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.     

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.     

Embedded star clusters and the formation of the Oort cloud: II. The effect of the primordial solar nebula

This paper deals with Oort cloud formation while the Sun was in an embedded cluster and surrounded by its primordial nebula. This work is a continuation of Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82], building on the model presented therein, and adding the aerodynamic drag and gravitational potential of the primordial solar nebula. Results are presented of numerical simulations of comets subject to the gravitational influence of the Sun, Jupiter, Saturn, star cluster and primordial solar nebula; some of the simulations included the gravitational influence of Uranus and Neptune as well. The primordial solar nebula was approximated by the minimum-mass Hayashi model [Hayashi, C., Nakozawa, K., Nakagawa, Y., 1985. In: Black, D.C., Matthews, M.S. (Eds.). Protostars and Planets II. Univ. of Arizona Press, Tucson, AZ] whose inner and outer radii have been truncated at various distances from the Sun. A comet size of 1.7 km was used for most of our simulations. In all of our simulations, the density of the primordial solar nebula decayed exponentially with an e-folding time of 2 Myr. It turns out that when the primordial solar nebula extends much beyond Saturn or Neptune, virtually no material will end up in the Oort cloud (OC) during this phase. Instead, the majority of the material will be on circular orbits inside of Jupiter if the inner edge of the disk is well inside Jupiter's orbit. If the disk's inner edge is beyond Jupiter's orbit, most comets end up on orbits in exterior mean-motion resonances with Saturn when Uranus and Neptune are not present. In those cases where the outer edge of the disk is close to Saturn or Neptune, the fraction of material that ends up in the subsequently formed OC is much less than that found in Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82] for the same cluster densities. This implies that for comets of roughly 2 km in size, the presence of the primordial solar nebula hinders OC formation. A byproduct of some of our simulations are endresults with a substantial fraction of the comets in the Uranus-Neptune scattered disk. A subsequent followup of this material is planned for the near future. In order to determine the effect of the size of the comets on OC formation efficiency, a set of runs with the same initial conditions but different cometary radii have been performed as well, from which it is determined that the threshold comet size to begin producing significant Oort clouds is roughly 20 km. This implies that the presence of the primordial solar nebula acts as a size-sorting mechanism, with large bodies unaffected by the gas drag and ending up in the OC while small bodies remain trapped in the planetary region, in the models studied.     

Sedna and the Oort Cloud around a migrating Sun

Recent numerical simulations have demonstrated that the Sun’s dynamical history within the Milky Way may be much more complex than that suggested by its current low peculiar velocity (Sellwood, J.A., Binney, J.J. [2002]. Mon. Not. R. Astron. Soc. 336, 785-796; Roškar, R., Debattista, V.P., Quinn, T.R., Stinson, G.S., Wadsley, J. [2008]. Astrophys. J. 684, L79-L82). In particular, the Sun may have radially migrated through the galactic disk by up to 5-6 kpc (Roškar, R., Debattista, V.P., Quinn, T.R., Stinson, G.S., Wadsley, J. [2008]. Astrophys. J. 684, L79-L82). This has important ramifications for the structure of the Oort Cloud, as it means that the Solar System may have experienced tidal and stellar perturbations that were significantly different from its current local galactic environment. To characterize the effects of solar migration within the Milky Way, we use direct numerical simulations to model the formation of an Oort Cloud around stars that end up on solar-type orbits in a galactic-scale simulation of a Milky Way-like disk formation. Surprisingly, our simulations indicate that Sedna’s orbit may belong to the classical Oort Cloud. Contrary to previous understanding, we show that field star encounters play a pivotal role in setting the Oort Cloud’s extreme inner edge, and due to their stochastic nature this inner edge sometimes extends to Sedna’s orbit. The Sun’s galactic migration heightens the chance of powerful stellar passages, and Sedna production occurs around ∼20-30% of the solar-like stars we study. Considering the entire Oort Cloud, we find its median distance depends on the minimum galactocentric distance attained during the Sun’s orbital history. The inner edge also shows a similar dependence but with increased scatter due to the effects of powerful stellar encounters. Both of these Oort Cloud parameters can vary by an order of magnitude and are usually overestimated by an Oort Cloud formation model that assumes a fixed galactic environment. In addition, the amount of material trapped in outer Oort Cloud orbits (a > 20,000 AU) can be extremely low and may present difficulties for traditional models of Oort Cloud formation and long-period comet production.     

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 Scattered Disk Population and the Oort Cloud

The trans-Neptunian belt has been subject to a strong depletion that has reduced its primordial population by a factor of one hundred over the solar system's age. One by-product of such a depletion process is the existence of a scattered disk population in transit from the belt to other places, such as the Jupiter zone, the Oort cloud or interstellar space. We have integrated the orbits of the scattered disk objects (SDOs) so far discovered by 2500 Myr to study their dynamical time scales and the probability of falling in each of the end states mentioned above, paying special attention to their contribution to the Oort cloud. We found that their dynamical half-time is close to 2.5 Gyr and that about one third of the SDOs end up in the Oort cloud.     

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.     

Evolution and instabilities of disks harboring super massive black holes

The bar formation is still an open problem in modern astrophysics. In this paper we present numerical simulations performed with the aim of analyzing the growth of the bar instability inside stellar-gaseous disks, where the star formation is triggered, and a central black hole is present. The aim of this paper is to point out the impact of such a central massive black hole on the growth of the bar. We use N-body-SPH simulations of the same isolated disk-to-halo mass systems harboring black holes with different initial masses and a different energy feedback on the surrounding gas. We compare the results of these simulations with the one of the same disk without a black hole in its center. We make the same comparison (disk with and without black hole) for a stellar disk in a fully cosmological scenario. A stellar bar, lasting 10 Gyrs, is present in all our simulations.     

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.     

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.     

From icy planetesimals to outer planets and comets

Numerical simulations of planet growth in the outer solar system shows thatgrwoth of Uranus and Neptune occurs in reasonably short time, well below the actual age of the system, without the need for ad hoc assumptions about excess mass or artificially low relative velocities among the icy planetesimals. Low velocities, which speed accretion, are a natural consequence of the non-power-law size distribution of planetesimals, just as in our earlier simulations of terrestial planet growth. Initial planetesimals of size ～ 100 km, predicted by formal expressions for gravitational instability in a thin disk of solid material, failed to produce sufficient debris in the size range 1 to 10 km to account for population of the Oort cloud with comet-sized bodies. However, our model of nonhomologous settling of grains to the midplane of the solar system shows that gravitational clumping did not wait until all solid material had settled to the midplane, as had been assumed in earlier models. Rather, the clumping occurred in successive portions of the material that reached the midplane, producing “initial” planetesimals probably of comet-like sizes. Models of subsequent collisional evolution show that such an initial size distribution, similar to known comets, would have been required in order to have an adequate comet-like size distribution available to feed the Oort cloud as the other planets reach full size. Comets are probably unaltered remnants of the initial population of planetesimals in the outer solar system, not fragments of larger bodies.     

Abundance Gradients as a tool for understanding the Formation of the Milky Way

According to the two-infall model for the chemical evolution of the Galaxy the halo and bulge formed on a relatively short timescale (0.8–1.0 Gyr) out of the first infall episode, whereas the disk accumulated much more slowly and ‘inside-out’ during a second independent infall episode. We explored the effects of a threshold in the star formation process, during both the halo and disk phases. In the comparison between model predictions and available data, we have focused our attention on abundance gradients as well as gas, stellar and star formation rate distributions along the disk. We suggest that the mechanism for the formation of the halo leaves detectable imprints on the chemical properties of the outer regions of the disk, whereas the evolution of the halo and the inner disk are almost completely disentangled. This is due to the fact that the halo and disk densities are comparable at large Galactocentric distances and therefore the gas lost from the halo can substantially contribute to building up the outer disk. We predict that the abundance gradients along the Galactic disk have increased in time during the first billion years of the disk evolution and remained almost constant in the last ~5Gyrs. This revised version was published online in September 2006 with corrections to the Cover Date.     

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.     

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.     

The Outer Part of the Scattered Disc from the Simulation of the Formation of Small-body Reservoirs

Considering the model of the initial disc of planetesimals consisting of 10,038 test particles, we simulated the formation of small-body reservoirs in the outer Solar System for the 2-Gyr period. We present the results from the simulation, which concern the part of the scattered disc with objects that have the semi-major axes larger than 50 AU and do not cross the Neptune’s orbit. A suitable border between the scattered disc and the inner Oort cloud, in terms of semi-major axis, appears to be no more than 2,500 AU. The simulated and observed values of perihelion distance and inclination to the Ecliptic typically cover the range between 30 and 40 AU and from 0° to 30°, respectively. No simulated or observed values of the inclination exceed 45°. The distributions of eccentricity and inclination in the simulation are more consistent with their observed counterparts, if the primary observational selection effects are imitated in the simulated distributions.     

Open star clusters in the spiral arms of our Galaxy

We consider the age distributions of open star clusters attributed to three segments of Galactic spiral arms. The smoothed distributions of clusters on the age-Galactocentric angle plane show a great nonuniformity. The time dependence of the formation rate of Galactic disk clusters recovered by taking into account selection effects and dynamical evolution of clusters shows that, on average, the formation rate of open star clusters decreases with time. This is in agreement with the increase in star formation rate into the past, as follows from the study of this process by the method of stellar population synthesis. The present time is the epoch of a current maximum of the cluster formation rate. In addition to the current maximum, there have been at least three more maxima with a period of 300–400 Myr and a duration of no more than 300 Myr. The age distributions are consistent with the pattern of star formation governed by the successive passages of density waves through each examined volume of the Galactic disk. The spiral structure becomes more complex when passing from the inner regions of the Galaxy to its outer regions.     

2-Gyr Simulation of the Oort-cloud Formation II. A Close View of the Inner Oort cloud after the First Two Giga-years

We simulate the formation of the Oort cloud (OC) till the age of 2 Gyr starting from an initial disc of planetesimals made by 10 038 test particles. The results on the outer part of the distant comet reservoir are reported by Neslu?an et al. (this issue). Here we deal with the evolution of the population and structure at 2 Gyr of the complementary inner part of the Oort cloud. The dynamical evolution of the massless test particles was followed via the numerical integration of their orbits. We considered the perturbations produced by four giant planets assuming they have their current orbits and masses, as well as the perturbations caused by the Galactic tide and passing stars. The efficiency of the formation of inner OC is found to be very low: only about 1.1% of all considered particles ended in this part of the OC. At 2 Gyr, the dynamics of the inner cloud is mainly governed by the dominant z-term of the Galactic tide. The number density of the bodies is proportional to the heliocentric distance, r, as r ^?3.53. The directional distribution of orbits is still strongly inhomogeneous. There are large empty regions in the space angles around the Galactic Equator points with the galactic longitude 90 and 270° (non-rotating frame), or there are only few bodies having the ecliptical latitude higher than +60° or lower than 60°. A strong concentration of objects at the Ecliptic is apparent up to ≈1,000 AU, with a possible—but still not proved—extension to ≈1,500 AU. Beyond r ≈ 6,000 AU, bodies directly above and below the Sun, with respect to the Ecliptic, are absent.     

The migrating embryo model for disk evolution

Abstract– A new view of disk evolution is emerging from self‐consistent numerical simulation modeling of the formation of circumstellar disks from the direct collapse of prestellar cloud cores. This has implications for many aspects of star and planet formation, including the growth of dust and high‐temperature processing of materials. A defining result is that the early evolution of a disk is crucially affected by the continuing mass loading from the core envelope, and is driven into recurrent phases of gravitational instability. Nonlinear spiral arms formed during these episodes fragment to form gaseous clumps in the disk. These clumps generally migrate inward due to gravitational torques arising from their interaction with a trailing spiral arm. Occasionally, a clump can open up a gap in the disk and settle into a stable orbit, revealing a direct pathway to the formation of companion stars, brown dwarfs, or giant planets. At other times, when multiple clumps are present, a low mass clump may even be ejected from the system, providing a pathway to the formation of free‐floating brown dwarfs and giant planets in addition to low mass stars. Finally, it has been suggested that the inward migration of gaseous clumps can provide the proper conditions for the transport of high‐temperature processed solids from the outer disk to the inner disk, and even possibly accelerate the formation of terrestrial planets in the inner disk. All of these features arising from clump formation and migration can be tied together conceptually in a migrating embryo model for disk evolution that can complement the well‐known core accretion model for planet formation.     

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).