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The Kuiper Belt as a Debris Disk Renu Malhotra University of Arizona a vast swarm of small bodies orbiting just beyond Neptune Art by Don Dixon (2000) 1
The Kuiper Belt as a Debris Disk
Renu MalhotraUniversity of Arizona
a vast swarm of small bodies orbiting just beyond NeptuneArt by Don Dixon (2000)
1
Dynamical classes
Multi-opposition TNOs+SDOs+Centaurs: orbital distribution
(data from MPC/05-july-2004)
0
0.2
0.4
5:33:2 2:1
30 35 40 45 50 550
10
20
30
40
a (AU)
• Resonant KBOs(e.g., 3:2, 2:1, 5:2)
• Main Belt (40 . a . 47 AU,ie, between 3:2 and 2:1)
• Scattered Disk(a > 50 AU & 30 < q . 36 AU)
– Extended Scattered Disk(a� 50 AU & q & 36 AU)
• Centaurs (q < aNeptune)
2
The Hot and Cold Main BeltMulti-opposition TNOs+SDOs+Centaurs: orbital distribution
(data from MPC/05-july-2004)
0
0.2
0.4
5:33:2 2:1
30 35 40 45 50 550
10
20
30
40
a (AU)
3
The Extended Scattered DiskMulti-opposition TNOs+SDOs+Centaurs: orbital distribution
(data from MPC/05-july-2004)
0
0.2
0.4
0.6
0.8
100 200 300 400 5000
10
20
30
40
a (AU)
4
The Edge of the Main Belt(Allen, Bernstein & Malhotra 2001, Trujillo & Brown 2001)
KB Radial distribution (Trujillo & Brown, 2001). 5
Size Distribution
Bernstein et al (2004).(Red =“Classical disk”= i≤5◦ and 38<d<55 AU;
Green =“Excited” class = complement of “classical”)
• Observed KBOs have radii10.R.1000 km– N(R > 50 km) � 5� 104
– main belt mass� 0:01 M⊕– total mass (<50AU) . 0:03M⊕– � 100� asteroid belt
• Size-class correlations– “excited” KBOs contain more large
objects & fewer small objects comparedto the “classical” KBOs
– largest CKBO is 1/60th mass of Pluto
• Collisional evolution models (Stern1995, Durda & Stern 2000) indicate thatcollisions are destructive for D . 100–300km, in the present environment
• The source of short period Jupiter-familycomets (JFCs): Uncertain. The scattereddisk may be the more likely source...
• Accretion models (Stern 1995, Kenyon & Luu 1999) indicate that R & 50 km KBOs must haveformed in a dynamically cold environment, ie, (e, i)initial . 0.001
– Some process has disturbed the Kuiper Belt & pumped up KBOs’ e’s and i’s6
Resonant Kuiper Belt Objects
-55 -50 -45 -40 -35 -30
-1
0
1
X (AU)
-40 -20 0 20 40
-40
-20
0
20
40
X/AU
J S U N
P
Pluto’s 3:2 mean motion resonance with Neptune
0 0.2 0.4 0.6 0.8 10
100
200
300
time (Gyr)
47
47.5
48
48.5
49
0
0.05
0.1
0.15
0.2
0
5
10
A weakly chaotic twotino
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Resonance sweeping by a migrating Neptune
Neptune Pluto/Plutino
Sun
30 AU 2/13/2
0
50
100
1503:2
2:1
5:3
8
Why would the giant planets migrate?
from Hahn & Malhotra (1999)
• cores of giant planets formedwithin a planetesimal disk
• planet–formation was likely not100% efficient
– residual planetesimal debris isleft over
• recently–formed planets scatterthe planetesimal debris, exchangeL with planetesimal disk
• Nbody simulations (Fernandez & Ip1984, Hahn & Malhotra 1999, Gomes,Morby, Levison 2004) show planetsevolve away from each other, ie,Jupiter inwards, Neptune outwards
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How far did Neptune migrate?• Neptune’s outward migration
causes its mean motionresonances (MMR’s) to sweepout across the Kuiper Belt
• KBOs get trapped at MMR’s,are dragged outwards,and have their e pumped up
• Malhotra (1993) showed thismechanism can account forPluto’s orbit (in 3:2 with e = 0.25,∆a ≈ 5 AU)
• The e-pumping depends uponNeptune’s ∆a
• A particle trapped at a j + k : j MMR has an adiabatic invariant,
B = a(√
1− e2 − jj+k)
2 ⇒ e(a)2 = 1−(
j+k√
ainitial/aj+k
)2
if einit = 0
• Plutinos (j = 2,k = 1) have emax = 0.33, so they were dragged fromainitial = 27.3 to a = 39.5 AU, i.e., ∆a ≈ 12 AU– hence, Neptune migrated ∆aNep = ∆a/(3/2)2/3 ≈ 9 AU
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SIMULATION OF ADIABATIC RESONANCE SWEEPING OF THE KUIPER BELT(from Malhotra, 1995)
0
0.1
0.2
0.3
0.4
0
10
20
30 35 40 45 500
50
100
150
a (AU)
3:24:3 5:3 2:1
Challenges
• Twotino population is too small– chaotic diffusion over 4 Gyr =⇒ p. 12
• Observed inclinations are difficult to explain(Plutinos, hot main belt)– non-adiabatic migration (Gomes, 2003)
• Inclination–size correlation– hot population formed closer to the Sun
• The edge at ∼ 50 AU– stellar encounter =⇒ p. 13– primordial edge at∼ 30 AU, KBOs pushe
out by the 2:1 (Levison & Morbidelli 2003
• The extended scattered disk– lost/rogue planets =⇒ p. 14– long term chaotic diffusion =⇒ p. 15– stellar encounter
• Mass loss ∼ 99%?!
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Survival rate of Plutinos and Twotinos
from Tiscareno (PhD thesis, 2004)
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Stellar encounter – perturbations on Kuiper Belt
from Ida, Larwood & Burkert (2000)
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Origin of extended–SDOsRogue planets?
from Morbidelli & Levison (2004)14
Origin of extended–SDOsLong term chaos – ‘Arnold diffusion’?
from Malhotra (2004, in preparation)15
Dust from the Kuiper BeltPresent-day distribution
model from Moro-Martin & Malhotra (2003)
• Dust density measured to be nearly constantin outer solar system (Pioneer 10,11; Voyagers1,2)
• KB dust production rate (1µm < R < 1mm)' 1× 1015 g y−1 (Landgraf et al 2002)(eqv. D ≈ 1 km comet ground to dust everyyear)
• Small particles (R . 0.5µm) are blown out byradiation pressure
• Bound dust grains spiral inward underPoynting-Robertson (PR) drag– temporary trapping in Neptune’s MMRs
produces azimuthal structure
• Gravitational scattering by Jupiter and Saturnejects most particles– very small fraction of KB dust grains enter
the inner solar system(“inner hole” in the KB debris disk)
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A History of Kuiper Belt Dust
• Theoretical models of Uranus-Neptuneformation suggest a total mass∼50M⊕ ina dynamically cold planetesimal disk, anda planet formation timescale∼107 yr (eg,Goldreich et al, 2004)– A collisional cascade in that disk would
produce dust at a rate 4–5 orders ofmagnitude larger than present
• The planets were mobilized towards theend of their formation, U-N undergoingoutward migration fuelled by the outerplanetesimal debris
• Shortly prior to the start of the migration,some mechanism disturbed the outerplanetesimal disk, exciting the e’s and i’s,perhaps stripping off the disk beyond ∼50AU– this event would have also caused a
‘spike’ in the dust production rate
• Thereafter, a rapid depletion ofplanetesimals led to a decline in the dustproduction rate
Planet accretion
Nep migration
A schematic history of the outer solar system dust productionrate
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