Primary Rotations of Asteroid Pairs

1. Primary Rotations of Asteroid Pairs P. Pravec, D. Vokrouhlický, D. Polishook, A. Harris, A. Galád, O. Vaduvescu, F. Pozo, A. Barr, P. Longa, F. Colas, F. Marchis, B. Macomber, J. Pollock, D. Pray, F. Vachier Presented on the 41th annual meeting of the Division for Planetary Sciences of the AAS 2009 October 8

2. Binary asteroidscan disrupt Binaries among small asteroids (NEAs and MBAs, D = 0.3 to 10 km) are an abundant population: the ~15% estimated fraction of binaries gives that there are ~5x104 binaries just among known MBA+NEAs. Most known binaries (with q < 0.2) have Free Energy> 0, so they are Hill unstable and can disrupt (Scheeres, CMDA 104, 103-128, 2009). Until last year, we hadn’t considered whether there might be observable components of recently disrupted (or failed) binaries orbiting the sun as now-individual asteroids in the known asteroid population.

3. Asteroid pairsfound on closely similar heliocentric orbits Vokrouhlický and Nesvorný (Astron. J. 136, 280-290, 2008; VN08) found a population of pairs of asteroids residing on closely similar orbits. Pravec and Vokrouhlický (Icarus, in press, 2009; PV09) extended the analysis and found numerous significant pairs up to d = 36 m/s (approx. the current relative encounter velocitybetween orbits).

4. Asteroid pairsfirst observed facts Pairs of asteroids • Found “everywhere” - in all zones where planetary perturbations are weak (Hungarias, entire main belt, Cybeles, Hildas) • Separated with low relative velocities - Distances in the 5-D space of current osculating elements up to d = 36 m/s, but distances in the 3-D space of proper elements dprop mostly < 10 m/s (where orbits stable enough) • Are young – age (time since separation) typically on an order of 105 yr • Wide range of mass ratios between pair members, up to ΔH = 5 mag, i.e., down to D2/ D1= 0.1 (mass ratio q down to 10-3) Are asteroid pairs related to or derived from binary asteroids?

5. Study of spin rates of paired asteroids If pairs formed by rotational fission of the parent body (“failed binary”) or by split of a binary, it could leave specific signatures in spin properties of paired asteroids. Our current study of spin properties: A sample of 22 primaries and 2 secondaries measured as of 2009 Aug 21, selected from PV09:

6. Primary rotations In pairs with small secondaries (ΔH > 2, D2/ D1 < 0.4), primaries rotate rapidly (P1 = 2.5 to 4.5 h) In pairs with larger secondaries (D2/ D1= 0.4 to 0.7), primaries rotate slower, distribution broader (median P1 ~ 7 h) The former group: the same range of primary spin rates as we observe in orbiting binaries (e.g., Pravec and Harris, Icarus 190, 250-259, 2007; PH07). Our hypothesis: A part of the rapidly rotating primary’s spin energy and angular momentum is transferred to the orbital motion during separation.

7. A model of pair separation The initial state is a close binary. The end state is a barely escaping satellite (parabolic orbit). Both the total energy and the total angular momentum are conserved during separation. The total angular momentum is close to critical (αL ~ 1), as we observe in small binary systems (PH07). Other assumptions: Rotation of the secondary is assumed unchanged during separation and taken to be P2 = 6 h (approx. the one measured secondary period). The spin vectors of both bodies and the normal to the mutual orbit are parallel (prograde rotations). Bulk density of both components is assumed to be 2 g/cm3.

8. A model of pair separation - fit Initial states: • αL= 0.7 and 1.2 (total angular momentum near the lower and upper values observed in orbiting binary systems) • initial separations A/b1 = 2 and 4 (orbit’s semimajor axis/medium semiaxis of the primary) Observed P1 values lie in between the two curves of computed final P1 vs mass ratio q (ΔH) for the two extreme binary angular momentum contents.

9. Implications The observed correlation of spin rates of primaries (larger members) of asteroid pairs with the size ratio between pair’s components • consistent with the pair formation by a gentle split of an original (transient) close binary system. The transient binary may be only momentary and the fissioned system can disrupt directly (Scheeres 2009). This mechanism does not work for binaries with size ratios >~ 0.6 (mass ratio q >~ 0.2) that have insufficient amount of spin energy to effect an escape and such pairs must remain bound, unless there are significant exogenous perturbations acting on the system (Scheeres 2009; Scheeres, Icarus 189, 370-385, 2007). Prediction: separated pairs with nearly equal-sized components do not exist.

10. Pairs – are they a final state of slowly evolving binaries, or rather being failed binaries? There is one observed difference between primaries of known orbiting (i.e., bound) binaries and primaries of separated pairs: • Amplitudes of primaries • wide range for separated pairs (at least some primaries far from rotational symmetry) • vs • low for orbiting binaries (primary shapes close to rotational symmetry) • Though separated as well as bound binaries (with q < 0.2) have Free Energy> 0 so they are Hill unstable and can (or did already) disrupt, primaries of the latter group may be too symmetrical to transfer energy to the satellite orbit, so their evolution is slow and they remain (apparently) bound.

11. Concluding remarks Paired asteroids appear to be components of disrupted (or failed) binaries. The currently known population of ~102 asteroid pairs (i.e., 1 pair per a few 103 asteroids) and assuming their typical age ~105 yr gives that a disruption rate of binaries is so high that a number of formed pairs becomes equal to the total asteroidal population in a few 108 yr. It is shorter than the median dynamical lifetime of small main-belt asteroids. It suggests that in a typical small MB asteroid (<10 km), a few or several satellites are formed (and lost) during its lifetime. One consequence is that a formation of satellites by fission of asteroids spun up by YORP contributes to (increases) the population of km-sized asteroids. Most smaller asteroids may be actually former secondaries of binaries.