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Planetesimal Accretion &
Collisions in the Kuiper Belt
Hilke E. Schlichting
Canadian Institute for Theoretical Astrophysics
KIAA
16th December 2009
16th Dec 2009
Hilke Schlichting (CITA)
Part1:
Planetesimal Accretion & its effect on
Planetary Spins
Mass & Angular Momentum is delivered
in 3 different phases:
Planetesimal
Accretion
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Giant
Impacts
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Post Giant
Impact
Accretion
Final
Planet
Collisionless accretion (e.g.
Lissauer & Kary 91, Dones &
Tremaine 93 )
Hill Radius:
1/ 3
 MP 

RH  a 
 3M Sun 
 200 RP @ 1AU
Earth-Moon distance=0.25 RH
Schlichting & Sari 2007
- Collisionless accretion for planetesimal sizes > 10m
- Semi-collisional accretion for planetesimal sizes < 10m
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Mean specific angular momentum accreted
Retrograde
Prograde
Schlichting & Sari 2007
16th Dec 2009
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Implications for Planetary Spins
Planetesimal
Accretion
Giant Impacts
Random Component of AM:
Maximally spinning
protoplanets, prograde
rotation
1 1/ 2
Lzrms 
N crit MR 2
7
Significant amount
of mass accreted
after giant impacts
Systematic Component of AM:
2
LzSpin  N 2 / 3crit MR 2
prograde
5
Lz
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Post Giant Impact
Accretion
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Semi-collisional
accretion of a small
fraction of the
planet’s mass
sufficient to alter
spin properties
Semi-collisional accretion might dominate growth of
protoplanets and post giant impact accretion.
Preference for prograde rotation
Solar System Comparison
- Terrestrial planets:
- consistent with spin properties of terrestrial
planets
- Asteroid belt:
-Two most massive Asteroids, Ceres (P~9.1h,
(90-β) ~ 12º, Thomas et al. 05) and Vesta
(P~5.3h, (90-β) ~ 40º, Drummond et al. 98),
display prograde rotation.
-Even smaller main-belt asteroids (r>150km)
display a preference for prograde rotation
16th Dec 2009
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Johansen & Lacerda 2009
Part2:
The Kuiper Belt Size Distribution
• ~40 AU from the Sun
• Source of the short period
comets
• ~1000 detected objects
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• Solar System debris disk
• Size estimates based on
brightness
– Typical radius R=100km
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The Size Distribution give Information about:
- formation process
(power law index above
the break, q1)
- collisional history
(location of break radius,
rbreak)
- material properties of
KBOs (power law index
below the break, q2)
(e.g. Stern 1996, Davis &
Farinella 1997, Kenyon & Luu
1999, O’Brien & Greenberg
2003, Pan & Sari 2005)
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q1 ~ 4.7
rbreak ~ 45km
(Fuentes et al. 2008,
Fraser & Kavelaars 2008)
(Pan & Sari 2005)
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Transiting Kuiper Belt Objects
KBOs < 10km too small to be detected directly
Observe indirectly using
stellar occultations
Occultation events produced by
KBOs are rare & of short duration
(Dyson 1992,
Axelrod et al. 1992)
Large number of star
hours & high frequency
• The Hubble Space Telescope has 3 Fine
Guidance Sensors (FGSs)
• FGS observations are ideal because of
1) high sampling frequency: 40 Hz
2) long baseline: 14 years
3) space based
4) good control sample
• Expected number of events 0 (q~3.0) to >
130 (q>4.5)
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Hilke Schlichting (CITA)
Transiting Kuiper Belt Objects
Fraunhofer Regime:
Shape of diffraction pattern does
NOT depend on KBO shape and
KBO size, Amplitude ~ r2
Fresnel scale 
a
2
 1.3km
for a=40 AU, λ=500nm
(Roques)
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Detection Method
30 km/s
4 km/s
1) Search for events by fitting
Fraunhofer Light curve template
(3 free parameters, velocity,
amplitude, mean)
2) For significant events we check
7 km/s
- guide stars properties (position
& subtend angular size)
Opposition
- compare velocity of best fit
with velocity for observation
geometry (assuming e<<1)
3) Compare with event rate in
control sample, check for
instrumental artifacts
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Best fit values:
r ~ 520 m r  amplitude
a ~ 45 AU
Chi-squared fit:
χ2 /dof=20.1/21
From the observations we know:
• θStar /θFresnel~ 0.3
• Ecliptic latitude +14 deg
•
•
•
•
•
(Schlichting et al. 2009, Nature)
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Compared PMT readings
Checked second FGS
No correlated noise
Examined the engineering
telemetry for HST
Less than 2% chance to be falsepositive
Cumulative KBO size distribution
q  3.9  0.3
N ( r  250m)  2.114..78  107 deg 2
Rule out inferred KBO surface densities from previous claimed detections
(Roques 2006, Chang 2006, 2007) by more than 5σ!
16th Dec 2009
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