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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
VII WORKSHOP ON
CATASTROPHIC DISRUPTIONS
IN THE SOLAR SYSTEM
(CD07)
Alicante (Spain)
June 26th to 29th, 2007
Info/mailing list: [email protected]
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
• A collisional model for TNOs
• Collisional evolution of TNOs and the migration of Neptune
• Results
• Conclusions
A collisional model for TNOs
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
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
zone 1
Zone 1:
35(1-0.13) AU< a <40(1+0.13) AU
e=0.13
i=6º
zone 2
zone 1
Zone 2:
40(1-0.05) AU< a <50(1+0.05) AU
e=0.05
i=5.5º
zone 2
zone 1
overla
p
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
zone 1
Ecliptic plane
zone 1
zone 2
Ecliptic plane
zone 1
zone 2
Ecliptic plane
zone 3
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.
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)
• 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
Results
Results
Results
Results
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.
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.
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.
• ...
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
Results
Results
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
Observables • Size distributions:
The Trans-Neptunian Objects
Bernstein et al. (2004)
Collisional evolution models
CAVEAT:
What about Q* for gravitational aggregates?
And for rotating bodies?
(See Housen et al., in 30’)
Observables • Size distributions:
The Trans-Neptunian Objects
Bernstein et al. (2004)
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
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
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
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?
