The The Evolution Evolution of of Kuiper Kuiper Belt Belt Objects: Objects: A A Dusty Dusty Disk Disk Connection Connection Ben Ben Bromley Bromley Department Department of of Physics Physics University University of of Utah Utah Scott Scott Kenyon Kenyon Smithsonian Smithsonian Astrophysical Astrophysical Observatory Observatory Department of Physics University of Utah TIARA KBO workshop Fall 2008 Formation of a solar system Kant (1755) and Laplace (1796): Nebular hypothesis QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. Start with a cloud of gas and dust around the Sun Conserve angular momentum, collapse to a flattened disk Planets form in rings within the disk Is this picture correct for the Solar System? Is it universal? Department of Physics University of Utah TIARA KBO workshop Fall 2008 Planetary disks QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. Young stars & gas/dust disks QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. Gas vanishes quickly (~ million years) Dust appears & lingers (~ 100 million years, despite radiation) Debris disks signify planet formation QuickTime?and a TIFF (Uncompressed) decompressor QuickTime?and a are needed to see this picture. TIFF (Uncompressed) decompressor are needed to see this picture. www.hubblesite.org www.spitzer.caltech.edu QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture Department of Physics University of Utah QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. TIARA KBO workshop Fall 2008 Overview I. “Generic” planet formation by coagulation II. Numerical simulations: what they can offer III. Debris disks: sampling planet formation in time via dust IV. The Kuiper Belt: simulation results V. Conclusion Department of Physics University of Utah TIARA KBO workshop Fall 2008 I. A theory for building planets Department of Physics University of Utah The dust settles Coagulation/slow growth Runaway growth The oligarchy Chaotic evolution A planetary system TIARA KBO workshop Fall 2008 A theory for building planets Dynamical times: P ~ a3/2 Surface density: Σ ~ a-3/2 Planet growth timescale: ~ P/Σ ~ a3 t1000 ~ 50 (a/40 AU)3 Myr ~ Myr at 5 AU; ~ 400 Myr at 80 AU Gas dissipation: exp(-t/tg), (a=orbital distance) tg ~ 3 Myr (important for growth inside ~ 20 AU [t1000 ~ tg]) Department of Physics University of Utah TIARA KBO workshop Fall 2008 The initial conditions Disk surface density Σgas ~ Σsolid ~ a-3/2 “MMSN” ~ 10 (a/AU)-1.5 g/cm2 1-10 μm grains (accumulated near the disk’s midplane) Σgas ~ 100 Σsolid Department of Physics University of Utah TIARA KBO workshop Fall 2008 A theory for building planets the “building blocks” emerge coagulation: growth by collisions/agglomeration create ~1 km-sized bodies within ~ 1 Myr (dynamical timescales?) key step, but details uncertain [turbulence, gravitational instability] (Goldreich & Ward 1973; Youdin & Shu 2002; Inaba & Barge 2006; Johansen et al., 2007) Department of Physics University of Utah TIARA KBO workshop Fall 2008 A theory for building planets Gravity kicks in Dynamical friction (energy exchange) and Viscous stirring (ang. momentum exchange): circularize large bodies, “heat” smaller bodies Collisional damping can mitigate the “heating” (e.g., Safronov 1973; Greenberg et al. 1978; Wetherill & Stewart 1989) Department of Physics University of Utah TIARA KBO workshop Fall 2008 A theory for building planets Runaway growth Accretion by large bodies (1+ km) is enhanced by gravitational focusing (σ > πr2) —> rapid growth of relatively few 100-1000 km oligarchs “To the dustbunny that hath, shall be given” Department of Physics University of Utah TIARA KBO workshop Fall 2008 Collisional cascade Growing planets stir up smaller bodies Stirring => collisions, beyond the shattering speed Smaller bodies ground to observable micron-sized grains as larger bodies grow Poynting-Robertson drag + radiation pressure remove grains quickly Thus halts runaway growth Department of Physics University of Utah TIARA KBO workshop Fall 2008 A theory for building planets The rule of the oligarchy Oligarchs “feed” until starvation; may remain on isolated Stable(?) orbits…. RH (Ida & Makino 1993; Kokubo & Ida 1998,2000) Department of Physics University of Utah TIARA KBO workshop Fall 2008 A theory for building planets a possible finale Chaotic/collisional growth, the oligarchy topples (orbits cross, enabling massive mergers) Department of Physics University of Utah TIARA KBO workshop Fall 2008 The role of chaos PLANET XING (merger?) Department of Physics University of Utah TIARA KBO workshop Fall 2008 II. A hybrid planet formation code Statistical coagulation code: ~1021 planetesimals N-body code: ~100 planets Supercomputing is essential (100,000 node-hrs/yr) Department of Physics University of Utah TIARA KBO workshop Fall 2008 A hybrid planet formation code Statistical coagulation code: Safranov’s particle-in-box method Bin according to mass, annuli, e.g. for annulus i, mass bin j: dnik/dt = +(mergers into mass bin, sum over i’,j’) - (mergers removing bodies; sum…) +(fragmented debris) +(effects from gas, PR drag) Collision outcomes (merger terms) depend on impact energy, tensile strength (Benz & Asphaug 1999) Algorithm for collision outcomes (redistribute mass) [n(m) ~ m-1.8 identical KE/unit mass, e.g., William & Wetherill 1994] Department of Physics University of Utah TIARA KBO workshop Fall 2008 A hybrid planet formation code Collision outcomes Impact energy: QI = 1/4 m1m2( V2+ Vesc2 )/(m1+m2)2 Disruption energy: Q* ~ Qb r--α + ρ Qg r-β Qb ~ 1 -- 108 erg/g ρ Qg ~ 10-4 -- 104 erg/g (e.g., Benz & Asphaug 1999) (bulk/tensile) (gravitational) α ~ 0, β ~ 1.25 Disruptive collisions: QI ~ Q* Large objects grow from collisions Smaller objects suffer losses Department of Physics University of Utah TIARA KBO workshop Fall 2008 A hybrid planet formation code Statistical coagulation code: Velocity evolution (“v”=>horizontal, vertical relative to VKep) : dv2/dt = (collisional damping) + (grav interactions--dynamical friction, viscous stirring) + (gas, PR drag) use analytical approx’s derived from N-body simulations (e.g., Ida & Makino 1992; Wetherill & Stewart 1993; Stewart & Ida 2000; Ohtsuki et al. 2002) Luminosity estimation: keep track of “sub-grid” debris collisions first approximation: optically thin re-processed starlight better: track optical depth through the annular grid (Kenyon et al. 1999) Department of Physics University of Utah TIARA KBO workshop Fall 2008 A hybrid planet formation code N-body code. Goal: to follow the few--O(100) largest objects directly, not statistically Direct force calculations + input from coagulation grid (e.g., da/dt) Adaptive 8th-order Richardson extrapolation integrator (switch for 6th order symplectic) CoM frame, rotating coordinates, Merger tracking Department of Physics University of Utah TIARA KBO workshop Fall 2008 A hybrid planet formation code Boltzmann solver cooling Coagulation Gravity Fragmentation heating Department of Physics University of Utah Merging R > 100 km (Direct) Radiation forces Gas pressure …. R < 100 km (Statistical) N-body code planets dust grains TIARA KBO workshop Fall 2008 Dynamic range Earth skimming “spy satellite” Binary Jupiters Scaled solar system: m x 50 Mergers Planet + dust “Grapefruit test” Planet formation Code validation Coagulation 200 Moons Planetesimals Department of Physics University of Utah (Bromley & Kenyon 2005) (Duncan, Levison & Lee 1998) (Duncan, Levison & Lee 1998) (Greenzweig & Lissauer 1990) (Bromley & Kenyon 2005) (Spaute et al. 1991; Weidenschilling et al. 1997) (Chambers 2000) (Ida & Makino 1993; Kokubo & Ida 1998; Stewart & Ida 2000) TIARA KBO workshop Fall 2008 III. Debris Disks In theory… Bright rings: Planets forming 10 Myr Dark rings: Mature planets 300 Myr Infer presence of icy planets (plutos) 2 Gyr Department of Physics University of Utah TIARA KBO workshop Fall 2008 Structure in a disk QuickTime?and a Microsoft Video 1 decompressor are needed to see this picture. Department of Physics University of Utah TIARA KBO workshop Fall 2008 Structure in a disk -- stochasticity QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. MMSN disks, 1 Gyr (identical starting conditions) Department of Physics University of Utah TIARA KBO workshop Fall 2008 Debris Disks - observational tests Is the coagulation/debris disk picture a good frame-work? Rise and Fall of luminous dust debris (10-100 Myr) Ldust /L* ~ Lmax (t/t0)-m (m ~ 1-2, t0 ~ 100 Myr) Lmax ~ 10-3 (Msolid,0 / MMMSN) Consistent with observations? Department of Physics University of Utah TIARA KBO workshop Fall 2008 Observations: Unresolved dusty debris disks Flux (arbitrary units) Clues in the infrared--reprocessed starlight Wavelength (μm) (Song et al. 2004) Department of Physics University of Utah TIARA KBO workshop Fall 2008 Unresolved dusty debris disks 0.3, 1 & 3 x MMSN A-star IR excess (data: Reike 2005, Su et al. 2006) Department of Physics University of Utah TIARA KBO workshop Fall 2008 Unresolved dusty debris disks 0.3, 1 & 3 x MMSN Solar-type-star IR excess (data: Reike 2005, Su et al. 2006) Department of Physics University of Utah TIARA KBO workshop Fall 2008 Resolved dusty debris disks HR 4796A 0.3, 1 & 3 x MMSN QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. Department of Physics University of Utah TIARA KBO workshop Fall 2008 Resolved dusty debris disks Large planets can migrate…. 0.3, 1 & 3 x MMSN QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. Src: APOD Department of Physics University of Utah TIARA KBO workshop Fall 2008 Debris disks, coagulation & planet formation Gas giant cores versus KBOs Make Jupiter at 5 AU within ~ Myr? Gas dynamics, chaotic orbits, important Key ingredient: gas traps dust debris; protoplanets accrete it (Rafikov 2004, KB 2008) At ~30+ AU, protoplanets reach “isolation mass” chaos not as important; slower growth… Stirred debris is not accreted, lost to PR drag & radiation pressure Department of Physics University of Utah TIARA KBO workshop Fall 2008 IV. KBO formation Simulations of in situ growth Predicting the size distribution: Quest for “q” Comparison with observations Coagulation & dynamics Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations Initial conditions: MMSN a ~30 to ~100 AU 1 m to 1 km e,i ~ 10-4 For starters: Qb ~ 103 erg/g, ρQg ~1, b = 1.25 Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations cumulative mass distribution Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations median eccentricity growth Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations maximum size of planets Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations size of largest objects (varying Σ from 1/3 to 3 x MMSN; 1 Gyr Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations Differential number distribution n(r), three power laws: n(r) ~ r q: -q ~ 3.5 below rS; (colllision dominated; Dohnanyi 1969) ~ 0 intermediate region rS < r < rL ~ 2.7 - 4, above rL, (accretion dominated) Break radius range r ~ 0.1 -- 20 km (rS and rL) q, rL (aka the break radius, rb) are time and Qb-dependent rmax ~ 1000 km Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations n(r) ~ r-q & sensitivity to bulk properties: Self-stirring models q_small q_large r_break: rS, rL _______________________________________________________________________________________ Qb < 104 erg/g Qb > 104 erg/g 3.5 3.5 3.5 - 4.0 2.7 - 3.5 1 km (rS~ rL) 0.1 km, 10 km Stellar flyby, Neptune stirring, earlier times, favor steeper q_large q_large, rL are anti-correlated (rL grows in time) Lower Qb increases size of possible disrupted (lost) objects; steepens n(r), pile-up in “transition zone” Department of Physics University of Utah TIARA KBO workshop Fall 2008 Destroying the Kuiper Belt (numerically) MMSN implies ~99% more mass in KBO’s than observed (~0.1 M_Earth) Self-stirring collisional cascade can reduce initial (~10 M_Earth) mass by ~95%…. Perturbers wanted: Neptune. Stellar flyby. Department of Physics University of Utah TIARA KBO workshop Fall 2008 Grinding down the Kuiper Belt Department of Physics University of Utah TIARA KBO workshop Fall 2008 Grinding down the Kuiper Belt Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO and the size distribution--simulations Department of Physics University of Utah TIARA KBO workshop Fall 2008 Comparisons Bernstein et al. (2004): qS ~ 2.3, qL ~ 5, rb ~ 70 km hot and cold CKBOs differ Fraser et al. (2004): q ~ 4.5 Lunch table consensus: qS ~ 2, qL ~ 4.7, rb ~ 30 km same for both hot and cold CKBOs Pan & Sari (2005): qS ~ 2 - 3, qL ~ 5, rb ~ 20 - 50 km Here: qS ~ 3.5, qL ~ 2.7 - 4, rS, rL => 0.1 -- 20 km predicted: a “bump” in n(r) Department of Physics University of Utah TIARA KBO workshop Fall 2008 Coagulation and Dynamics Nice model: -- Heavy primordial nebula (~10 MMSN) -- Gas giants form, 5 AU to 15 AU -- “Rearrangement” at 700 Myr -- Pre-KBOs already in place (a<30 AU) -- Scattered KBO disk formed Goal: -- build seeds for KB via coagulation, then let dynamics take over -- estimate Σ, n® at 700 Myr; -- (stellar flyby to truncate disk?) Department of Physics University of Utah TIARA KBO workshop Fall 2008 Coagulation and Dynamics Coagulation’s in situ formation of plutos (outside of a ~ 20 AU) explains lack of massive planets beyond gas giants Model also grows objects in < 100 Myr, seeds of the Scattered Disk Interplay between coagulation (“early”) and dynamics (“late”) form the Kuiper Belt as we see it: “Freeze out” coagulation with dynamics (Nice); Large r slope of n®, rb can constrain freeze-out time Department of Physics University of Utah TIARA KBO workshop Fall 2008 Grinding down the Kuiper Belt Department of Physics University of Utah TIARA KBO workshop Fall 2008 Grinding down the Kuiper Belt -- stellar flyby e < 0.04 e < 0.2 e > 0.5 (Sedna-like) Department of Physics University of Utah TIARA KBO workshop Fall 2008 A stellar flyby QuickTime?and a GIF decompressor are needed to see this picture. Department of Physics University of Utah TIARA KBO workshop Fall 2008 Perihelion (AU) After the flyby orbits of scattered planets Eccentricity Sedna (Brown, Trujillo & Rabinowitz 2004) 2000 CR103 Inclination (degrees) Eris (Brown, Trujillo & Rabinowitz 2005) Department of Physics University of Utah Orbital distance (AU) TIARA KBO workshop Fall 2008 Putting it altogether Initial conditions: Mass distribution (a,r) Gas fraction Material properties, e.g., snowlines Coagulation Collisions Dynamics Formation timescales Migration Flyby’s? Observations: Colors, composition Cratering records Department of Physics University of Utah Orbital distributions Size distributions (q) TIARA KBO workshop Fall 2008 V. Conclusion KBO’s provide a snapshot of planet formation of large (10+ km) objects Debris Disks yield a “movie” of small (dusty) objects (around stars of various ages) Together, we get a more more complete framework for understanding planet formation Rise & fall of debris disks => coagulation is the right picture, in general To nail down this framework, accurate observations of the Kuiper Belt are *required*! Department of Physics University of Utah TIARA KBO workshop Fall 2008 V. Conclusion (really) 1. Why are inclinations so high? 2. Why are cold disk objects so small & red? 3. Where did Sedna come from? 4. Was the solar nebula heavy (~200 M_Earth), unlike many analogs? 5. Why is the KB truncated (either @ 30 AU or 50 AU)? 6. Where did the gas giants come from? (its not all about dynamics!) Department of Physics University of Utah TIARA KBO workshop Fall 2008 Department of Physics University of Utah TIARA KBO workshop Fall 2008 Comparison w/Bernstein et al. 2004 Department of Physics University of Utah TIARA KBO workshop Fall 2008 Sedna & the edge of the Kuiper Belt Other stars: extended disks; Our Sun: KBOs to ~50 AU No apparent “disk physics” to create edge Sedna’s orbit ~70 -- 1000 AU How did it get there? QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. Department of Physics University of Utah TIARA KBO workshop Fall 2008 A Stellar Flyby? Most stars are born in a cluster Cluster “evaporates” through stellar encounters A pairwise encounter early in Sun’s history: Scatter Sedna from an extended disk Shave off outer part of disk--KB’s edge QuickTime?and a TIFF (Uncompressed) decompressor are needed to see this picture. Plausibility? Akiko Soemori Department of Physics University of Utah TIARA KBO workshop Fall 2008 Competing processes a balancing act Dynamical friction “cools” protoplanets Gravitational stirring “heats” the dust Merging Fragmentation Large bodies accumulate mass Gas & radiation remove mass (grains) Depletion of mass supply for planets Department of Physics University of Utah TIARA KBO workshop Fall 2008 Summary of inputs for icy planet formation Initial m-to-km planetesimals low e, i (below ~10-3) Tensile strangth, QI Coagulation (growth), grav. focusing (10-100 km) Fragmentation, cratering, damping Dynamical friction damps e, i; keeps grav focusing strong Viscuous stirring of small bodies Collionsional cascade! Reign of the Oligarchs Department of Physics University of Utah TIARA KBO workshop Fall 2008 KBO structure -- a snapshot Classical KB: cold (low e,i) & hot (higher e,i) a ~ 40 AU Resonant disk Scattered disk (high a, e, i ~ 30+ degrees) Low mass (<<90% MMSN) <--!!! Department of Physics University of Utah TIARA KBO workshop Fall 2008 IV. KBO formation formation time Gas giants Plutos gas content a Department of Physics University of Utah TIARA KBO workshop Fall 2008
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