that Vysheslavia might have been placed on its peculiar orbit by a slow inward drift of the semimajor axis due to the Yarkovsky effect. Numerical simulations confirm that such evolutionary processes can take 100–500 Myr, a period comparable to but still shorter than the probable age of the family (on the order of a Gyr), depending on the thermal properties of Vysheslavia's surface, the orientation of its spin axis, and its size. We have also integrated orbits of the asteroids 7340 (1991 UA 2) and 1993 FR 58, located very close to but outside the chaotic zone that triggers Vysheslavia's orbit instability, and we show that the orbits of these asteroids may also slowly evolve toward the chaotic zone. Such an erosion of the asteroid families, caused by a slow leakage to the nearby powerful resonances, could be fairly common in the main asteroid belt.

Mean Motion Resonances in The Asteroid Belt

The Kirkwood gaps in the main asteroidal belt (2 – 3.5 AU) coincide with the mean motion resonances with Jupiter (4/1, 3/1, 5/2, 7/3, 2/1). Similarly, several narrower gaps are observed in the outer asteroid belt (3.5 – 4 AU) at places of 11/6, 9/5, 7/4 and 5/3 Jovian resonances (Holman and Murray 1996). As it is now generally accepted, the formation and preservation of these gaps is due to the chaos of the resonant space and efficient ejection of the primordial and collisionaly injected bodies towards high eccentricities and planet-crossing orbits.The Jovian mean motion resonances are not the most important in what concerns the chaos of the observed (i.e. remaining) asteroid population. It was estimated by Šidlichovský and Nesvorný (1998) that about 40% of known objects have the Lyapunov time less than 105 years. It was later found (Nesvorný and Morbidelli 1998, 1999; Morbidelli and Nesvorný 1999) that the resonances responsible for this chaos are, in decreasing order of importance: 1) three-body resonances with Jupiter and Saturn, 2) exterior resonances with Mars, 3) moderate order Jovian resonances, and 4) three-body resonances with Mars and Jupiter.

The origin of chondrules at jovian resonances

Isotopic dating indicates that chondrules were produced a few million years after the solar nebula formed. This timing is incompatible with dynamical lifetimes of small particles in the nebula and short time scales for the formation of planetesimals. Temporal and dynamical constraints can be reconciled if chondrules were produced by heating of debris from disrupted first-generation planetesimals. Jovian resonances can excite planetesimal eccentricities enough to cause collisional disruption and melting of dust by bow shocks in the nebular gas. The ages of chondrules may indicate the times of Jupiter's formation and dissipation of gas from the asteroidal region.

Periodic orbit families near the 4:1 jovian resonance

An enlarged averaged Hamiltonian is introduced to compute several families of periodic orbits of the planar elliptic 3-body problem, in the Sun–Jupiter–Asteroid system, near the 4:1 resonance. Four resonant critical point families are found and their stability is studied. The families of symmetric periodic orbits of the elliptic problem appear near the corresponding fixed points computed in this model. There is a good agreement for moderate eccentricity of the asteroid for three of these families, whereas the remaining family cannot be considered as a family of periodic orbits of the real model.

Dynamical Behavior of Asteroids Near Resonance: the 4:1 gap and the 7:2 Group

A comparative study of the evolution of the Sun–Jupiter–Asteroid system near the 4:1 and 7:2 resonances is performed by means of two techniques that proceed differently from the Hamiltonian corresponding to the planar restricted elliptic three-body problem. One technique is based on the classical Schubart averaging while the other is based on a mapping method in which the perturbing part of the Hamiltonian is expanded and the resulting terms are ordered according to a weight function that depends on the powers of eccentricities and the coefficients of the terms. For the mapping method the effect of Saturn on the asteroidal evolution is introduced and the degree of chaos is estimated by means of the Lyapunov time. Both methods are shown to lead to similar results and can be considered a suitable tool for describing the evolution of asteroids in the Kirkwood gap and the group corresponding to the 4:1 and 7:2 Jovian resonances, respectively.

On the Asteroidal Population of the First-Order Jovian Resonances

The frequency map analysis was applied to the fairly realistic models of the 2/1, 3/2, and 4/3 jovian resonances and the results were compared with the asteroidal distribution at these commensurabilities. The presence of the Hecuba gap at the 2/1 and of the Hilda group in the 3/2 is explained on the basis of different rates of the chaotic transport (diffusion) in these resonances. The diffusion in the most stable 2/1-resonant region is almost two orders in magnitude faster than the diffusion in the region which accommodates the Hildas. In the 2/1 commensurability there are two possible locations for long-surviving asteroids: the one centered at an eccentricity of 0.3 near the libration stable centers with small libration amplitude and the other at a slightly lower eccentricity with a moderate libration amplitude (∼90°). Surprisingly, all asteroids observed in the 2/1 resonance (8 numbered and multi-opposition objects in Bowell's catalog from 1994) occupy the moderate-libration area and avoid the area in a close vicinity of the libration stable centers. Possible explanations of this fact were discussed. Concerning the 4/3 resonance, the only asteroid in the corresponding stable region is 279 Thule, in spite of the fact that this region is almost as regular (although not as extensive) as the one where the Hilda group in the 3/2, with 79 members, is found.

Towards a Dynamical History of ‘Proto-Encke‘

There are too few active comets to account for the observed zodiacal dust. Rather we look to the collisional fragmentation and erosion of sub-kilometre meteoroids in orbit close to the ecliptic. Since 1975 we have also been aware of an apparently massive meteoroidal swarm in probable 7:2 mean motion resonance with Jupiter, seemingly at the heart of the Taurid Complex and connecting therefore with the near-ecliptic system through the so-called Stohl Stream. The notable absence of pre-1786 apparitions of 2P/Encke took on a new significance with the 1983 detection by IRAS of its asymmetric trail inside this resonance. Thus it was possible all these meteoroidal components were ultimately derived from a continuously eroded, substantially dormant, librating progenitor within the trail whose more volatile inclusions are exposed from time to time and expelled either singly or severally as independent comets. A Taurid progenitor of this kind (proto-Encke) dominating the inner Solar System environment probably then accounts for most of the recorded enhancements of the larger meteoroid flux to Earth, including ‘Tunguska’ bodies as well. Terrestrial dust insertions which control mean temperature and hence climate are also inferred based upon the libration and nodal precession half-periods of proto-Encke (~0.2kyr, ~2.5 kyr respectively) albeit the longer of these cycles was not at first evident in the terrestrial record (Asher & Clube 1993). Recently however this cycle appears to have been confirmed as a significant (long term) global warming/meridional atmospheric circulation/iceberg calving cycle with the correct phase producing the so-called mini-Heinrich and Heinrich events of the Holocene and late Upper Pleistocene respectively, i.e., during the past ~60 kyr BP. The comparative stability of this terrestrial cycle, in contrast with the weakness of the observed resonance, suggests a fairly recent diversion therefore from a much stronger sungrazing 7:2 Jovian resonance in which proto-Encke’s and Jupiter’s longitudes of perihelion are related by \({\varpi _p}E \approx \varpi J\,or\,\varpi J + \pi \). Thus both the Hephaistos Stream and the Taurid Complex could have formed together during a recent close planetary encounter, say with Mercury ~5 kyr BP. It follows that we envisage a single large progenitor in 7:2 Jovian sungrazing resonance for 50 kyr or so which undergoes repeated tidal stress: a continuous dust-induced major glaciation is thus sustained on Earth for most of this dynamical timescale before a disruptive planetgrazing event finally brings its sungrazing status to an end and produces the present meteoroidal complex. This evolutionary sequence almost certainly requires that the original sungrazing stream still exists (without its source): a potentially significant fact because it may have a direct bearing on both the observed zodiacal bands and the original progenitor orbit as well as the known periodic variation of solar radiance and convected magnetic field, of possible relevance to the solar cycle. While these aspects have to be further explored, the purpose of the present investigation is to describe some preliminary modelling with a view to inferring the likely dynamical history of proto-Encke.

Intermittent Trajectories in the 3/1 Jovian Resonance

The statistical behaviour of intermittent trajectories at the 3/1resonance is investigated. The elliptic planar restricted three-body problemis used as a model. Distribution functions for time intervals D betweeneccentricity bursts are obtained and theoretically interpreted. For smallervalues of D the distribution is found to be of Poisson type, while in itstail it is described by a power law Dα. This change in thedistribution occurs for values of D in the range105™106Jupiter periods. The power-lawindexαfor the integral distributions lies in the range (-2,-1) and istrajectory dependent. The algebraic decay in the tails of the distributionsis explained by the phenomenon of sticking of orbits to the chaos borderduring long intervals between bursts.

Chaotic asteroidal trajectories exhibiting multiple bursts of eccentricity: A statistical analysis

For chaotic asteroidal trajectories exhibiting multiple bursts of eccentricity in the 3/1 Jovian resonance, we derive the distribution function of time intervals between such bursts. At the onset, the resulting distribution decays exponentially. In the tail, an algebraic decay is observed, with the power-law index for the integral distribution in the range −2 to −1.