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Planetary Dynamics at the Outer Limits

E. Chiang UC Berkeley

keywords: debris disks imaging of extrasolar -orbit

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 2.9:2 2.9:2 b

“resonant width” Δ a res

Neptune- Orbit-Orbit Resonance Resonant KBOs (~26%) Orbital Migration by Ejection Resonance Sweeping (3:2) Snapshot

Wave pattern rotates rigidly with 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

Eccentric begets eccentric ring

Equilibrium belt 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- 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 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 )

not confirmed: only 2 epochs not thermal emission from planetary

40 RJ reflective dust disk?

Variable Hα emission? HR 8799 Orbital resonances afford stability A-type 30-60 Myr old d:c = 2:1 resonance with 4 Super- Other possibilities include d:c:b = 4:2:1 e:d:c = 4:2:1

dynamical < 20 Jupiter masses each log(L/L!) log(age / yr) Cloudy spectra unlike spectra Cloudy brown dwarfs brown 7-10 6-7 M M J J Pan-STARRS (once a week, 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 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 Œ 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- 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 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(

-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 -like outcomes emerge from chaos Observed Simulated

Stirring of KBOs by Rogue Ice Short-Period

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> > > Raising Sedna’s Peri by Stellar Encounters Praesepe cluster M44

Before After

· ∼ 3 ∼ n∗ 4 /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) (UC Berkeley) 1992 QB1: “Smiley” Size depends on observed brightness and intrinsic reflectivity ()

Quaoar Ixion Planetary Protection Mechanism: Orbit-Orbit Resonance

Neptune makes 3 orbits for every 2 orbits of Pluto

“Dance of the ” 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

2003 UB313 (mapp = 19) Diameter = 2397±100 km

vs.

Pluto Diameter = 2274 km I.A.U. definition “Dwarf Planets” (a) orbits the (b) hydrostatic (round)

Nix “Easter Bunny” shape (c) not a satellite (d) not cleared its neighborhood

“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 (1:1)

1 “Large” 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 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 burning limit

detection of a Jupiter or 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 established by Neptune. 3. The orbits of many Kuiper Belt Objects are dynamically excited. 4. Pluto is not alone in having an orbital companion.

Pluto 1999 TC 36