The scattered disk population as a source of Oort cloud comets: evaluation of its current and past role in populating the Oort cloud

We have integrated the orbits of the 76 scattered disk objects (SDOs), discovered through the end of 2002, plus 399 clones for 5 Gyr to study their dynamical evolution and the probability of falling in one of the following end states: reaching Jupiter's influence zone, hyperbolic ejection, or transfer to the Oort cloud. We find that nearly 50% of the SDOs are transferred to the Oort cloud (i.e., they reach heliocentric distances greater than 20,000 AU in a barycentric elliptical orbit), from which about 60% have their perihelia beyond Neptune's orbit (31 AU<q<36 AU) at the moment of reaching the Oort cloud. This shows that Neptune acts as a dynamical barrier, scattering most of the bodies to near-parabolic orbits before they can approach or cross Neptune's orbit in non-resonant orbits (that may allow their transfer to the planetary region as Centaurs via close encounters with Neptune). Consequently, Neptune's dynamical barrier greatly favors insertion in the Oort cloud at the expense of the other end states mentioned above. We found that the current rate of SDOs with radii R>1 km incorporated into the Oort cloud is about 5 yr⁻¹, which might be a non-negligible fraction of comet losses from the Oort cloud (probably around or even above 10%). Therefore, we conclude that the Oort cloud may have experienced and may be even experiencing a significant renovation of its population, and that the trans-neptunian belt—via the scattered disk—may be the main feeding source.     

Coupling dynamical and collisional evolution of small bodies: II. Forming the Kuiper belt, the Scattered Disk and the Oort Cloud

The Oort Cloud, the Kuiper belt and the Scattered Disk are dynamically distinct populations of small bodies evolving in the outer regions of the Solar System. Whereas their collisional activity is now quiet, gravitational interactions with giant planets may have shaped these populations both dynamically and collisionally during their formation. Using a hybrid approach [Charnoz, S., Morbidelli, A., 2003. Icarus 166, 141-166], the present paper tries to couple the primordial collisional and dynamical evolution of these three populations in a self-consistent way. A critical parameter is the primordial size-distribution. We show that the initial planetesimal size distribution that allows an effective mass depletion of the Kuiper belt by collisional grinding, would decimate also the population of comet-size bodies that end in the Oort Cloud and, in particular, in the Scattered Disk. As a consequence, the Oort Cloud and the Scattered Disk would be too anemic, by a factor 20 to 100, relative to the estimates achieved from the observation of the fluxes of long period and Jupiter family comets, respectively. For these two reservoirs to have a sufficient number of comets, the initial size distribution in the planetesimal disk had to be such that the mass depletion by collisional erosion of the Kuiper belt was negligible. Consequently the current mass deficit of the Kuiper belt needs to be explained by dynamical mechanisms.     

On The Origin of The High-Perihelion Scattered Disk: The Role of The Kozai Mechanism And Mean Motion Resonances

We study the transfer process from the scattered disk (SD) to the high-perihelion scattered disk (HPSD) (defined as the population with perihelion distances q > 40 AU and semimajor axes a>50 AU) by means of two different models. One model (Model 1) assumes that SD objects (SDOs) were formed closer to the Sun and driven outwards by resonant coupling with the accreting Neptune during the stage of outward migration (Gomes 2003b, Earth, Moon, Planets 92, 29–42.). The other model (Model 2) considers the observed population of SDOs plus clones that try to compensate for observational discovery bias (Fernández et al. 2004, Icarus , in press). We find that the Kozai mechanism (coupling between the argument of perihelion, eccentricity, and inclination), associated with a mean motion resonance (MMR), is the main responsible for raising both the perihelion distance and the inclination of SDOs. The highest perihelion distance for a body of our samples was found to be q = 69.2 AU. This shows that bodies can be temporarily detached from the planetary region by dynamical interactions with the planets. This phenomenon is temporary since the same coupling of Kozai with a MMR will at some point bring the bodies back to states of lower-q values. However, the dynamical time scale in high-q states may be very long, up to several Gyr. For Model 1, about 10% of the bodies driven away by Neptune get trapped into the HPSD when the resonant coupling Kozai-MMR is disrupted by Neptune’s migration. Therefore, Model 1 also supplies a fossil HPSD, whose bodies remain in non-resonant orbits and thus stable for the age of the solar system, in addition to the HPSD formed by temporary captures of SDOs after the giant planets reached their current orbits. We find that about 12 – 15% of the surviving bodies of our samples are incorporated into the HPSD after about 4 – 5 Gyr, and that a large fraction of the captures occur for up to the 1:8 MMR (a ⋍ 120 AU), although we record captures up to the 1:24 MMR (a ≃ 260 AU). Because of the Kozai mechanism, HPSD objects have on average inclinations about 25°–50°, which are higher than those of the classical Edgeworth–Kuiper (EK) belt or the SD. Our results suggest that Sedna belongs to a dynamically distinct population from the HPSD, possibly being a member of the inner core of the Oort cloud. As regards to 2000 CR₁₀₅ , it is marginally within the region occupied by HPSD objects in the parametric planes (q,a) and (a,i), so it is not ruled out that it might be a member of the HPSD, though it might as well belong to the inner core.     

The formation of the Oort cloud in open cluster environments

We study the influence of an open cluster environment on the formation and current structure of the Oort cloud. To do this, we have run 19 different simulations of the formation of the Oort cloud for 4.5 Gyrs. In each simulation, the Solar System spends its first 100 Myrs in a different open cluster environment before transitioning to its current field environment. We find that, compared to forming in the field environment, the inner Oort cloud is preferentially loaded with comets while the Sun resides in the open cluster and that most of this material remains locked in the interior of the cloud for the next 4.4 Gyrs. In addition, the outer Oort cloud trapping efficiencies we observe in our simulations are lower than previous formation models by about a factor of 2, possibly implying an even more massive early planetesimal disk. Furthermore, some of our simulations reproduce the orbits of observed extended scattered disk objects, which may serve as an observational constraint on the Sun's early environment. Depending on the particular open cluster environment, the properties of the inner Oort cloud and extended scattered disk can vary widely. On the other hand, the outer portions of the Oort cloud in each of our simulations are all similar.     

The occurrence of high-order resonances and Kozai mechanism in the scattered disk

By means of numerical methods we explore the relevance of the high-order exterior mean motion resonances (MMR) with Neptune that a scattered disk object (SDO) can experience in its diffusion to the Oort cloud. Using a numerical method for estimate the strength of these resonances we show that high-eccentricity or high-inclination resonant orbits should have evident dynamical effects. We investigate the properties of the Kozai mechanism (KM) for non-resonant SDO's and the conditions that generate the KM inside a MMR associated with substantial changes in eccentricity and inclination. We found that the KM inside a MMR is typical for SDO's with Pluto-like or greater inclinations and is generated by the oscillation of ω inside the mixed (e,i) resonant terms of the disturbing function. A SDO diffusing to the Oort cloud should experience temporary captures in MMR, preferably of the type 1:N, and when evolving inside a MMR and experiencing the KM it can reach regions where the strength of the resonance drops and consequently there is a possibility of being decoupled from the resonance generating by this way a long-lived high-perihelion scattered disk object (HPSDO).     

Long-Period Comets and the Oort Cloud

Long-period (LP) comets, Halley-type (HT) comets, and even some comets of the Jupiter family, probably come from the Oort cloud, a huge reservoir of icy bodies that surrounds the solar system. Therefore, these comets become important probes to learn about the distant Oort cloud population. We review the fundamental dynamical properties of LP comets, and what is our current understanding of the dynamical mechanisms that bring these bodies from the distant Oort cloud region to the inner planetary region. Most new comets have original reciprocal semimajor axes in the range2 × 10^-5 < 1/a_orig < 5 × 10^-5AU^-1. Yet, this cannot be taken to represent the actual space distribution of Oort cloud comets, but only the region in the energy space in which external perturbers have the greatest efficiency in bringing comets to the inner planetary region. The flux of Oort cloud comets in the outer planetary region is found to be at least several tens times greater than the flux in the inner planetary region. The sharp decrease closer to the Sun is due to the powerful gravitational fields of Jupiter and Saturn that prevent most Oort cloud comets from reaching the Earth’s neighborhood (they act as a dynamical barrier). A small fraction of ～10^-2 Oort cloud comets become Halley type (orbital periods P < 200 yr), and some of them can reach short-period orbits with P < 20 yr. We analyze whether we can distinguish the latter, very ‘old” LP comets, from comets of the Jupier family coming from the Edgeworth-Kuiper belt.     

Peripheral Structures of Planetary Systems

We analyze the conditions for the formation and time evolution of peripheral comet structures of solar-type planetary systems. In the Solar system, these include the Kuiper belt, the Oort cloud, the comet spear, and the Galactic comet ring that marks the Galactic orbit of the Sun. We consider the role of the viscosity of a protoplanetary gas–dust disk, major planets, field stars, globular clusters, giant molecular clouds, and the Galactic gravitational field in the formation of these peripheral structures marked by comets and asteroids. We give a list of the closest past and future passages of neighboring stars through the solar Oort cloud that perturb the motion of its comets and, thus, contribute to the enhancement of its cometary activity, on the one hand, and to the replenishment of the solar comet spear with new members, on the other hand.     

Long-term effects of the Galactic tide on cometary dynamics

We introduce a model for integrating the effects of Galactic tides on Oort cloud comets, which involves two procedures, according to the values of the osculating semi-major axis a and eccentricity e. Ten simulations of the dynamics of 10⁶ comets over 5 Gyr are performed using this model. We thus investigate the long-term effects of the Galactic tide with and without a radial component, the effects of the local density of the Galactic disk, and those of the Oort constants. Most of the results may be understood in terms of the integrability or non-integrability of the system. For an integrable system, which occurs for moderate semi-major axes with or without radial component, the dynamics is explained by periodic variation of the cometary perihelion, inducing the depletion of the outer region of the Oort cloud, a constant flux from the inner region after 500 Myr, and the quick formation of a reservoir of comets with argument of perihelion near 26.6°. When the system is non-integrable, the efficiency of the tide in reducing the cometary perihelion distance is enhanced both by replenishing the Oort cloud domain from which comets are sent toward the planetary system, and by reducing the minimal value that the perihelion distance may reach. No effects of varying the Oort constants were observed, showing that the flat rotation curve is a satisfactory approximation in Oort cloud dynamics.     

The Meudon Multicolor Survey (2MS) of Centaurs and trans-neptunian objects: extended dataset and status on the correlations reported

We present here the latest B−V, V−R, and R−I color measurements obtained with the CFH12K mosaic camera of the 3.6-m Canada-France-Hawaii Telescope (CFHT). This work is the latest extension of the Meudon Multicolor Survey (2MS) and extends the total number of Centaurs and trans-neptunian objects (TNOs) in the dataset to 71. With this large and homogeneous dataset, we performed relevant statistical analyses to search for correlations with physical and orbital parameters and interrelations with related populations (cometary nuclei and irregular satellites). With a larger dataset, we confirm the correlations found for the Classical TNOs in our previous survey: some colors are significantly correlated with perihelion distance and inclination. The only exception is with the eccentricity. However, results strongly depend on which objects are considered Classicals, and with a dynamically more restricted definition these correlations are no longer present. We also find that strongly significant trends with orbital parameters are not detected for Centaurs, Plutinos or scattered disk objects (SDOs). We also make for the first time reliable statistical comparison between TNOs and related populations (e.g., Centaurs, irregular satellites, short period comets—i.e., SPCs). We find that (1) the colors of SPCs do not match either their TNO or Centaur precursors, and this suggests that some process modifies the surface of SPCs at entry into the inner Solar System. The only exception concerns colors of SDOs from which we could statistically assess that SPCs and SDOs could be drawn from a same single parent distribution. (2) Not surprisingly, Centaurs are compatible with each of the Edgeworth-Kuiper belt dynamical groups at a highly significant level except with the SDOs. (3) Centaurs' colors still present a strong dichotomy between a neutral/slightly red group (e.g., Chiron) and a very red group (e.g., Pholus). (4) The irregular satellite population is not compatible with any of the Centaur, Plutino or Classical populations; however, the similarity of their color properties with SDOs suggests that both groups can be extracted from the same parent distribution. However, due to the small number of Centaurs and SDOs these conclusions cannot be taken as definitive.     

Why we study the geological record for evidence of the solar oscillation about the galactic midplane

The Solar System oscillates about the plane defined by the disk of matter in our Galaxy. This oscillatory motion gives rise to a substantial modulation in the tidally induced flux of Oort cloud comets. An observational determination of the quasi-periodicity of this motion carries with it significant information about the population, distributions, dynamics and origins of short-period and long-period comets. An additional incentive for emphasizing such a study is the information about dark disk matter that a period can yield. If dark disk matter is completely negligible, the amplitude of the solar motion will be sufficiently large that the peak-to-trough flux ratio will be ≈ 2.5 and the plane-crossing period will exceed 40 Myr. Dark disk matter comparable in mass to bright disk matter and distributed in any manner is inconsistent with K-dwarf distributions and can be rejected as a working hypothesis. But if a modest fraction of the disk matter is dark and distributed like the interstellar medium, as is consistent with limits deduced from K-giant and K-dwarf velocity distributions, the peak-to-trough flux ratio can increase to a factor of 4 even though the solar z amplitude is decreased. In that case the period can be as little as 30 Myr and the implied Oort population is smaller by a factor of 3. We should carefully reconsider the geological record as a potential discriminator of these options.     

Embedded star clusters and the formation of the Oort cloud: III. Evolution of the inner cloud during the Galactic phase

In a previous publication [Brasser, R., Duncan, M.J., Levison, H.F., 2006. Icarus 184, 59-82], models of the inner Oort cloud were built which included the effect of an embedded star cluster on cometary orbits about the Sun. The main conclusions of that paper were that the formation efficiency is about 10% and the median distance of the cloud to the Sun only depends on the mean density of gas and stars the Sun encountered. Here we report on the results of simulations which followed the ensuing dynamical evolution of these comet clouds in the current Galactic environment once the Sun left the embedded star cluster. The goal is to determine whether or not the dynamical influence of passing Galactic field stars and the Galactic tidal field is sufficient to replenish the current outer cloud (semi-major axis a>20,000 AU) with enough material from the inner cloud (a<20,000 AU). Since visible new comets come directly from the outer cloud, a mass estimate only exists for the latter, with a lower limit of 1 M_⊕ [Francis, P.J., 2005. Astrophys. J. 635, 1348-1361]. Knowing the amount of expansion of the inner cloud may therefore yield an estimate of the mass of said (unseen) inner cloud. Our results indicate that typically only 10% of the comets from the inner cloud land in the outer cloud and are bound after 4.5 Gyr. If one assumes that in the extreme case all or the majority of the current population of the outer cloud has come from the inner cloud, then a typical value of the mass of the inner cloud is about 10 M_⊕. The results of [Brasser, R., Duncan, M.J., Levison, H.F., 2006. Icarus 184, 59-82] showed that ∼10% of comets from the Jupiter-Saturn region were implanted in the inner Oort cloud, which implies an uncomfortably large value of about 100 M_⊕ for the mass of solids in the primordial Jupiter-Saturn region. This extreme case might be remedied in two says: either the effect of Giant Molecular Cloud complexes on the inner Oort cloud must be much more severe than originally thought, or there was a two-stage formation process for the Oort cloud, in which the outer cloud was largely populated by comets scattered once the Sun had left its primordial birth cluster.     

Tidal Breakup of Comets

In the context of the survival of periodic comets of different origins, rotational breakup and tidal disruption could be important, especially of the short period comets injected from the Kuiper belt. This is because long-period comets from the distant Oort cloud tend to be subject to thermal stress and volatile 'explosion' far more severely. A simple calculation using the Öpik method of random planetary close encounters was performed to estimate the probability of tidal disruption of comets and scattered Kuiper belt objects (SKBOs) during their orbital migration. It was found that a large fraction of the short period comets and SKBOs might have been internally fragmented by single or multiple close encounters with the outer planets.     

Structure and Dynamics of the Centaur Population: Constraints on the Origin of Short-Period Comets

The origin of Jupiter-family comets is linked to the intermediate stage of evolution through the Centaur region. Thus the structure of the Centaur population provides important constraints on sources of short-period comets. We show that our model of the Oort cloud evolution gives results which are consistent with the orbital distribution of observed Centaurs. In particular, it explains the existence of the large population of Centaurs with semimajor axes greater than 60 AU. The main source for these objects is the inner Oort cloud. Both Jupiter-family and Halley-type comets are produced by Centaurs originating from the Oort cloud. The injection rate for Jupiter-family comets coming from the inner Oort cloud is, at least, not less than that for a model based on the observed sample of high-eccentricity trans-Neptunian objects.     

Why we study the geological record for evidence of the solar oscillation about the galactic midplane

The Solar System oscillates about the plane defined by the disk of matter in our Galaxy. This oscillatory motion gives rise to a substantial modulation in the tidally induced flux of Oort cloud comets. An observational determination of the quasi-periodicity of this motion carries with it significant information about the population, distributions, dynamics and origins of short-period and long-period comets. An additional incentive for emphasizing such a study is the information about dark disk matter that a period can yield. If dark disk matter is completely negligible, the amplitude of the solar motion will be sufficiently large that the peak-to-trough flux ratio will be 2.5 and the plane-crossing period will exceed 40 Myr. Dark disk matter comparable in mass to bright disk matter and distributed in any manner is inconsistent with K-dwarf distributions and can be rejected as a working hypothesis. But if a modest fraction of the disk matter is dark and distributed like the interstellar medium, as is consistent with limits deduced from K-giant and K-dwarf velocity distributions, the peak-to-trough flux ratio can increase to a factor of 4 even though the solar z amplitude is decreased. In that case the period can be as little as 30 Myr and the implied Oort population is smaller by a factor of 3. We should carefully reconsider the geological record as a potential discriminator of these options.     

Structure and evolution of the Jupiter family

Both physical and dynamical issues are important in order to judge the origin and evolution of the Jupiter family of short-period comets. The steady-state condition for maintaining this structure at its present size by captures from the classical Oort cloud is reviewed on the basis of recent results concerning the absolute number of Jupiter family comets as a function of perihelion distance as well as the coupled physical and dynamical evolutions that evidently occur. Like in most earlier investigations, a clear shortage is found in the classical Oort cloud source. The shortage seems, however, less extreme than sometimes assumed. Monte Carlo simulations are envisaged as a way to shed further light on the fate of Jupiter family comets.     

Reassessing the formation of the inner Oort cloud in an embedded star cluster

We re-examine the formation of the inner Oort comet cloud while the Sun was in its birth cluster with the aid of numerical simulations. This work is a continuation of an earlier study (Brasser, R., Duncan, M.J., Levison, H.F. [2006]. Icarus 184, 59–82) with several substantial modifications. First, the system consisting of stars, planets and comets is treated self-consistently in our N-body simulations, rather than approximating the stellar encounters with the outer Solar System as hyperbolic fly-bys. Second, we have included the expulsion of the cluster gas, a feature that was absent previously. Third, we have used several models for the initial conditions and density profile of the cluster – either a Hernquist or Plummer potential – and chose other parameters based on the latest observations of embedded clusters from the literature. These other parameters result in the stars being on radial orbits and the cluster collapses. Similar to previous studies, in our simulations the inner Oort cloud is formed from comets being scattered by Jupiter and Saturn and having their pericentres decoupled from the planets by perturbations from the cluster gas and other stars. We find that all inner Oort clouds formed in these clusters have an inner edge ranging from 100 AU to a few hundred AU, and an outer edge at over 100,000 AU, with little variation in these values for all clusters. All inner Oort clouds formed are consistent with the existence of (90377) Sedna, an inner Oort cloud dwarf planetoid, at the inner edge of the cloud: Sedna tends to be at the innermost 2% for Plummer models, while it is 5% for Hernquist models. We emphasise that the existence of Sedna is a generic outcome. We define a ‘concentration radius’ for the inner Oort cloud and find that its value increases with increasing number of stars in the cluster, ranging from 600 AU to 1500 AU for Hernquist clusters and from 1500 AU to 4000 AU for Plummer clusters. The increasing trend implies that small star clusters form more compact inner Oort clouds than large clusters. We are unable to constrain the number of stars that resided in the cluster since most clusters yield inner Oort clouds that could be compatible with the current structure of the outer Solar System. The typical formation efficiency of the inner Oort cloud is 1.5%, significantly lower than previous estimates. We attribute this to the more violent dynamics that the Sun experiences as it rushes through the centre of the cluster during the latter’s initial phase of violent relaxation.     

The size distribution of trans-Neptunian bodies

The magnitude distribution of the trans-Neptunian bodies composed of the Kuiper Belt Objects (KBOs) and Scattered Disk Objects (SDOs) is determined for absolute magnitudes H?7, using maximum likelihood estimation methods. This is translated into a corresponding size distribution. This gave a differential size index of q=3.966±0.15 for KBOs and q=3.016±0.32 for SDOs. It was found that these two distributions were statistically different. The KBOs were further split into classical KBOs and Plutinos which had indices of q=4.074±0.18 and q=3.301±0.37, respectively. There was no statistical evidence that these are different populations. The classical KBOs were further split and examined for four different semi-major axis ranges and it was found that there was moderate evidence that the entire sample was not well represented by one index. The distribution indices of the SDOs were compared with the distributions of short period comets and found to be similar. It is likely that the scattered disk population is the source of the short period comets.     

Persistent evidence of a jovian mass solar companion in the Oort cloud

We present updated dynamical and statistical analyses of outer Oort cloud cometary evidence suggesting that the Sun has a wide-binary jovian mass companion. The results support a conjecture that there exists a companion of mass ≈ orbiting in the innermost region of the outer Oort cloud. Our most restrictive prediction is that the orientation angles of the orbit plane in galactic coordinates are centered on Ω, the galactic longitude of the ascending node = 319° and i, the galactic inclination = 103° (or the opposite direction) with an uncertainty in the orbit normal direction subtending <2% of the sky. Such a companion could also have produced the detached Kuiper Belt object Sedna. If the object exists, the absence of similar evidence in the inner Oort cloud implies that common beliefs about the origin of observed inner Oort cloud comets must be reconsidered. Evidence of the putative companion would have been recorded by the Wide-field Infrared Survey Explorer (WISE) which has completed its primary mission and is continuing on secondary objectives.     

Origin of oort cloud comets in the interstellar space

Comets must form a major part of the interstellar medium. The solar system provides a flux of comets into the interstellar space and there is no reason to suspect that many other stars and their surrounding cometary systems would not make a similar contribution. Occasionally interstellar comets must pass through the inner solar system, but Whipple (1975) considers it unlikely that such a comet is among the known cases of apparently hyperbolic comets. Even so the upper limit for the density of unobserved interstellar comets is relatively high.In addition, we must consider the possibility that comets are a genuine component of interstellar medium, and that the Oort Cloud is merely a captured part of it (McCrea, 1975). Here we review various dynamical possibilities of two-way exchange of comet populations between the Solar System and the interstellar medium. We describe ways in which a traditional Oort Cloud (Oort, 1950) could be captured from the interstellar medium. However, we note that the so called Kuiper belt (Kuiper, 1951) of comets cannot arise through this process. Therefore we have to ask how necessary the concept of the yet unobserved Kuiper belt is for the theory of short period comets.There has been considerable debate about the question whether short period comets can be understood as a captured population of the Oort Cloud of comets or whether an additional source has to be postulated. The problem is made difficult by the long integration times of comet orbits through the age of the Solar System. It would be better to have an accurate treatment of comet-planet encounters in a statistical sense, in the form of cross sections, and to carry out Monte Carlo studies. Here we describe the plan of action and initial results of the work to derive cross sections by carrying out large numbers of comet — planet encounters and by deriving approximate analytic expressions for them. Initially comets follow parabolic orbits of arbitrary inclination and perihelion distance; cross sections are derived for obtaining orbits of given energy and inclination after the encounter. The results are used in subsequent work to make evolutionary models of the comet population.