Debris Disks, Kuiper Belt, Fomalhaut

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⊕♁

3 AU-3

π (100

km)2

1 km s-1

KBOs = test particles

3.1:2

3:2

conjunction

3:2 3:2 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

tmigrate ≡ a/(da/dt) ≥ 107 yr

6

tmigrate = 10 yr

The Kuiper Belt: The Global View

Big KBOs are excited

U8 A 0

7

6

80 AU

678

7

130 AU

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)

eforced (a) = closed non-crossing orbits

planetary wire (secular approximation)

b3/2 (aplanet /a)

eplanet (1) b3/2 (aplanet /a)

Wyatt et al. 99 Kalas et al. 05

chaotic zone N J S

U

Constraining ap and Mp using the sharp inner belt edge

Lecar et al. 2001

Inner belt edge = Outer edge of planet’s “chaotic zone” Chaotic zone width ~ (Mplanet/Mstar)2/7 aplanet

Surface brightness from Kalas et al. 05

Planetary chaotic zone = Region where first-order resonances overlap m+1:m

x

m:m−1

∆x

∆s

Regular Chaotic zone

Chaotic zone

#3 #2 conjunction #1

Chaotic #3

#1

Random walk

Orbit crossing and ejection

. . .

in a and e #2

Wisdom 1980 Duncan et al. 1989 Quillen 2006

chaotic zone N J S

U

Constraining ap and Mp using the sharp inner belt edge

Lecar et al. 2001

Inner belt edge = Outer edge of planet’s “chaotic zone” Chaotic zone width ~ (Mplanet/Mstar)2/7 aplanet

Surface brightness 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 A-type star 30-60 Myr old with 4 Super-Jupiters

Orbital resonances afford stability d:c = 2:1 resonance 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

log(L/L! )

6-7 MJ

7-10 MJ

log(age/yr)

Gemini Planet Imager (GPI) 2012

Pan-STARRS (once a week, mag 24) 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

i.e., if x < m:m−1

m+1:m

x

!

Mp M∗

then chaos

∆s

"2/7

a

2x ∆x

x

Deriving the chaotic zone width I. The kick at conjunction

x!a

Mp

Kick in eccentricity ∆e

ap Ωp a = ap + x

1 GMp ∆v ∼ ∆t ∆e ∼ 2 v v x Mp ! a "2 ∼ M∗ x

Kick in semimajor axis ∆x ! GM∗ Use Jacobi constant: CJ ≈ − − Ωp M∗ (a + x)(1 − e2 ) 2(a + x)

x∆x ∆x 2 ∼ ⇒ 2 ∼ (∆e) ⇒ a a

!

"2 # $ Mp a 5 M∗ x

g., if ωplanet = ωbelt (nested ellipses) aplanet = 115 AU then eplanet = 0.12 Mplanet = 0.5MJ

Mbelt > Mparent bodies ∼ 3M⊕

Enough material for gas giant core

Asymmetric capture: Migration-shifted potentials V

π

Direct

Φ t2librate ∆Φ ∼ torbital tmigrate

Indirect

Results If Mplanet ↑ then aplanet ↓ Planet position too far from dust belt

→ ∴ Mplanet < 3 MJ Planet also evacuates Kirkwood-type gaps

Chiang et al. 2008 Kalas et al. 2008

Number of stable parent bodies (in 0.1 AU bins)

1000 100

0.3 MJ

11:9 6:5

5:4 4:3 9:7

10 4:3

100

1 MJ

7:5

10 3:2

100

3 MJ

10 5:3

100

10 MJ

7:4

10 1 90 100 110 120 130 140 150 Time-averaged semimajor axis (AU)

Results 1.0

If Mplanet ↑ then edust ↑ 0.8

→ ∴ Mplanet < 3 MJ

Relative o

Surface brightness profiles broaden too much

K05 model 0.1 MJ, apl=120 AU 0.3 MJ, apl=115.5 AU 1 MJ, apl=109 AU 3 MJ, apl=101.5 AU 10 MJ, apl=94 AU

0.6

0.4

Mbelt > Mparent bodies ∼ 3M⊕

Enough material for gas giant core

0.2 0.0 100

120 140 160 180 Semimajor axis a (AU)

200

• 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) aplanet = 115 AU then eplanet = 0.12 Mplanet = 0.5MJ

• Extrasolar debris disks are nascent Kuiper belts

•

Belts are gravitationally sculpted by planets

Fomalhaut b: Planet-Debris Disk Interaction

chaotic width

t = 100 0 Myr Myr Step 1: Screen parent bodies for gravitational stability

tage ∼ 108 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 6

1000

Nominal Diameter at 42 AU (km) 100 10

log N( Mparent bodies ∼ 3M⊕

Enough material for gas giant core Chiang et al. 2008 Kalas et al. 2008

Number of stable parent bodies (in 0.1 AU bins)

1000 100

0.3 MJ

11:9 6:5

5:4 4:3 9:7

10 4:3

100

1 MJ

7:5

10 3:2

100

3 MJ

10 5:3

100

10 MJ

7:4

10 1 90 100 110 120 130 140 150 Time-averaged semimajor axis (AU)

Measuring Debris Disk Masses N

dN/ds ∝ s−q

s sblow svisible ∼ 0.2µm

850 µm flux consistent w/

MSED (stop ) ∼ 0.01M⊕ q = 7/2(Dohnanyi) stop ∼ 10 cm [from tcollision (stop ) ∼ tage ]

ssubmm ∼ 100 µm

stop

˙∗ M ˙∗ M ˙∗ M ˙∗ M

˙" = 103 M 2 ˙ = 10 M" ˙" = 10M ˙" = 1M

Packed planetary systems

Packed formation

Instability and ejection

Stability restored

occurs when planets outweigh parent disk

Signature recorded in Kuiper belt

Regularization by dynamical friction

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

> > > > >

> > >>

>

>

>

>

>

>

> > >

>

> >

>

>

>

>

>

>

> >

>

>

>

>

>

> > >

> > >

>

>

> >

>

>

> >> >

>

>

> >

> >

>

>

>

>

> l

>

>

>

> > > > >

>

> > >

> > >

>

>

>

>

>

> >

>

>

Short-Period Comets

Raising Sedna’s Peri by Stellar Encounters

Before

Typical open cluster

Praesepe cluster M44

After · n∗ ∼ 4 stars/pc3 (R1/2 ∼ 2 pc) · t ∼ 200 Myr · !v∗2 "1/2 ∼ 1 km/s Fernandez & Brunini 00

Discovery of Kuiper Belt Object (KBO) #3

1992 QB1: “Smiley”

David Jewitt (U Hawaii) Jane Luu (UC Berkeley)

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

Number

Resonant KBOs 12 6 0

Number

5:1 4:1 3:1 5:2 7:3 2:1 9:5 7:4 80 40 0

Number

5:3 8:5 3:2 10:7 7:5 11:8 4:3 6 3 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

“Dwarf Planets”

Nix

“Easter Bunny”

Hydra

“Santa”

I.A.U. definition (a) orbits the Sun (b) hydrostatic (round) shape (c) not a satellite (d) not cleared its neighborhood

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

vs. ~1 Large Jovian Trojan (“Large” ≡ 130-230 km diameter assuming 12-4% visual albedo)

Neptune

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 ⇒

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. 3. The orbits of many Kuiper Belt Objects are dynamically excited. 4. Pluto is not alone in having an orbital companion.

Pluto

Charon

1999 TC 36