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.     

Structure and mass function of three young open clusters

Using UBVRI CCD data taken from 104-cm Sampurnanand Telescope, ARIES, Nainital, we present the structure, initial mass function and mass segregation of three young age (∼10 Myr) open star clusters: NGC 2129, NGC 1502 and King 12. Based on photometric as well as astrometric criteria, the cluster member stars as well as field stars have been identified. We construct luminosity function which is further used to estimate the mass functions by employing theoretical stellar evolutionary isochrones. The entire cluster region mass function (MF) slopes for NGC 2129, NGC 1502 and King 12 are obtained as −2.55 ± 0.14, −2.73 ± 0.36 and −1.94 ± 0.12 respectively. It is found that changes in the MF slope of King 12 are significantly different compared to NGC 2129 and NGC 1502 from inner region to outer region. The MF slope for King 12 is steeper at larger radii. The dynamical relaxation times for all three clusters are found to be less than age of the clusters. This indicates that all these clusters are dynamically relaxed. We show that for NGC 1502 and King 12, passing off of low mass stars from the inner region of the clusters to the halo occurs during the course of evolution.     

The Role of Giant Molecular Clouds in the Evolution of the Oort Comet Cloud

We estimated the gravitational influence of giant molecular clouds passing near the Solar system on the orbital evolution of Oort cloud comets. We performed a comparative analysis of the accuracies of the following two methods of allowance for the perturbations from giant molecular clouds: the impulse approximation and numerical integration. The impulse approximation yields fairly accurate estimates of the change in the energy of Oort cloud comets and the probability of their ejection under the influence of a molecular cloud if the path of the Solar system does not cross its boundary and if the molecular cloud may be treated as a point perturbing mass. The comet survival probability in the Oort cloud depends significantly on the internal structure of the perturbing molecular cloud and the impact parameter of the encounter. The most massive injection of comets into the planetary region and their ejection from the Oort cloud take place if the Solar system passes through a giant molecular cloud composed of several high-mass condensations. In this case, most of the comets injected into the planetary region were initially comets of the inner Oort cloud (a 10^–4 AU) with high orbital eccentricities.     

Tidal gravitational forces: The infall of “new” comets and comet showers

The tidal gravitational field of the Galaxy directed into the galactic plane changes the angular momentum of comets in the Oort cloud. For comet orbits with semimajor axis greater than 2 × 10⁴ AU, the change of angular momentum in one orbit is sufficient to bring comets from the Oort cloud into the visible region, causing the infall of “new” comets. The limiting size orbit is weakly dependent on the angle between the major axis of the comet orbit and the galactic plane. The flux of comets into the inner Solar System caused by the galactic tidal field will be continuous and nearly isotropic. This effect appears to exclude any determination of the trajectories of passing stars by analysis of the angular distribution of new comets. The production of intense comet showers by the tidal field of a solar companion or of an interstellar cloud is considered. We show that the direction of a solar companion cannot be found from the present distribution of observable comets. The frequency of comet showers induced by encounters with interstellar clouds is found to be much lower than that from passing stars, and the tidal fields of interstellar clouds are not strong enough to cause comet showers of sufficient intensity to result in Earth impacts.     

Long-period comet flux in the planetary region: Dynamical evolution from the Oort cloud

This study analyzes the evolution of 2 × 10⁵ orbits with initial parameters corresponding to the orbits of comets of the Oort cloud under the action of planetary, galactic, and stellar perturbations over 2 × 10⁹ years. The dynamical evolution of comets of the outer (orbital semimajor axes a > 10⁴ AU) and inner (5 × 10³ < a (AU) < 10⁴) parts of the comet cloud is analyzed separately. The estimates of the flux of “new” and long-period comets for all perihelion distances q in the planetary region are reported. The flux of comets with a > 10⁴ AU in the interval 15 AU < q < 31 AU is several times higher than the flux of comets in the region q < 15 AU. We point out the increased concentration of the perihelia of orbits of comets from the outer cloud, which have passed several times through the planetary system, in the Saturn-Uranus region. The maxima in the distribution of the perihelia of the orbits of comets of the inner Oort cloud are located in the Uranus-Neptune region. “New” comets moving in orbits with a < 2 × 10⁴ AU and arriving at the outside of the planetary system (q > 25 AU) subsequently have a greater number of returns to the region q < 35 AU. The perihelia of the orbits of these comets gradually drift toward the interior of the Solar System and accumulate beyond the orbit of Saturn. The distribution of the perihelia of long-period comets beyond the orbit of Saturn exhibits a peak. We discuss the problem of replenishing the outer Oort cloud by comets from the inner part and their subsequent dynamical evolution. The annual rate of passages of comets of the inner cloud, which replenish the outer cloud, in the region q < 1 AU in orbits with a > 10⁴ AU (～ 5.0 × 10^?14 yr^?1) is one order of magnitude lower than the rate of passage of comets from the outer Oort cloud (～ 9.1 × 10^?13 yr^?1).     

Injection of Oort Cloud comets: the fundamental role of stellar perturbations

We present Monte Carlo simulations of the dynamical evolution of the Oort cloud over the age of the Solar System, using an initial sample of one million test comets without any cloning. Our model includes perturbations due to the Galactic tide (radial and vertical) and passing stars. We present the first detailed analysis of the injection mechanism into observable orbits by comparing the complete model with separate models for tidal and stellar perturbations alone. We find that a fundamental role for injecting comets from the region outside the loss cone (perihelion distance q > 15 AU) into observable orbits (q < 5 AU) is played by stellar perturbations. These act in synergy with the tide such that the total injection rate is significantly larger than the sum of the two separate rates. This synergy is as important during comet showers as during quiescent periods and concerns comets with both small and large semi-major axes. We propose different dynamical mechanisms to explain the synergies in the inner and outer parts of the Oort Cloud. We find that the filling of the observable part of the loss cone under normal conditions in the present-day Solar System rises from <1% for a < 20 000 AU to about 100% for a ? 100 000 AU.     

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.     

The outcome of the protoplanetary disk of very massive stars

We suggest that planets, brown dwarfs, and even low mass stars can be formed by fragmentation of protoplanetary disks around very massive stars (M ? 100 M_⊙). We discuss how fragmentation conditions make the formation of very massive planetary systems around very massive stars favorable. Such planetary systems are likely to be composed of brown dwarfs and low mass stars of ～0.1–0.3 M_⊙, at orbital separations of ～ few × 100–10⁴ AU. In particular, scaling from solar-like stars suggests that hundreds of Mercury-like planets might orbit very massive stars at ～10³ AU where conditions might favor liquid water. Such fragmentation objects can be excellent targets for the James Webb Space Telescope and other large telescopes working in the IR bands. We predict that deep observations of very massive stars would reveal these fragmentation objects, orbiting in the same orbital plane in cases where there are more than one object.     

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.     

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.     

A Study of Potential Earth-like Planets in the GJ 876 Planetary System

We perform numerical simulations to investigate potential Earth-like planets in the GJ 876 planetary system. We show that the secular resonances ν₁ and ν₂ (resulting respectively from the inner and outer giant planets) can excite the eccentricities of Earth-like planets with orbits 0.21 AU ≤ a < 0.50 AU and cause them to be ejected out of the system in a short time. However, in the dynamical sense, Earth-like planets potentially exist in the region 0.50 AU ≤ a ≤ 1.00 AU, in stable low-eccentricity orbits which may last up to 10⁵ yr.     

The frequency and intensity of comet showers from the Oort cloud

We simulate the Oort comet cloud to study the rate and properties of new comets and the intensity and frequency of comet showers. An ensemble of ∼10⁶ comets is perturbed at random times by a population of main sequence stars and white dwarfs that is described by the Bahcall-Soneira Galaxy model. A cloning procedure allows us to model a large ensemble of comets efficiently, without wasting computer time following a large number of low eccentricity orbits. For comets at semimajor axis a = 20,000 AU, about every 100 myr a star with mass in the range 1M_⊙−2M_⊙ passes within ∼10,000 AU of the Sun and triggers a shower that enhances the flux of new comets by more than a factor of 10. The time-integrated flux is dominated by the showers for comets with semimajor axes less than ∼30,000 AU. For semimajor axes greater than ∼30,000 AU the comet loss rate is roughly constant and strong showers do not occur. In some of our simulations, comets are also perturbed by the Galactic tidal field. The inclusion of tidal effects increases the loss rate of comets with semimajor axes between 10,000 and 20,000 AU by about a factor of 4. Thus the Galactic tide, rather than individual stellar perturbations, is the dominant mechanism which drives the evolution of the Oort cloud.     

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.     

Evolution of the Oort cloud angular momentum: Numerical simulation

This paper considers the evolution of a flat svarm of cometary bodies (under the effect of the passage of stars), initially moving in one direction along the circular orbits with radii 1.4×10⁴<r<2×10⁴ AU and along elliptic orbits with semi-major axes 5×10³<a<1×10⁴ AU and with perihelia within 50<q<100 AU. Numerical simulation shows that the original flat belt of comets is thermalizing. Its root-mean-squarez-coordinate grows withr. A cometary cloud forms with a dense flattened inner core and a rarefied halo (the Oort cloud proper). The value =N _core/N _halo varies within a wide range (up to the order of magnitude) depending on the model used (N _core andN _halo are the numbers of comets in the core and the halo, respectively).The hypothesis of a massive Oort cloud (Marochniket al., 1988) implies that the Oort cloud should have a large angular momentum. This paper employs numerical simulation to calculate Oort cloud models to which the initially flat located at the periphery of the solar nebula rotating cometary swarms is evolving in time. The loss of the initial angular momentum over the time of the Oort cloud evolution is not large.     

Near-parabolic cometary flux in the outer solar system

The flux of near-parabolic comets in the outer-planetary region is estimated on the presumption that the major planets and the galactic tide control the dynamics of comets. It is found that the flux of the Oort cloud comets (semi-major axis > 20000 AU) is similar to the case of a strong comet shower derived on the presumption that the galactic tidal force were not operative. On the other hand, the flux of comets with semi-major axes <- 20000 AU is found to be an increasing function of q (perihelion distance) until q reaches 20 AU, while for a 45000 AU it is a rapidly increasing function for q 12 AU. In other words, for comets of the inner extension of the Oort cloud the planetary perturbation acts as a strong barrier for them to penetrate into the inner planetary region.     

Embedded star clusters and the formation of the Oort Cloud

Observations suggest most stars originate in clusters embedded in giant molecular clouds [Lada, C.J., Lada, E.A., 2003. Annu. Rev. Astron. Astrophys. 41, 57-115]. Our Solar System likely spent 1-5 Myrs in such regions just after it formed. Thus the Oort Cloud (OC) possibly retains evidence of the Sun's early dynamical history and of the stellar and tidal influence of the cluster. Indeed, the newly found objects (90377) Sedna and 2000 CR₁₀₅ may have been put on their present orbits by such processes [Morbidelli, A., Levison, H.F., 2004. Astron. J. 128, 2564-2576]. Results are presented here of numerical simulations of the orbital evolution of comets subject to the influence of the Sun, Jupiter and Saturn (with their current masses on orbits appropriate to the period before the Late Heavy Bombardment (LHB) [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461]), passing stars and tidal force associated with the gas and stars of an embedded star cluster. The cluster was taken to be a Plummer model with 200-400 stars, with a range of initial central densities. The Sun's orbit was integrated in the cluster potential together with Jupiter and Saturn and the test particles. Stellar encounters were incorporated by directly integrating the effects of stars passing within a sphere centred on the Sun of radius equal to the Plummer radius for low-density clusters and half a Plummer radius for high-density clusters. The gravitational influence of the gas was modeled using the tidal force of the cluster potential. For a given solar orbit, the mean density, 〈ρ〉, was computed by orbit-averaging the density of material encountered. This parameter proved to be a good measure for predicting the properties of the OC. On average 2-18% of our initial sample of comets end up in the OC after 1-3 Myr. A comet is defined to be part of the OC if it is bound and has q>35 AU. Our models show that the median distance of an object in the OC scales approximately as 〈ρ〉^−1/2 when . Our models easily produce objects on orbits like that of (90377) Sedna [Brown, M.E., Trujillo, C., Rabinowitz, D., 2004. Astrophys. J. 617, 645-649] within ∼1 Myr in cases where the mean density is or higher; one needs mean densities of order to create objects like 2000 CR₁₀₅ by this mechanism, which are reasonable (see, e.g., Guthermuth, R.A., Megeath, S.T., Pipher, J.L., Williams, J.P., Allen, L.E., Myers, P.C., Raines, S.N., 2005. Astrophys. J. 632, 397-420). Thus the latter object may also be part of the OC. Close stellar passages can stir the primordial Kuiper Belt to sufficiently high eccentricities (e?0.05; Kenyon, S.J., Bromley, B.C., 2002. Astron. J. 123, 1757-1775) that collisions become destructive. From the simulations performed it is determined that there is a 50% or better chance to stir the primordial Kuiper Belt to eccentricities e?0.05 at 50 AU when . The orbit of the new object 2003 UB₃₁₃ [Brown, M.E., Trujillo, C.A., Rabinowitz, D.L., 2005. Astrophys. J. 635, L97-L100] is only reproduced for mean cluster densities of the order of , but in the simulations it could not come to be on its current orbit by this mechanism without disrupting the formation of bodies in the primordial Kuiper Belt down to 20 AU. It is therefore improbable that the latter object is created by this mechanism.     

Identifying clouds over the Pierre Auger Observatory using infrared satellite data

We describe a new method of identifying night-time clouds over the Pierre Auger Observatory using infrared data from the Imager instruments on the GOES-12 and GOES-13 satellites. We compare cloud identifications resulting from our method to those obtained by the Central Laser Facility of the Auger Observatory. Using our new method we can now develop cloud probability maps for the 3000 km² of the Pierre Auger Observatory twice per hour with a spatial resolution of ∼2.4 km by ∼5.5 km. Our method could also be applied to monitor cloud cover for other ground-based observatories and for space-based observatories.     

CCD Washington photometry of three highly field star contaminated open clusters in the third Galactic quadrant

We present CCD photometry in the Washington system C and T₁ passbands down to T₁ ～ 19.5 magnitudes in the fields of Czernik 26, Czernik 30, and Haffner 11, three poorly studied open clusters located in the third Galactic quadrant. We measured T₁ magnitudes and C ? T₁ colors for a total of 6472 stars distributed throughout cluster areas of 13.6′ × 13.6′ each. Cluster radii were estimated from star counts in appropriate-sized boxes distributed throughout the entire observed fields. Based on the best fits of isochrones computed by the Padova group to the (C ? T₁, T₁) color-magnitude diagrams (CMDs), we derived color excesses, heliocentric distances and ages for the three clusters. These are characterized by a relatively small angular size and by a high field star contamination. We performed a firm analysis of the field star contamination of the CMDs and examined different relationships between the position in the Galaxy of known open clusters located within 1 kpc around the three studied ones, their age and their interstellar visual absorption. We confirm previous results in the sense that the closer the cluster birthplace to the Galactic plane, the higher the interstellar visual absorption. We also found that the space velocity dispersion perpendicular to the Galactic plane diminishes as the clusters are younger. The positions, interstellar visual absorptions, ages, and metallicities of the three studied clusters favor the hypothesis that they were not born in the recently discovered Canis major (CMa) dwarf galaxy before it was accreted by the Milky Way.