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The Role of the Galaxy in the Dynamical Evolution of Transneptunian Objects Martin Duncan Queen's University at Kingston, Canada In collaboration with Ramon Brasser Observatoire de Nice, France & Harold Levison and Luke Dones, Southwest Research Institute, Boulder, USA Outline • Brief background on Inner and Outer Oort cloud • Brief background on embedded star clusters • Numerical simulations • Results of computations • Ongoing work and Summary Oort cloud - Oort cloud is cloud of comets surrounding the Sun (Oort, 1950). - Isotropic beyond a~10 000 AU, but there may exist massive inner region (Hills 1981) from which long-period comets are rare. - Inner part (likely flattened) may be related to current scattered disk (Duncan & Levison 1997) and/or a population produced in putative primordial star cluster environment (Gaidos 1995, Fernandez 1997, Eggers 1999, Fernandez & Brunini 2000, Morbidelli & Levison 2004, Kenyon & Bromley 2004, Brasser et al 2005 - this talk) - Several simulations done in the past to form the Oort cloud, yet none incorporating both embedded star cluster environment and gas drag from primordial solar nebula. Early Model of Oort Cloud formation (Duncan, Quinn and Tremaine 1987) Assumed current giant planet orbits and masses with comets started on very eccentric orbits (a ~ 2000 AU) with pericentres (q) distributed from just inside Jupiter to just outside Neptune. Included tidal field from Galactic plane and passing stars representative of current solar neighbourhood Torquing due to Galactic Tides Galactic Disc (slab of constant density ρG) r F = -4π G ρG z Torque dJ/dt = r X F For high eccentricity J α q1/2, where q is pericentric distance. Thus tidal torque will change q and can define tidal torquing time = Δq/(dq/dt) for say Δq = 10 AU. Example of evolution of perihelion distance, q, versus semimajor axis, a, for a comet reaching Oort cloud in current Solar environment (Dones et al 2004) Tidal torque evolves q at constant a Diffuse in a at constant q Oort Cloud Dynamics In current Galactic environment (upper red curve) Jup & Sat (lower 2 blue curves) tend to eject comets with peris in their vicinities. Comets with peris in Ura Nep zone and beyond (top 2 blue curves) can have peris lifted by tides before ejection. Origin of The Oort Cloud Dones, Levison, Duncan & Weissman 2004 (DLDW04) integrated the orbits of several thousand test particles. Initial orbits were uniform in semimajor axis between 4 &40 AU with small eccentricities & inclinations (unlike DQT87) Forces included Sun and 4 giant planets, Galactic tides (both disk and radial components) & passing stars. Origin of Oort Cloud (DLDW04) Scattered Disk a) By 4 Gyr, equal numbers (2.5% of original) in outer cloud (a > 20,000 AU) vs. inner cloud Outer Cloud b) Scattered disk population is ~1/10 of outer cloud Inner Cloud Mass Estimates of Outer Oort Cloud (DBDL08) Mass Estimates of Outer Oort Cloud (part 2) Oort cloud: Formation in “Standard Model” (DLDW04) Outer OC formation efficiency only ~3% after 4 Gyr in current environment and inner cloud comparable to outer cloud in mass. May be problematic: 1) Mass of protoplanetary disk may have been low ( as current migration theory suggest it was - Gomes et al 2004). If so, is Standard Model too inefficient, especially since stripping by Giant Molecular Clouds was not included? Then again, mass of typical comet is unknown, so estimates of mass vary greatly ( ~ 1 - 60 Earth masses: Francis 2004). 2) Ratio of # of scattered objects to # in OC seems too high in simulations (but there are large observational uncertainties). 3) Does not produce Sedna-like orbits (a ~ 500, q ~ 75) 2003 VB12: “SEDNA” (Brown, Trujillo & Rabinowitz) R magnitude: 20.5, H=1.7 Extremely red Not detected in IR by Spitzer or IRAM -> D < 1800 km, so it's smaller than Pluto. Probably bigger than Quaoar (D = 1250 km). a = 530 AU (3 oppositions) q = 76 AU !! i = 12 degrees Now at 90 AU --> will reach perihelion in 2076!) Would only be detectable in survey over ~ 2% of orbit Origin? Probably early encounter with passing star (cf. Morbidelli & Levison 2004; Kenyon & Bromley 2004) Possible Chronology of Oort Cloud Formation • (THIS WORK): First few million years: Sun forms in embedded star cluster (discussed next), Jupiter and Saturn cores (and possibly Uranus and Neptune close in) form. Jupiter and Saturn accrete gas, rapidly approaching current masses, and such large masses very quickly scatter planetesimals in their vicinities. Passing stars and cluster tidal field lift pericentres ⇒ inner Oort Cloud. •(ONGOING WORK): Subsequent evolution involves evolution on longer timescales of scattered disk from current Uranus and Neptune zone and the early inner Oort cloud as perturbed by Giant Molecular Clouds and evolving stellar background. Also investigating extent of capture of comets from disks of passing stars during embedded phase. Embedded star clusters Embedded clusters •Young (1-5 Myr) star-forming regions, fraction of mass in stars ~1030% • Difficult to observe in the visible; most done in the IR •Very dense environment (typically 102-103 Msun pc-3 in stars; but Trapezium and others have >104 Msun pc-3 in stars - e.g. Gutherman et al 2005 find 24-91% of stars in 3 clusters are in regions denser than 104 Msun pc-3 ) • Residual gas ultimately blown away, most likely by massive stars (O & B-type) • Open clusters are not the normal evolutionary outcome - most embedded cluster dissolve (Lada & Lada 2003) and most stars are thought to have formed in embedded clusters of 100-1000 stars. Plummer potential arises from ρ(r) = ρ0 / (1 + r 2/ rc2) 5/2 1) Construct N-body realization (including realistic mass spectrum and assumed star formation efficiency ~ 10-25%.) 2) Integrate all stars in chosen fixed potential (NOT including star-star scattering). Two examples at right. 3) For each ~ solar-mass star, record encounter parameters as other stars enter ‘sphere of influence’ influence’ of fixed radius (~ 0.5-1 Plummer radius) centred on chosen star. Encounter parameters are later used in SWIFT integrations to compute stellar perturbations on comets. Cluster simulations Numerical simulations • Planets: Jovians: pre-LHB orbits (the ‘Nice model’) but current masses; parameters: either only Jup+Sat or J+S+U+N • Cluster: Plummer potential produces tidal field; parameters: central density ρ0 , core radius, lifetime (~5 Myr) • Sun: Orbit in cluster simulated simultaneously to get time-varying tides; parameters: inclination, eccentricity, semi-major axis • Stars: Introduced via previously determined ‘catalog’ of encounters from N-body realization, integrated directly while in ‘sphere of influence’, then removed. • Gas (if present): Drag formula using local density ; parameters: density profile, inner/outer cutoff Dense cluster, just Jup+Sat, no gas drag Dense cluster, just Jup+Sat, no gas drag Positions of 2000 CR105 and (90377) Sedna Comet Clouds for different cluster densities Example of models for the “Sedna region” Gas Drag Deceleration due to drag ∝ (ρg/rc) vr2 where ρg is gas density and vr is relative velocity. We often assume comet size rc = 1.7 km (derived from recent long-period comet observations) but compare with runs with larger sizes. For low inclination eccentric orbits orbiting in Hayashi profile gas disk, angular momentum roughly conserved. This leads to increase of pericentre! and may lift comets away from scattering planets. Gas drag added: minimum mass gas disk, dissipation time 2 Myr Gas drag added: minimum mass gas disk, dissipation time 2 Myr Gas drag added: minimum mass gas disk, dissipation time 2 Myr 5 x minimum mass gas but truncated at 10 AU; decay time = 2 Myr Different configurations at 3 Myr (typical cluster lifetime) Puffing Up the Inner Cloud (BDL08)? Start with inner clouds of BDL06 (recall ρ0 is central density of initial embedded star cluster). Subject them to 4 Gyr of passing stars in current Galactic environment. Only small fraction of comets evolve from inner to outer cloud, especially in systems that originally produced a Sedna-like population. Capture of inner cloud objects from passing stars? (Morbidelli & Levison 2004; Kenyon & Bromley 2004) Capture of inner cloud objects from passing stars? (Morbidelli & Levison 2004; Kenyon & Bromley 2004) Capture of inner cloud objects from passing stars? (Morbidelli & Levison 2004; Kenyon & Bromley 2004) Summary on Origins of Oort Cloud in Early Solar Environment • Standard Model: Model: Planetesimal clearing without gas and using existing planetary orbits/Galactic tidal field is very inefficient (~2.5%) at creating the outer Oort Cloud, does not produce “Sednas” Sednas” and produces a [scattered disk / Oort cloud] mass ratio probably larger than inferred from observations. •Within a Dense Embedded Star Cluster the efficiency of populating the (mostly inner) Oort cloud is 5-20%, depending on the cluster density and stellar orbit. A dense embedded star cluster can reproduce orbits of Sedna and CR105. • Protoplanetary Gas drag produces a size-sorting: large objects like Sedna are relatively unaffected while km-sized bodies tend to be deposited interior and exterior to the scattering planets. The mass, extent and duration of gas disk determine the efficiency of Oort cloud formation. •“Puffing -up” -up” of an inner cloud to replenish outer cloud in 4 Gyr in current Galactic environment is inefficient (1-10%). However, we are currently investigating the effects of Giant Molecular Clouds, especially early on when Sun’ Sun’s velocity relative to GMCs (including its birth GMC) is only 1-5 km/s. km/s. •Capture of icy bodies from passing stars in early embedded phase may cumulatively add significantly to inner/outer cloud and is being investigated.