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Pluto and the Kuiper Belt the Solar System Beyond Neptune

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Planetary Dynamics at the Outer Limits E. Chiang UC Berkeley keywords: Kuiper belt debris disks imaging of extrasolar planets orbit-orbit resonance Sample Blinking Sample Blinking M ~ 0.1 M⊕ -1 3 AU-3 π (100 km)2 1 km s KBOs = test particles 3.1:2 3:2 3:23:2 conjunction 2.9:2 2.9:2 b “resonant width” Δ a res Neptune-Pluto Orbit-Orbit Resonance Resonant KBOs (~26%) Orbital Migration by Planetesimal Ejection Resonance Sweeping Plutino (3:2) Snapshot Wave pattern rotates rigidly with Neptune 2:1 = Planetary Speedometer 7 6 tmigrate ≡ a/(da/dt) ≥ 10 yr tmigrate = 10 yr The Kuiper Belt: The Global View Big KBOs are excited 70 AU 678 80 AU 130 AU 678 678 Fomalhaut Eccentric planet begets eccentric ring Equilibrium belt orbits are eccentric and aligned with the planet’s orbit closed non-crossing orbits planetary wire (secular approximation) Dissipative relaxation of parent bodies onto non-crossing (forced eccentric) orbits Relaxation occurs during: • Present-day collisional cascade • Prior coagulation (2) b3/2(aplanet/a) eforced(a)= (1) eplanet b3/2(aplanet/a) closed non-crossing orbits planetary wire (secular approximation) Wyatt et al. 99 Kalas et al. 05 chaotic zone N Constraining ap and Mp U using the sharp inner J S belt edge Lecar et al. 2001 Inner belt edge = Outer edge of planet’s “chaotic zone” Chaotic zone width ~ Surface brightness 2/7 (Mplanet/Mstar) aplanet from Kalas et al. 05 x m +1:m m : m − 1 ∆ x ∆ s = Region where first-order = Regionwhere Planetary chaotic zone Planetary chaotic resonances overlap Regular #3 Chaotic zone #2 conjunction #1 Chaotic zone Orbit crossing Chaotic and ejection Random walk #1 #3 . in a and e Wisdom 1980 Duncan et al. 1989 #2 Quillen 2006 chaotic zone N Constraining ap and Mp U using the sharp inner J S belt edge Lecar et al. 2001 Inner belt edge = Outer edge of planet’s “chaotic zone” Chaotic zone width ~ Surface brightness 2/7 (Mplanet/Mstar) aplanet from Kalas et al. 05 Candidate planet (0.5 Jupiter mass) not confirmed: only 2 epochs not thermal emission from planetary atmosphere 40 RJ reflective dust disk? Variable Hα emission? HR 8799 Orbital resonances afford stability A-type star 30-60 Myr old d:c = 2:1 resonance with 4 Super-Jupiters Other possibilities include d:c:b = 4:2:1 e:d:c = 4:2:1 dynamical masses < 20 Jupiter masses each Cloudy spectra unlike brown dwarfs 6-7 MJ ) ! L/L log( 7-10 MJ log(age/yr) Pan-STARRS (once a week, Gemini Planet Imager (GPI) mag 24) 2012 and LSST (once every few days, mag 24.5) PS1 LSST site Deriving the chaotic zone width Resonance overlap Resonance spacing ∆s x 2 ∼ a ! a " if ∆x>∆s ∆x 2 7 x M / i.e., if x< p a m 1 !M∗ " − +1: m then chaos m : m ∆s 2x Deriving the chaotic zone width ∆x x I. The kick at conjunction x ! a Mp Kick in eccentricity ∆e ap Ω ∆v 1 GM p ∆e ∼ ∼ p ∆t v v x2 a 2 Mp a = ap + x ∼ M∗ !x" Kick in semimajor axis ∆x GM ∗ 2 Use Jacobi constant: CJ ≈− − Ωp!M∗(a + x)(1 − e ) 2(a + x) x x x M 2 a 5 ⇒ ∆ ∼ e 2 ⇒ ∆ ∼ p a2 (∆ ) a M x ! ∗ " # $ e.g., if ωplanet = ωbelt (nested ellipses) Mbelt >Mparent bodies ∼ 3M⊕ aplanet =115AU then eplanet =0.12 Enough material for gas giant core Mplanet =0.5MJ Asymmetric capture: Migration-shifted potentials “V” Direct Φ π t2 ∆Φ ∼ librate torbitaltmigrate Indirect Results 1000 5:4 4:3 11:9 9:7 0.3 M 100 J 6:5 If Mplanet ↑ then aplanet ↓ 10 Planet position too far 4:3 7:5 from dust belt 1 M 100 J → ∴ Mplanet < 3 MJ 10 3:2 3 M Planet also evacuates 100 J Kirkwood-type gaps 10 5:3 7:4 10 M 100 J Number of stable parent bodies (in 0.1 AU bins) 10 1 90 100 110 120 130 140 150 Chiang et al. 2008 Time-averaged semimajor axis (AU) Kalas et al. 2008 Results 1.0 K05 model 0.1 MJ, apl=120 AU 0.3 M , a =115.5 AU If M ↑ then e ↑ J pl planet dust 1 MJ, apl=109 AU 3 M , a =101.5 AU 0.8 J pl Surface brightness 10 MJ, apl=94 AU profiles broaden too much o →∴ Mplanet < 3 MJ 0.6 Relative 0.4 Mbelt >Mparent bodies ∼ 3M⊕ Enough material for gas giant core 0.2 0.0 100 120 140 160 180 200 Semimajor axis a (AU) • The Kuiper belt comprises tens of thousands of icy, rocky objects having sizes greater than 100 km • Many KBOs occupy highly eccentric and inclined orbits that imply a violent past • Pluto and other Resonant KBOs share special gravitational relationships with Neptune e.g., if ωplanet = ωbelt (nested ellipses) Extrasolar debris disks are aplanet =115AU • nascent Kuiper belts then eplanet =0.12 M =0.5M planet J • Belts are gravitationally sculpted by planets Fomalhaut b: Planet-Debris Disk Interaction chaotic width t = 1000 Myr Myr Step 1: Screen parent bodies for gravitational stability 8 tage ∼ 10 yr Step 2: Replace parent bodies with dust grains ∆t = tcollision =0.1 Myr Step 3: Integrate dust grains with radiative force for collisional lifetime tcollision ∼ torb/τ ∼ 0.1 Myr Parent bodies collide once in system age Collisional Cascade Distribution of sizes of Kuiper belt objects Nominal Diameter at 42 AU (km) 1000 100 10 1 6 4 Classical ) -2 2 Excited ) (deg R 0 Measured Extrapolated log N(<m -2 -4 Most visible grains are just large 20 25 30 35 enough to avoid stellar blow-out mR Results 1000 5:4 4:3 11:9 9:7 0.3 M 100 J 6:5 If Mplanet ↑ then aplanet ↓ 10 Planet position too far 4:3 7:5 from dust belt 1 M 100 J → ∴ Mplanet < 3 MJ 10 3:2 3 M Planet also evacuates 100 J Kirkwood-type gaps 10 5:3 7:4 10 M Mbelt >Mparent bodies ∼ 3M⊕ 100 J Enough material for gas giant Number of stable parent bodies (in 0.1 AU bins) 10 core 1 90 100 110 120 130 140 150 Chiang et al. 2008 Time-averaged semimajor axis (AU) Kalas et al. 2008 Measuring Debris Disk Masses − N dN/ds ∝ s q s sblow svisible ssubmm stop ∼ 0.2µm ∼ 100 µm ˙ 3 ˙ M∗ = 10 M" ˙ 2 ˙ M∗ = 10 M" 850 m flux consistent w ˙ ˙ µ / M∗ = 10M" ˙ ˙ M∗ = 1M" MSED(stop) ∼ 0.01M⊕ q =7/2(Dohnanyi) stop ∼ 10 cm [from tcollision(stop) ∼ tage] Packed planetary systems Instability Regularization Packed Stability and ejection by dynamical formation restored friction occurs when planets outweigh parent disk Signature recorded in Kuiper belt Dynamical friction: Small bodies slow big bodies Numerical simulations of packed planetary systems Solar system-like outcomes emerge from chaos Observed Simulated Stirring of KBOs by Rogue Ice Giants > > > > > > > > Short-Period Comets > > > > > > > > > > > > > > > > > > > > > > > l > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > Raising Sedna’s Peri by Stellar Encounters Praesepe cluster M44 Before After · ∼ 3 ∼ n∗ 4 stars/pc (R1/2 2 pc) Typical open · t ∼ 200 Myr cluster 2 1/2 ·!v∗" ∼ 1km/s Fernandez & Brunini 00 Discovery of Kuiper Belt Object (KBO) #3 David Jewitt (U Hawaii) Jane Luu (UC Berkeley) 1992 QB1: “Smiley” Size depends on observed brightness and intrinsic reflectivity (albedo) Quaoar Ixion Planetary Protection Mechanism: Orbit-Orbit Resonance Neptune makes 3 orbits for every 2 orbits of Pluto “Dance of the Plutinos” The Orbit of Sedna Resonant KBOs 12 6 Number 0 5:1 4:1 3:1 5:2 7:3 2:1 9:5 7:4 80 40 Number 0 5:3 8:5 3:2 10:7 7:5 11:8 4:3 6 3 Number 0 13:10 9:7 14:11 5:4 11:9 6:5 1:1 2003 UB313 “Xena” Bigger than Pluto Palomar 48-inch / M. Brown, C. Trujillo, & D. Rabinowitz (Caltech, Yale) Hubble Space Telescope 2003 UB313 (mapp = 19) Diameter = 2397±100 km vs. Pluto Diameter = 2274 km I.A.U. definition “Dwarf Planets” (a) orbits the Sun (b) hydrostatic (round) Nix “Easter Bunny” shape (c) not a satellite (d) not cleared its neighborhood Hydra “Santa” What we know: • The Kuiper belt comprises tens of thousands of icy, rocky objects having sizes greater than 100 km • The Kuiper belt is the source of short-period comets • Pluto and other Resonant KBOs share special gravitational relationships with Neptune • Many KBOs, especially large ones, occupy highly eccentric and inclined orbits that imply a violent past • Other star systems have their own Kuiper belts First discovered Neptune Trojan (1:1) 1 “Large” Neptune Trojan in 60 ° ⇒ ~10-30 Large Neptune Trojans Neptune vs. ~1 Large Jovian Trojan (“Large” ≡ 130-230 km diameter assuming 12-4% visual albedo) based on Mike Brown’s survey limits: 1 Earth mass at less than 200 AU 1 Neptune at less than 500 AU 1 Jupiter (in reflected light) at less than 1000 AU based on Hipparcos and Tycho-2 cannot be a self-luminous main-sequence star above the hydrogen burning limit infrared detection of a Jupiter or brown dwarf could be interesting birth ring daughter dust particle Theoretical Snapshots of Resonant KBOs ⇐ Plutinos 3:2 • • Twotinos 2:1 ⇒ Chiang & Jordan 2002 Observational Facts and Theoretical Deductions 1. Pluto is the largest known member of a swarm of billions of outer solar system bodies that supply new comets. 2. Pluto and the Plutinos are locked in an orbital resonance established by Neptune.
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