Jupiter Family Comets Population Research Articles

The Gateway from Centaurs to Jupiter-family Comets: Thermal and Dynamical Evolution

It was recently proposed that there exists a “gateway” in the orbital parameter space through which Centaurs transition to Jupiter-family comets (JFCs). Further studies have implied that the majority of objects that eventually evolve into JFCs should leave the Centaur population through this gateway. This may be naively interpreted as gateway Centaurs being pristine progenitors of JFCs. This is the point we want to address in this work. We show that the opposite is true: gateway Centaurs are, on average, more thermally processed than the rest of the population of Centaurs crossing Jupiter’s orbit. Using a dynamically validated JFC population, we find that only ∼20% of Centaurs pass through the gateway prior to becoming JFCs, in accordance with previous studies. We show that more than half of JFC dynamical clones entering the gateway for the first time have already been JFCs—they simply avoided the gateway on their first pass into the inner solar system. By coupling a thermal evolution model to the orbital evolution of JFC dynamical clones, we find a higher than 50% chance that the layer currently contributing to the observed activity of gateway objects has been physically and chemically altered, due to previously sustained thermal processing. We further illustrate this effect by examining dynamical clones that match the present-day orbits of 29P/Schwassmann-Wachmann 1, P/2019 LD2 (ATLAS), and P/2008 CL94 (Lemmon).

Dynamics of small bodies in orbits between Jupiter and Saturn

We examine the dynamics of small bodies in orbits similar to that of comet 29P/Schwassmann-Wachmann 1, i.e. near-circular orbits between Jupiter and Saturn. As of late 2019, there are 14 other known bodies in this region that lie in similar orbits. Previous research has shown that this region of the solar system, which in this work we call the “near Centaur region” (NCR), is not stable, suggesting that any bodies found in it would have very short lifetimes. We performed 20 Myr high-precision numerical simulations of the evolution of massless particles, initially located in the Kuiper belt but close to Neptune, with perihelia slightly below 33 au (“Neptune crossers”). Some of these particles quickly migrate inward, passing through the NCR before becoming Jupiter Family Comets. We find that objects in the NCR do indeed generally travel through it very quickly. However, our simulations reveal that resonant behavior in this region is somewhat common and can trap objects for up to 100 Kyr. We summarize the dynamics of 29P and other observed bodies in the region—two of which seem to be clearly exhibiting resonant behavior—and use our simulations to put limits on the reservoir size of the Neptune crossers, which at its time determines the reservoir size of the Kuiper belt. Finally, we put some constraints on the current population of Centaurs and particularly of the NCR population, based on the injection rates required to keep the observed population of Jupiter family comets in steady-state.

Using atmospheric impact data to model meteoroid close encounters

ABSTRACT Based on telescopic observations of Jupiter-family comets (JFCs), there is predicted to be a paucity of objects at sub-kilometre sizes. However, several bright fireballs and some meteorites have been tenuously linked to the JFC population, showing metre-scale objects do exist in this region. In 2017, the Desert Fireball Network (DFN) observed a grazing fireball that redirected a meteoroid from an Apollo-type orbit to a JFC-like orbit. Using orbital data collected by the DFN, in this study, we have generated an artificial data set of close terrestrial encounters that come within 1.5 lunar distances (LD) of the Earth in the size-range of 0.01–100 kg. This range of objects is typically too small for telescopic surveys to detect, so using atmospheric impact flux data from fireball observations is currently one of the only ways to characterize these close encounters. Based on this model, we predict that within the considered size-range 2.5 × 108 objects ($0.1{{\ \rm per\ cent}}$ of the total flux) from asteroidal orbits (TJ > 3) are annually sent on to JFC-like orbits (2 < TJ < 3), with a steady-state population of about 8 × 1013 objects. Close encounters with the Earth provide another way to transfer material to the JFC region. Additionally, using our model, we found that approximately 1.96 × 107 objects are sent on to Aten-type orbits and ∼104 objects are ejected from the Solar system annually via a close encounter with the Earth.

Potential Themis Family Asteroid Contribution to the Jupiter-Family Comet Population.

Recent dynamical analyses suggest that some Jupiter family comets (JFCs) may originate in the main asteroid belt instead of the outer solar system. This possibility is particularly interesting given evidence that icy main-belt objects are known to be present in the Themis asteroid family. We report results from dynamical analyses specifically investigating the possibility that icy Themis family members could contribute to the observed population of JFCs. Numerical integrations show that such dynamical evolution is indeed possible via a combination of eccentricity excitation apparently driven by the nearby 2:1 mean-motion resonance with Jupiter, gravitational interactions with planets other than Jupiter, and the Yarkovsky effect. We estimate that, at any given time, there may be tens of objects from the Themis family on JFC-like orbits with the potential to mimic active JFCs from the outer solar system, although not all, or even any, may necessarily be observably active. We find that dynamically evolved Themis family objects on JFC-like orbits have semimajor axes between 3.15 au and 3.40 au for the vast majority of their time on such orbits, consistent with the strong role that the 2:1 mean-motion resonance with Jupiter likely plays in their dynamical evolution. We conclude that a contribution from the Themis family to the active JFC population is plausible, although further work is needed to better characterize this contribution.

Mid-infrared spectra of comet nuclei

Comet nuclei and D-type asteroids have several similarities at optical and near-IR wavelengths, including near-featureless red reflectance spectra, and low albedos. Mineral identifications based on these characteristics are fraught with degeneracies, although some general trends can be identified. In contrast, spectral emissivity features in the mid-infrared provide important compositional information that might not otherwise be achievable. Jovian Trojan D-type asteroids have emissivity features strikingly similar to comet comae, suggesting that they have the same compositions and that the surfaces of the Trojans are highly porous. However, a direct comparison between a comet and asteroid surface has not been possible due to the paucity of spectra of comet nuclei at mid-infrared wavelengths. We present 5–35 µm thermal emission spectra of comets 10P/Tempel 2, and 49P/Arend-Rigaux observed with the Infrared Spectrograph on the Spitzer Space Telescope. Our analysis reveals no evidence for a coma or tail at the time of observation, suggesting the spectra are dominated by the comet nucleus. We fit each spectrum with the near-Earth asteroid thermal model (NEATM) and find sizes in agreement with previous values. However, the NEATM beaming parameters of the nuclei, 0.74–0.83, are systematically lower than the Jupiter-family comet population mean of 1.03 ± 0.11, derived from 16- and 22-µm photometry. We suggest this may be either an artifact of the spectral reduction, or the consequence of an emissivity low near 16 µm. When the spectra are normalized by the NEATM model, a weak 10-µm silicate plateau is evident, with a shape similar to those seen in mid-infrared spectra of D-type asteroids. A silicate plateau is also evident in previously published Spitzer spectra of the nucleus of comet 9P/Tempel 1. We compare, in detail, these comet nucleus emission features to those seen in spectra of the Jovian Trojan D-types (624) Hektor, (911) Agamemnon, and (1172) Aneas, as well as those seen in the spectra of seven comet comae. The comet comae present silicate features with two distinct shapes, either trapezoidal, or more rounded, the latter apparently due to enhanced emission near 8 to 8.5 µm. The surfaces of Tempel 2, Arend-Rigaux, and Hektor best agree with the comae that present trapezoidal features, furthering the hypothesis that the surfaces of these targets must have high porosities in order to exhibit a spectrum similar to a comet coma. An emissivity minimum at 15 µm, present in the spectra of Tempel 2, Arend-Rigaux, Hektor, and Agamemnon, is also described, the origin of which remains unidentified. The compositional similarity between D-type asteroids and comets is discussed, and our data supports the hypothesis that they have similar origins in the early Solar System.

An updated estimate of the number of Jupiter-family comets using a simple fading law

It has long been hypothesised that the Jupiter-family comets (JFCs) come from the scattered disc, an unstable planetesimal population beyond Neptune. This viewpoint has been widely accepted, but a few issues remain, the most prominent of which are the total number of visible JFCs with a perihelion distance q<2.5 AU and the corresponding number of objects in the scattered disc. In this work we give a robust estimate of the number of visible JFCs with q<2.5 AU and diameter D>2.3 km based on recent observational data. This is combined with numerical simulations that use a simple fading law applied to JFCs that come close to the Sun. For this we numerically evolve thousands of comets from the scattered disc through the realm of the giant planets and keep track of their number of perihelion passages with perihelion distance q<2.5 AU, below which the activity is supposed to increase considerably. We can simultaneously fit the JFC inclination and semi-major axis distribution accurately with a delayed power law fading function and the maximum perihelion distance below which the observational data is complete is q~2.3 AU. From observational data we calculate that a JFC with diameter D=2.3 km has a typical total absolute magnitude H_T=10.8, and the steady-state number of active JFCs with diameter D>2.3 km and q<2.5 AU is of the order of 300 (but with large uncertainties), approximately a factor two higher than earlier estimates. The increased JFC population results in a scattered disc population of 6 billion objects and decreases the observed Oort cloud to scattered disc population ratio to 13, virtually the same as the value of 12 obtained with numerical simulations.

The size-distribution of scattered disk TNOs from that of JFCs between 0.2 and 15 km effective radius

We investigate the differential size–frequency distribution (SFD) of Jupiter Family Comets (JFCs) in order to determine whether they are primordial accreted objects or collisional fragments as suggested by current models of the evolution of Trans-Neptunian Objects (TNOs). We develop a list of effective radii and their uncertainties for 161 active JFCs from published sources and compute the observed differential size–frequency distribution using a Probability Index technique. The radii range from 0.2 to 15.4km and average 1.9km. The peak of the distribution is near 1.0km. This is then corrected for the effects of observational selection using a model published earlier by Meech et al. (Meech, K.J., Hainaut, O.R., Marsden, B.G. [2004]. Icarus 170, 463–491). We estimate that the total number of active JFCs between 0.2 and 15.4km is approximately 2300 indicating that our current sample of the of active JFC population is far from complete. The active JFC size–frequency distribution, over the range from 0.6 to 10km where it is best defined, is found to be closer to an exponential distribution in character than a power-law. We then develop a statistical model, based on the assumption of a steady state, for converting the distribution of active JFCs to the SFD of the source population among the TNOs. The model includes the effects of devolatization (that produces a large sub-class of defunct nuclei) and surficial mass-loss. Comparison with available TNO observations shows that to simultaneously attain continuity with the data on objects in the hot TNO population (Fuentes et al. [2010]. Astrophys. J. 722, 1290–1304), satisfy constraints on the number of TNOs set by the occultation detections of Schlichting et al. (Schlichting, H.E. et al. [2012]. Astrophys. J. 761, 150), and to remain within upper limits set by the Taiwanese–American Occultation Survey (TAOS; Zhang et al. [2013]. Astron. J. 146, ID 14, 10pp.) the total JFC population must contain a large fraction of small defunct nuclei. The effective power-law index of the inferred TNO differential SFD between 1 and 10km is −4.5±0.5 indicating a population in this range that is not in fully relaxed collisional equilibrium. We conclude that the cometary nuclei so far visited by spacecraft and many JFCs are primordial accreted objects relatively unaffected by collisional evolution. We find a turndown in the slope of the predicted TNO cumulative distribution near 1km radius rather than near 10km that is seen in many TNO evolutionary calculations. This may or may not represent the onset of a collisional cascade.

Thermal properties, sizes, and size distribution of Jupiter-family cometary nuclei

We present results from SEPPCoN, an on-going Survey of the Ensemble Physical Properties of Cometary Nuclei. In this report we discuss mid-infrared measurements of the thermal emission from 89 nuclei of Jupiter-family comets (JFCs). All data were obtained in 2006 and 2007 using imaging capabilities of the Spitzer Space Telescope. The comets were typically 4–5AU from the Sun when observed and most showed only a point-source with little or no extended emission from dust. For those comets showing dust, we used image processing to photometrically extract the nuclei. For all 89 comets, we present new effective radii, and for 57 comets we present beaming parameters. Thus our survey provides the largest compilation of radiometrically-derived physical properties of nuclei to date. We have six main conclusions: (a) The average beaming parameter of the JFC population is 1.03±0.11, consistent with unity; coupled with the large distance of the nuclei from the Sun, this indicates that most nuclei have Tempel 1-like thermal inertia. Only two of the 57 nuclei had outlying values (in a statistical sense) of infrared beaming. (b) The known JFC population is not complete even at 3km radius, and even for comets that approach to ∼2AU from the Sun and so ought to be more discoverable. Several recently-discovered comets in our survey have small perihelia and large (above ∼2km) radii. (c) With our radii, we derive an independent estimate of the JFC nuclear cumulative size distribution (CSD), and we find that it has a power-law slope of around −1.9, with the exact value depending on the bounds in radius. (d) This power-law is close to that derived by others from visible-wavelength observations that assume a fixed geometric albedo, suggesting that there is no strong dependence of geometric albedo with radius. (e) The observed CSD shows a hint of structure with an excess of comets with radii 3–6km. (f) Our CSD is consistent with the idea that the intrinsic size distribution of the JFC population is not a simple power-law and lacks many sub-kilometer objects.

The persistent activity of Jupiter-family comets at 3–7 AU

We present an analysis of comet activity based on the Spitzer Space Telescope component of the Survey of the Ensemble Physical Properties of Cometary Nuclei. We show that the survey is well suited to measuring the activity of Jupiter-family comets at 3–7AU from the Sun. Dust was detected in 33 of 89 targets (37±6%), and we conclude that 21 comets (24±5%) have morphologies that suggest ongoing or recent cometary activity. Our dust detections are sensitivity limited, therefore our measured activity rate is necessarily a lower limit. All comets with small perihelion distances (q<1.8AU) are inactive in our survey, and the active comets in our sample are strongly biased to post-perihelion epochs. We introduce the quantity ∊fρ, intended to be a thermal emission counterpart to the often reported Afρ, and find that the comets with large perihelion distances likely have greater dust production rates than other comets in our survey at 3–7AU from the Sun, indicating a bias in the discovered Jupiter-family comet population. By examining the orbital history of our survey sample, we suggest that comets perturbed to smaller perihelion distances in the past 150yr are more likely to be active, but more study on this effect is needed.

Bulk density of small meteoroids

Aims. Here we report on precise metric and photometric observations of 107 optical meteors, which were simultaneously recorded at multiple stations using three different intensified video camera systems. The purpose is to estimate bulk meteoroid density, link small meteoroids to their parent bodies based on dynamical and physical density values expected for different small body populations, to better understand and explain the dynamical evolution of meteoroids after release from their parent bodies. Methods. The video systems used had image sizes ranging from 640 × 480 to 1360 × 1036 pixels, with pixel scales from 0.01 ◦ per pixel to 0.05 ◦ per pixel, and limiting meteor magnitudes ranging from Mv =+ 2.5 to +6.0. We find that 78% of our sample show noticeable deceleration, allowing more robust constraints to be placed on density estimates. The density of each meteoroid is estimated by simultaneously fitting the observed deceleration and lightcurve using a model based on thermal fragmentation, conservation of energy and momentum. The entire phase space of the model free parameters is explored for each event to find ranges of parameters which fit the observations within the measurement uncertainty. Results. (a) We have analysed our data by first associating each of our events with one of the five meteoroid classes. The average density of meteoroids whose orbits are asteroidal and chondritic (AC) is 4200 kg m −3 suggesting an asteroidal parentage, possibly related to the high-iron content population. Meteoroids with orbits belonging to Jupiter family comets (JFCs) have an average density of 3100 ± 300 kg m −3 . This high density is found for all meteoroids with JFC-like orbits and supports the notion that the refractory material reported from the Stardust measurements of 81P/Wild 2 dust is common among the broader JFC population. This high density is also the average bulk density for the 4 meteoroids with orbits belonging to the Ecliptic shower-type class (ES) also related to JFCs. Both categories we suggest are chondritic based on their high bulk density. Meteoroids of HT (Halley type) orbits have a minimum bulk density value of 360 +400 −900 kg m −3 . This is consistent with many previous works which suggest bulk cometary meteoroid density is low. SA (Sun-approaching)-type meteoroids show a density spread from 1000 kg m −3 to 4000 kg m −3 , reflecting multiple origins. (b) We found two different meteor showers in our sample: Perseids (10 meteoroids, ∼11% of our sample) with an average bulk density of 620 kg m −3 and Northern Iota Aquariids (4 meteoroids) with an average bulk density of 3200 kg m −3 , consistent with the notion that the NIA derive from 2P/Encke.

The atmospheric influence, size and possible asteroidal nature of the July 2009 Jupiter impactor

Near-infrared and mid-infrared observations of the site of the 2009 July 19 impact of an unknown object with Jupiter were obtained within days of the event. The observations were used to assess the properties of a particulate debris field, elevated temperatures, and the extent of ammonia gas redistributed from the troposphere into Jupiter’s stratosphere. The impact strongly influenced the atmosphere in a central region, as well as having weaker effects in a separate field to its west, similar to the Comet Shoemaker-Levy 9 (SL9) impact sites in 1994. Temperatures were elevated by as much as 6 K at pressures of about 50–70 mbar in Jupiter’s lower stratosphere near the center of the impact site, but no changes above the noise level (1 K) were observed in the upper stratosphere at atmospheric pressures less than ∼1 mbar. The impact transported at least ∼2 × 10 15 g of gas from the troposphere to the stratosphere, an amount less than derived for the SL9 C fragment impact. From thermal heating and mass-transport considerations, the diameter of the impactor was roughly in the range of 200–500 m, assuming a mean density of 2.5 g/cm 3. Models with temperature perturbations and ammonia redistribution alone are unable to fit the observed thermal emission; non-gray emission from particulate emission is needed. Mid-infrared spectroscopy of material delivered by the impacting body implies that, in addition to a silicate component, it contains a strong signature that is consistent with silica, distinguishing it from SL9, which contained no evidence for silica. Because no comet has a significant abundance of silica, this result is more consistent with a “rocky” or “asteroidal” origin for the impactor than an “icy” or “cometary” one. This is surprising because the only objects generally considered likely to collide with Jupiter and its satellites are Jupiter-Family Comets, whose populations appear to be orders of magnitude larger than the Jupiter-encountering asteroids. Nonetheless, our conclusion that there is good evidence for at least a major asteroidal component of the impactor composition is also consistent both with constraints on the geometry of the impactor and with results of contemporaneous Hubble Space Telescope observations. If the impact was not simply a statistical fluke, then our conclusion that the impactor contained more rocky material than was the case for the desiccated Comet SL9 implies a larger population of Jupiter-crossing asteroidal bodies than previously estimated, an asteroidal component within the Jupiter-Family Comet population, or compositional differentiation within these bodies.

The Scattered Disk as the Source of the Jupiter Family Comets

The short-period Jupiter family comets (JFCs) are thought to originate in the Kuiper Belt; specifically, a dynamical subclass of the Kuiper Belt known as the is argued to be the dominant source of JFCs. However, the best estimates from observational surveys indicate that this source may fall short by more than 2 orders of magnitude of the estimates obtained from theoretical models of the dynamical evolution of Kuiper Belt objects into JFCs. We reexamine the scattered disk as a source of the JFCs and make a rigorous estimate of the discrepancy. We find that the uncertainties in the dynamical models combined with a change in the size distribution function of the scattered disk at faint magnitudes (small sizes) beyond the current observational limit offer a possible but problematic resolution to the discrepancy. We discuss several other possibilities: that the present population of JFCs is a large fluctuation above their long-term average, that larger scattered disk objects tidally break up into multiple fragments during close planetary encounters as their orbits evolve from the trans-Neptune zone to near Jupiter, or that there are alternative source populations that contribute significantly to the JFCs. Well-characterized observational investigations of the Centaurs, objects that are transitioning between the trans-Neptune Kuiper Belt region and the inner solar system, can test the predictions of the non-steady state and the tidal breakup hypotheses. The classical and resonant classes of the Kuiper Belt are worth reconsideration as significant additional or alternate sources of the JFCs.

Optical observations of 23 distant Jupiter Family Comets, including 36P/Whipple at multiple phase angles

We present photometry on 23 Jupiter Family Comets (JFCs) observed at large heliocentric distance, primarily using the 2.5m Isaac Newton Telescope (INT). Snap-shot images were taken of 17 comets, of which 5 were not detected, 3 were active and 9 were unresolved and apparently inactive. These include 103P/Hartley 2, the target of the NASA Deep Impact extended mission, EPOXI. For 6 comets we obtained time-series photometry and use this to constrain the shape and rotation period of these nuclei. The data are not of sufficient quantity or quality to measure precise rotation periods, but the time-series do allow us to measure accurate effective radii and surface colours. Of the comets observed over an extended period, 40P/Vaisala 1, 47P/Ashbrook-Jackson and P/2004 H2 (Larsen) showed faint activity which limited the study of the nucleus. Light-curves for 94P/Russell 4 and 121P/Shoemaker-Holt 2 reveal rotation periods of around 33 and 10 hours respectively, although in both cases these are not unique solutions. 94P was observed to have a large range in magnitudes implying that it is one of the most elongated nuclei known, with an axial ratio a/b \ge 3. 36P/Whipple was observed at 5 different epochs, with the INT and ESO's 3.6m NTT, primarily in an attempt to confirm the preliminary short rotation period apparent in the first data set. The combined data set shows that the rotation period is actually longer than 24 hours. A measurement of the phase function of 36P's nucleus gives a relatively steep \beta = 0.060 \pm 0.019. Finally, we discuss the distribution of surface colours observed in JFC nuclei, and show that it is possible to trace the evolution of colours from the Kuiper Belt Object (KBO) population to the JFC population by applying a 'de-reddening' function to the KBO colour distribution.

The fundamental role of the Oort cloud in determining the flux of comets through the planetary system

A model of the Oort cloud has been developed by accounting for planetary, stellar and Galactic perturbations using numerical symplectic integrations covering 4.5 Gyr. The model is consistent with the broad dynamical characteristics of the observed cometary populations injected from the Oort cloud into dieren t regions of the Solar system. We show that the majority of observed high-eccentricity trans-Neptunian objects, Centaurs and short-period comets have visited the Oort cloud (a > 1000 au) during their dynamical history. Assuming from observations that the near-parabolic ux from the Oort cloud with absolute magnitudes H10 10 4 au is approximately 1 comet per year, our calculations imply a present Oort cloud population of 5 10 11 comets with H10 10 4 au. The number of comets reaching the planetary region from the Oort cloud (a>1000 au) is more than an order of magnitude higher per unit perihelion distance immediately beyond Neptune than in the observable zone q 30 au and 60 200 au and/or q >40 au, and they are found mostly to originate from initial orbits with 25 60 au. Objects that have visited the Oort cloud represent a substantial fraction of the Jupiter-family comet population, achieving short-period orbits by a process of gradual dynamical transfer, including a Centaur stage, from the outer Solar system to near-Earth space. A similar mechanism produces Halley-type comets, in addition to the well-known diusion process operating at small perihelion distances.

Hilda asteroids among Jupiter family comets

Hilda asteroids and comets are similar from the compositional point of view. The D-taxonomic class prevailing among Hildas has all the characteristics found in cometary spectra. Jupiter Family Comets (JFCs) coming from the trans-neptunian region are under the gravitational control of Jupiter, making them a dynamically unstable population with a mean dynamical lifetime of 10 4 to 10 5 years . In contrast, Hilda asteroids residing in the 3:2 mean motion resonance with Jupiter are a very stable population. But once they escape from the resonance, they are dynamically controlled by Jupiter, and in this sense their behavior resembles that of JFC. We performed a numerical simulation to analyze the dynamical evolution that Hildas follow after escaping from the resonance, and their contribution to the JFC population. We found that 8% of the particles leaving the resonance end up impacting Jupiter. 98.7% of the escaped Hildas live at least 1000 years as a JFC, with a mean lifetime of 1.4 × 10 6 years . In particular, escaped Hildas stay mainly in the region of perihelion distances greater than 2.5 AU . On the other hand, the number of escaped Hildas reaching the inner Solar System ( q < 2.5 AU ) is negligible. So, there are almost no Hilda asteroids among the NEO population. We also analyzed the possibility that the Shoemaker–Levy 9 were an escaped Hilda asteroid. In this case, it would be possible to give stronger constraints to its pre-capture orbital elements.

The Dynamics of Known Centaurs

We have numerically investigated the long-term dynamical behavior of known Centaurs. This class of objects is thought to constitute the transitional population between the Kuiper belt and the Jupiter-family comets (JFCs). In our study, we find that over their dynamical lifetimes these objects diffuse into the JFCs and other sinks, and they also make excursions into the scattered disk, but (not surprisingly) do not diffuse into the parameter space representing the main Kuiper belt. These Centaurs spend most of their dynamical lifetimes in orbits of eccentricity 0.2–0.6 and perihelion distance 12–30 AU. Their orbital evolution is characterized by frequent close encounters with the giant planets. Most of these Centaurs will escape from the solar system (or enter the Oort cloud), while a fraction will enter the JFC population and a few percent will impact a giant planet. Their median dynamical lifetime is 9 Myr, although there is a wide dispersion in lifetimes, ranging from less than 1 Myr to more than 100 Myr. We find the dynamical evolution of this sample of Centaurs to be less orderly than the planet-to-planet handoff described in previous investigations. We discuss the implications of our study for the spatial distribution of the Centaurs as a whole.

From Magnitudes to Diameters: The Albedo Distribution of Near Earth Objects and the Earth Collision Hazard

A recently published model of the Near Earth Object (NEO) orbital–magnitude distribution (Bottke et al., 2002, Icarus 156, 399–433.) relies on five intermediate sources for the NEO population: the ν 6 resonance, the 3:1 resonance, the outer portion of the main belt (i.e., 2.8–3.5 AU), the Mars-crossing population adjacent to the main belt, and the Jupiter family comet population. The model establishes the relative contribution of these sources to the NEO population. By computing the albedo distribution of the bodies in and/or near each of the five sources, we can deduce the albedo distribution of the NEO population as a function of semimajor axis, eccentricity, and inclination. A problem with this strategy, however, is that we do not know a priori the albedo distribution of main belt asteroids over the same size range as observed NEOs (diameter D<10 km). To overcome this problem, we determined the albedo distribution of large asteroids in and/or near each NEO source region and used these results to deduce the albedo distribution of smaller asteroids in the same regions. This method requires that we make some assumptions about the absolute magnitude distributions of both asteroid families and background asteroids. Our solution was to extrapolate the observed absolute magnitude distributions of the families up to some threshold value H thr, beyond which we assumed that the families' absolute magnitude distributions were background-like. We found that H thr=14.5 provides the best match to the color vs heliocentric distance distribution observed by the Sloan Digital Sky Survey. With this value of H thr our model predicts that the debiased ratio between dark and bright (albedo smaller or larger than 0.089) objects in any absolute-magnitude-limited sample of the NEO population is 0.25±0.02. Once the observational biases are properly taken into account, this agrees very well with the observed C/S ratio (0.165 for H<20). The dark/bright ratio of NEOs increases to 0.87±0.05 if a size-limited sample is considered. We estimate that the total number of NEOs larger than a kilometer is 855±110, which, compared to the total number of NEOs with H<18 (963±120), shows that the usually assumed conversion H=18↞ D=1 km slightly overestimates the number of kilometer-size objects. Combining our orbital distribution model with the new albedo distribution model, and assuming that the density of bright and dark bodies is 2.7 and 1.3 g/cm 3, respectively, we estimate that the Earth should undergo a 1000 megaton collision every 63,000±8000 years. On average, the bodies capable of producing 1000 megaton of impact energy are those with H<20.6. The NEOs discovered so far carry only 18±2% of this collision probability.

Mean Motion Resonances in the Trans-neptunian Region: I. The 2:3 Resonance with Neptune

The stability of the 2:3 mean motion resonance with Neptune is systematically explored and compared to the observed resonant population. It is shown that orbits with small and moderate amplitudes of the resonant angle are stable over the age of the Solar System. The observed resonant population is distributed within the stability limits. There exists an interval of large resonant amplitudes, where orbits are marginally unstable. Resonant objects starting in this interval may leave the resonance by slow increase of their resonant amplitudes on a time scale of several billion years. These objects eventually attain Neptune–crossing trajectories and contribute to the flux of Jupiter–family comets. The number of objects leaking from the 2:3 resonance per time interval is calibrated by the number of objects needed to keep the Jupiter–family comets population in steady state. This allows us to compute the upper limit of the number of resonant objects with cometary size. The effects of collisions and mutual gravitational scattering are discussed in this context.