1. David Vokrouhlický & David Nesvorný Plan of the talk: a) classical asteroid families (3D clustering) Plan of the talk: a) classical asteroid families (3D clustering) b) very young asteroid families (5D clustering) b) very young asteroid families (5D clustering) c) asteroid pairs - even younger families? or c) asteroid pairs - even younger families? or objects that underwent other types objects that underwent other types of catastrophic dissociations? of catastrophic dissociations? d) further observations needed to resolve that… d) further observations needed to resolve that… David Vokrouhlický & David Nesvorný Plan of the talk: a) classical asteroid families (3D clustering) Plan of the talk: a) classical asteroid families (3D clustering) b) very young asteroid families (5D clustering) b) very young asteroid families (5D clustering) c) asteroid pairs - even younger families? or c) asteroid pairs - even younger families? or objects that underwent other types objects that underwent other types of catastrophic dissociations? of catastrophic dissociations? d) further observations needed to resolve that… d) further observations needed to resolve that… Pairs of asteroids probably of common origin Pairs of asteroids probably of common origin

2. Proper Orbital Elements of Asteroids

3. Characteristic Orbital Evolution in the MB Example: (32) Pomona; osculating orbital elements a=2.59 AU, e=0.083, I=5.53 deg elements a=2.59 AU, e=0.083, I=5.53 deg

4. Osculating elements Proper elements e p  p Characteristic Orbital Evolution in the MB Example: (32) Pomona; osculating orbital elements a=2.59 AU, e=0.083, I=5.53 deg elements a=2.59 AU, e=0.083, I=5.53 deg

5. Asteroid Families: classical

6. Asteroid Families: classical (historical excursion) K. Hirayama, AJ 31, 185 (1918)

7. Asteroid Families: Identification technique An example: Koronis family as a cluster of objects within a distance d < 70 m/s from each other (k a =5/4, k e =k i =2, of the order of unity)

8. Family in (a,e) is nearly cut in two near 2.92 AU. Family in (a,e) is nearly cut in two near 2.92 AU. Both sides of family are bracketed by powerful mean motion resonances (5:2 and 7:3 MMR with Jupiter). Both sides of family are bracketed by powerful mean motion resonances (5:2 and 7:3 MMR with Jupiter). Family members do not appear to have crossed these resonances. Family members do not appear to have crossed these resonances. – No substantial contributions of family members in both (a,e) and (a,i) can be seen on the left side of 5:2 or right side of 7:3. Asteroid Families: Koronis & Karin

9. Asteroid Families: Koronis & Karin (cntd.) Koronis family (~2.5Gy old) harbors Karin family (~5.8 My old) as a result of a secondary fragmentation

10. Asteroid Families: very young ones

11. Asteroid Families: very young ones (cntd.)

12. a (AU) ei (deg)  (deg)  (deg) We searched for asteroid mini-clusters in AstOrb catalogue of osculating orbital elements using metrics We found 4 new very young and compact clusters about (1270) Datura, (14627) Emilkowalski, (16598) 1992 YC2 and (21509) Lucascavin. Asteroid Families: very young ones (cntd.)

13. We integrated backwards 840 clones of each asteroid 20 from the orbital uncertainty interval 41 Yarkovsky clones Picking 10 7 of their combinations we found past epochs for which is smaller than 5 m/s (k 1 =1, k 2 =1/2). This lead us to determine that Datura cluster is 450  50 ky old. Asteroid Families: very young ones (cntd.)

14. Asteroid Families: on a track to even younger ones… We repeated the AstOrb search for close clusters relaxing now the condition of 3 members at least… As a result we noted a peculiar behavior of the cumulative distribution function N(<d) for pairs of asteroids.

15. Asteroid Families: on a track to even younger ones… We repeated the AstOrb search for close clusters relaxing now the condition of 3 members at least… As a result we noted a peculiar behavior of the cumulative distribution function N(<d) for pairs of asteroids. N(<d) ~ d α  small d values: α ~ 1,  intermediate d values: α ~ 2,  large d values: α ~ 5. 1 2 5

16. Asteroid Families: on a track to even younger ones… We repeated the AstOrb search for close clusters relaxing now the condition of 3 members at least… As a result we noted a peculiar behavior of the cumulative distribution function N(<d) for pairs of asteroids. N(<d) ~ d α  small d values: α ~ 1,  intermediate d values: α ~ 2,  large d values: α ~ 5. 1 2

17. Asteroid Families: on a track to even younger ones… We repeated the AstOrb search for close clusters relaxing now the condition of 3 members at least… As a result we noted a peculiar behavior of the cumulative distribution function N(<d) for pairs of asteroids. N(<d) ~ d α  small d values: α ~ 1,  intermediate d values: α ~ 2,  large d values: α ~ 5.

18. Asteroid Families: on a track to even younger ones… The tightest pairs have similar values of the mean anomaly M and are only few m/s apart in the d-metrics. (we find such tight pairs of orbits among MB, Hungaria and Hilda orbits only)

19. Asteroid Families: on a track to even younger ones… Where the tightest pairs are?  ~ 25% in the youngest known families  ~ 25% in the classical known families  ~ 50% in the background population 5 x 10 -4 2 x 10 -4 1 x 10 -4 7 x 10 -4

20. Asteroid Families: on a track to even younger ones… How big are they?  < 10 km sizes (down to < km)  median mass ratio ~ 5-10

21. Asteroid Pairs: statistical robustness check… Is all this real? or a fluke? We used two methods to check real existence of most of the pairs. 1) We created a number of fake MB asteroid populations with the same (a,e,i) long-range distribution and random distribution of (Ω, ϖ ). We then repeated our search for the closest pairs and constructed N(<d) - curve 2.

22. Asteroid Pairs: statistical robustness check… Is all this real? or a fluke? We used two methods to check real existence of most of the pairs. 2) We used a semi-numerical method to estimate probability to find n-asteroids in an elementary volume V ~ d 5 : p n (d).

23. Asteroid Pairs: statistical robustness check… Is all this real? or a fluke? We used two methods to check real existence of most of the pairs. 2) We used a semi-numerical method to estimate probability to find n-asteroids in an elementary volume V ~ d 5 : p n (d). Summing over the whole space filled with M cells we obtain the overall probability to find a cell with n objects.

24. Asteroid Pairs: the case of pairs in very young families… Asteroid pairs in very young families, including Karin, are very likely just original fragments thrown onto very similar orbits… Note: application of the previous statistical methods is not straightforward because of correlation of the secular angles with (a,e,i)

25. Asteroid Pairs: the case of pairs in very young families… … indeed, in the Datura case this relation is still very well preserved. 1)Datura-2003SQ168 tightest to each other

26. Asteroid Pairs: the case of pairs in very young families… … indeed, in the Datura case this relation is still very well preserved. 1)Datura-2003SQ168 tightest to each other 2)2001VN36 in M9/16 exterior resonance

27. Asteroid Pairs: the case of pairs in very young families… … even in the Karin case, there are still intrigue and clumpy correlations between (i,Ω) and (e, ϖ ).

28. Asteroid Pairs: reconstruction of the formation state… Holy grail: use backward integration of the two orbits to reconstruct the exact configuration of the two objects when they became unbound. Two principal obstacles:  Lyapunov timescale typically 100-1000 ky (different orbital realizations from the current uncertainty interval)  Yarkovsky-clone dispersion typically 20-100 ky (different orbital realizations due to different values of the Yarkovsky forces) We used 20 orbital clones, 51 Yarko clones  1020 possible past histories of each orbit; at each time t in the past we determined their minimum distance  (t) in space for 10 6 synthetic pairs. ( ORBFIT9 for orbit uncertainty, SWIFT_MVS for orbit propagation)

29. Asteroid Pairs: reconstruction of the formation state… (6070) Rheinland – (54827) 2001 NQ8 D ~ 4.6,1.8 km asteroids in the inner MB; d ~ 5.8 m/s 50,15 year orbital arcs  ~ 50 ky “Yarko-wall”

30. Asteroid Pairs: reconstruction of the formation state… (6070) Rheinland – (54827) 2001 NQ8 D ~ 4.6,1.8 km asteroids in the inner MB; d ~ 5.8 m/s 50,15 year orbital arcs  ~ 50 ky “Yarko-wall”  at 17 ky  = min(  (t)) ~ 250 km

31. Asteroid Pairs: reconstruction of the formation state… (6070) Rheinland – (54827) 2001 NQ8 D ~ 4.6,1.8 km asteroids in the inner MB; d ~ 5.8 m/s 50,15 year orbital arcs  ~ 50 ky “Yarko-wall”  at 17 ky  = min(  (t)) ~ 250 km  compare with ~ 900 km Hill sphere of influence of Rheinland

32. Asteroid Pairs: reconstruction of the formation state… (6070) Rheinland – (54827) 2001 NQ8 D ~ 4.6,1.8 km asteroids in the inner MB; d ~ 5.8 m/s 50,15 year orbital arcs  at the closest encounter relative speed is only ~0.25 m/s (as opposed to ~ 3 m/s escape speed from Rheinland) and the out-of-plane component is ~0.03 m/s

33. Asteroid Pairs: reconstruction of the formation state… (1270) Datura –2003 SQ168 D ~ 9.5,1.4 km asteroids in the inner MB; d ~ 0.9 m/s 80,6 year orbital arcs  ~ 85 ky “Yarko-wall”  at 1 ky  = min(  (t)) ~ 3x10 5 km (to be compared with ~ 2000 km Hill sphere of influence of Datura)  just ordinary conjunction of the two orbits

34. Asteroid Pairs: reconstruction of the formation state… (1270) Datura –2003 SQ168 D ~ 9.5,1.4 km asteroids in the inner MB; d ~ 0.9 m/s 80,6 year orbital arcs  consistent with the idea that these two asteroids are just primordial fragments from 450 ky old Datura-family formation (more observations of 2003 SQ168 needed to determine if an earlier close encounter is real)

35. Asteroid Pairs: speculations about their origin… Is there any common process that produces 75% of the pairs not included in the very young families?  Catastrophic collisions – yet smaller asteroid families (large mass ratio does not really fit, nor large abundance among Hungarias)  direct YORP fission (plausible, because of low separation velocity in the out-of-plane direction and many of the d<10 m/s pairs dominated by the (  a,  e) 2D subspace; in addition, we estimate D>5km MB asteroids might be YORP fissioned every 2-5 ky)  “retarded” YORP fission – binary splitting (might be closely related to the previous mechanism if many of binaries originally produced by YORP fission)

36. Asteroid Pairs: speculations about their origin… What we need next to decide about the origin of the pairs? Various observations might give us necessary clues:  light-curve observations might help to better constrain the sense and range of the Yarkovsky forces; they might also indirectly hint the YORP fission mechanism, since one of the asteroids should rotate slowly (Dan Scheeres, private comm.)  astrometry observations that in many cases should tighten the orbital uncertainty interval  new surveys (such as PanSTARRS) will complete our information (e.g. new members in mini-clusters?) and extend the data to smaller sizes