1. Universidad de Alicante. Alicante (Spain) Modelling the populations of Trans-Neptunian Objects adriano@dfists.ua.es Paula G. Benavidez & Adriano Campo Bagatin Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal

2. VII WORKSHOP ON CATASTROPHIC DISRUPTIONS IN THE SOLAR SYSTEM (CD07) Alicante (Spain) June 26th to 29th, 2007 Info/mailing list: adriano@dfists.ua.es

3. Universidad de Alicante. Alicante (Spain) Modelling the populations of Trans-Neptunian Objects adriano@dfists.ua.es Paula G. Benavidez & Adriano Campo Bagatin Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal

4. A collisional model for TNOs Collisional evolution of TNOs and the migration of Neptune Results Conclusions

5. A collisional model for TNOs

6. eccentricity (e) inclination (i) 3 populations: Plutinos Classical Disk Scattered Disk (MPC database) A collisional model for TNOs

7. PlutinosClassical DiskScattered Disk a (AU) 38-4042-4835-50 s s s e 0.130.060.05 0.180.10 i (º) 4333179 A collisional model for TNOs

8. zone 1 Zone 1: 35(1-0.13) AU< a <40(1+0.13) AU e=0.13 i=6º

9. zone 2 zone 1 Zone 2: 40(1-0.05) AU< a <50(1+0.05) AU e=0.05 i=5.5º

10. zone 2 zone 1 overlap

11. zone 2 zone 1 overlap zone 3 Zone 3: 40(1-0.18) AU< a <50(1+0.18) AU e=0.18 i=25º

12. zone 1 Ecliptic plane

13. zone 1 zone 2 Ecliptic plane

14. zone 1 zone 2 Ecliptic plane zone 3

15. A collisional model for TNOs Collisional evolution for each zone: PIAB model, with distribution for V Ri. Interactions in overlapping zones: Accurately, considering how much objects spend in common zones. Fragmentation/cratering/reaccumulation model: Petit & Farinella (1993), updated.

16. A collisional model for TNOs Some parameters for physics and evolution: Zone 1 (Plutinos) Zone 2 (Classical Disk) Zone 3 (Scattered Disk) a (AU) 35-4040-50 [MPC] 0.130.050.18 +1s [MPC] 65.525 (km/s) [Dell’Oro et al., 2001] 1.250.931.00 Scaling laws for S: Gravity, G. + “strain rate effect” (Davis), Hydrocode (weak mortar)

17. 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

18. Results

22. M 0= 10 M T ABCD M f (M T ) 3.43.52.83.4 slope-0.164-0.169-0.168-0.163 N(D>2500 km) 27 2627 D tr (km)~120~150~160 M 0= 30 M T ABCD M f (M T ) 8.2 6.78.2 slope-0.166-0.159 N(D>2500 km) 64656365 D tr (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.

23. Preliminary Conclusions Main features are almost independent on different initial distributions (with same M 0 ). 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.

24. 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....

25. Universidad de Alicante. Alicante (Spain) Modelling the populations of Trans-Neptunian Objects adriano@dfists.ua.es Adriano Campo Bagatin, Paula G. Beneavidez Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal

31. Results

33. Introduction Asteroid Population Intrinsic ProbabilityImpact Velocity ( km/s ) Reference Main Belt2.19 – 3.513.93 – 7.69 Farinella and Davis (1992) Main Belt 3.97- Yoshikawa and Nakamura (1994) Main Belt2.865.2 Bottke et al. (1994) Main Belt4.384.22 Vedder (1998) Trojans (L 4 )6.37 – 6.554.83 – 4.97 Marzari et al. (1996) Trojans (L 4 )7.12 – 8.464.66 Dell’Oro et al. (1998) Trojans (L 5 )5.20 – 5.404.79 – 4.99 Marzari et al. (1996) Trojans (L 5 )6.50 – 6.864.51 Dell’Oro et al. (1998) Hildas2.21 – 2.411.62 - 4.56 Dahlgreen (1998) TNOs Davis and Farinella (1997)

34. Observables Size distributions: The Trans-Neptunian Objects Bernstein et al. (2004)

35. Collisional evolution models CAVEAT: What about Q* for gravitational aggregates? And for rotating bodies? (See Housen et al., in 30’)

36. Observables Size distributions: The Trans-Neptunian Objects Bernstein et al. (2004)

37. 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

38. Collisional evolution models Campo Bagatin and Benavidez (POSTER SESSION P6.5) Trans-Neptunian Objects ZonesTransition size [km] Plutinos Classical Disk Scattered Disk Total 90-120 40-50 60-90

39. 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

40. 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?