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Universidad de Alicante. Alicante (Spain)
Modelling the populations of
Trans-Neptunian Objects
Paula G. Benavidez & Adriano Campo Bagatin Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal
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VII WORKSHOP ON
CATASTROPHIC DISRUPTIONS
IN THE SOLAR SYSTEM
(CD07)
Alicante (Spain)
June 26th to 29th, 2007
Info/mailing list: [email protected]
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Universidad de Alicante. Alicante (Spain)
Modelling the populations of
Trans-Neptunian Objects
Paula G. Benavidez & Adriano Campo Bagatin Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal
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• A collisional model for TNOs
• Collisional evolution of TNOs and the migration of Neptune
• Results
• Conclusions
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A collisional model for TNOs
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ecc
entr
icit
y (
e)
incl
inati
on (
i)
3 populations:
Plutinos
Classical Disk
Scattered Disk
(MPC database)
A collisional model for TNOs
2 2e i A
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Plutinos Classical Disk Scattered Disk
a (AU) 38-40 42-48 35-50
< > s < > s < > s
e 0.13 0.06 0.05 0.05 0.18 0.10i (º) 4 3 3 3 17 9
A collisional model for TNOs
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zone 1
Zone 1:
35(1-0.13) AU< a <40(1+0.13) AU
e=0.13
i=6º
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zone 2
zone 1
Zone 2:
40(1-0.05) AU< a <50(1+0.05) AU
e=0.05
i=5.5º
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zone 2
zone 1
overla
p
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zone 2
zone 1
overla
p
zone 3
Zone 3:
40(1-0.18) AU< a <50(1+0.18) AU
e=0.18
i=25º
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zone 1
Ecliptic plane
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zone 1
zone 2
Ecliptic plane
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zone 1
zone 2
Ecliptic plane
zone 3
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A collisional model for TNOs
• Collisional evolution for each zone:
PIAB model, with distribution for VRi.
• Interactions in overlapping zones:
Accurately, considering how much <time>
objects spend in common zones.
• Fragmentation/cratering/reaccumulation model:
Petit & Farinella (1993), updated.
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A collisional model for TNOs
Some parameters for physics and evolution:6 3 3
0 10 / , 0.05, =1 g/cmKES erg cm f
4 4.5( ) , ( )tr trdN D D D dD dN D D D dD
Zone 1 (Plutinos)
Zone 2 (Classical Disk)
Zone 3 (Scattered Disk)
a (AU) 35-40 40-50 40-50<e>
[MPC]0.13 0.05 0.18
<i (º)> +1s[MPC]
6 5.5 25
<V> (km/s)[Dell’Oro et al., 2001]
1.25 0.93 1.00
0 0 010 (30) , ( 3) 0.3 0.5M M M z M
Scaling laws for S:
Gravity, G. + “strain rate effect” (Davis), Hydrocode (weak mortar)
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• Migration of Neptune? (Ida et al., 1999; Gomes et al., 2004; Hahn & Malhotra, 2005)
• What about collisional evolution in this scenario?
• Was collisional evolution ever efficient enough to deplete the mass of the belt to present estimates?
Collisional evolution of TNOs and the migration of Neptune
A: Present position and orbital elements.
B: Present position, but initially “cold” (i=3º, e=0.01).
C: Disk between 20 and 35 AU, “cold”.
D: Disk initially as in C, migrating and “heating” up to present values.
4 different evolving scenarios
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Results
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Results
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Results
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Results
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Results
MM0=0=10 M10 MTT A B C D
Mf (MT ) 3.4 3.5 2.8 3.4
slope -0.164 -0.169 -0.168 -0.163
N(D>2500 km) 27 27 26 27
Dtr (km) ~120 ~150 ~160
MM0=0=30 M30 MTT A B C D
Mf (MT ) 8.2 8.2 6.7 8.2
slope -0.166 -0.159
N(D>2500 km) 64 65 63 65
Dtr (km) ~100 ~120 ~130
A: Present position and orbital elements.
B: Present position, but initially “cold” (i=3º, e=0.01).
C: Disk between 20 and 35 AU, “cold”.
D: Disk initially as in C, migrating and “heating” up.
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Preliminary Conclusions
• Main features are almost independent on different initial distributions (with same M0).
• Different strength scaling-laws imply only slight variations.
• Change in the power-law distribution around 100-150 km.
• M reduces quickly (~100 Myr) to ½ of its initial value.
• Collisional evolution, under different initial conditions, may only be responsible for ~65-75% mass depletion:
Other mechanisms are required to get actual mass.
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To be continued...
• Estimate gravitational aggregate (rubble-piles) ratios.
• Introduce Neptune migration in a consistent way.
• Re-do simulations with orbital elements from the CFEPS.
• Introduce more realistic physics for low velocity collisions.
• ...
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Universidad de Alicante. Alicante (Spain)
Modelling the populations of
Trans-Neptunian Objects
Adriano Campo Bagatin, Paula G. BeneavidezDepartamento de Física, Ingeniería de Sistemas y Teoría de la Señal
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Results
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Results
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Introduction
Asteroid Population
Intrinsic Probability Impact Velocity (km/s)
Reference
Main Belt 2.19 – 3.51 3.93 – 7.69 Farinella and Davis (1992)
Main Belt 3.97 - Yoshikawa and Nakamura (1994)
Main Belt 2.86 5.2 Bottke et al. (1994)
Main Belt 4.38 4.22 Vedder (1998)
Trojans (L4) 6.37 – 6.55 4.83 – 4.97 Marzari et al. (1996)
Trojans (L4) 7.12 – 8.46 4.66 Dell’Oro et al. (1998)
Trojans (L5) 5.20 – 5.40 4.79 – 4.99 Marzari et al. (1996)
Trojans (L5) 6.50 – 6.86 4.51 Dell’Oro et al. (1998)
Hildas 2.21 – 2.41 1.62 - 4.56 Dahlgreen (1998)
TNOs Davis and Farinella (1997)
18 1 2(10 )yr km
-4MB5×10 P -1
MB10 V
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Observables • Size distributions:
The Trans-Neptunian Objects
Bernstein et al. (2004)
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Collisional evolution models
CAVEAT:
What about Q* for gravitational aggregates?
And for rotating bodies?
(See Housen et al., in 30’)
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Observables • Size distributions:
The Trans-Neptunian Objects
Bernstein et al. (2004)
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Theoretical studies
Pan and Sari (2005)
Trans-Neptunian Objects
“Break” confirmed by
Davis and Farinella (1997) collisional model,
Krivov et al. (2005) kinetic model.
(Also Kenyon and Bromley, 2004)
An analytical model
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Collisional evolution models
Campo Bagatin and Benavidez (POSTER SESSION P6.5)
Trans-Neptunian Objects
Zones Transition size [km]
PlutinosClassical DiskScattered Disk
Total
90-12090-12040-5060-90
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Open questions and conclusions
• The Trans-Neptunian region does not look collisionally relaxed (and will stay like this) above 50-100 km sizes.
(Similar behaviour seems to apply at least to Hildas.)
• We need un-biased data to extrapolate current distributions in a reliable way and compare models to.
About TNOs
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Open questions and conclusions
• How did the Scattered Disk (and the Centaur population?) form and evolve?
• Are TNOs larger than a transition diameter mostly pristine bodies?
• What fraction of km—size populations are gravitational aggregates?
About TNOs
• Is (was) the Trans-Neptunian population beyond 50 AU also a collisional system?
• What was the initial mass of this part of the solar system?
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