Chaos-assisted capture in the formation of Kuiper-belt binaries Sergey Astakhov UniqueICs, Saratov, Russia and NIC Forschungszentrum Jülich,Germany Ernestine Lee FivePrime Therapeutics, San Francisco, Calif. USA David Farrelly Department of Chemistry, Utah State University, Logan, Utah, USA

Currently; ~ 24 NEA binaries ~ 26 Main Belt binaries ~ 22 TNO binaries (K. S. Noll, Asteroids, Comets, Meteors, 2005)

r prim r sec Main Belt TNO << 1~ < ~ 10> ~ 100 Eccen. ~ 0~

Main belt binaries – collisional origin Origin of TNO binaries?

Hill Sphere – mutual gravity dominates solar tides

Binary TNO formation models must explain… mass ratios: msec/mprim ~ 0.1 – 1 (~0.5, rp ~ 70 km) Moderate eccent. (ebin ~ ) Large semimajor axis (abin) compared to primary radius (a/r p ~300) abin ~ 1 - 4% Hill radius (a/r H ~0.04) (1998 WW31)

and explain … Step 1: initial capture Step 2: Post-capture “Keplerization” Require a source of dissipation or other means of energy loss Zero-velocity (energy) surface in circular RTBP

Model comparison

Chaos-assisted capture

Phase space of Hill problem is divided into three parts periodic orbits quasiperiodic trajectories (KAM tori) chaotic transients at the edge of stability – “stickiness”, gravitational capture short-lived scattering trajectories bound unbound How do gravitating particles form bound (stable) configurations?

Sticky Tori Chaotic orbits cling to “sticky” KAM tori Opportunity for capture into nearby tori Capture above Lagrange points possible.

Long-lived chaotic orbits

(i) Form a “nascent” long-living binary in the Hill sphere in a chaotic layer prograde retrograde

Capture in the Hill sphere and stabilization Intruder scattering lads to (ii) capture in Hill sphere and (iii) Keplerization by small (~ 1 – 2% binary mass) intruder scattering (orbit reduction)

Algorithm

4-body Hill equations (Scheeres, 1998): Sun + binary + small intruder (relative to Sun)

Statistics of stabilization Each chaotic binary orbit exposed to ~ 5000 intruders Each orbit ends up with a capture probability Stabilization is most efficient by small intruders (~1% of the total binary mass).

Post-capture Keplerization through multiple intruder scattering After 200 encounters, binary survival probabilities ~ 10 times higher for equal masses Eccentricities tend to be moderate Semimajor axes in observed range m 2 /m 1 = 1 m 2 /m 1 = 0.05

Why are equal mass binaries more stable? Intruder dwell-times in Hill sphere Dwell-times somewhat longer for unequal mass proto- binaries Dwell-times << proto- binary lifetime in absence of intruders

Suggests a simplified model Nascent chaotic binary time scales >> intruder dwell times – assume binary elliptical orbit Neglect solar tides Set intruder mass to zero Binary partners are now the “primaries” Intruder is “mass-less test particle” Elliptic Restricted Three-body problem

Detecting chaos in the ERTBP limit: Fast Lyapunov indicator

Elliptic RTBP Chaos-assisted capture robust to moderate ellipticity Detect chaos using Fast Lyapunov Indicator (FLI) Fast Lyapunov IndicatorCorresponding SOS in CRTBP

Intruders get stuck in Hill sphere resonances unequal masses destabilization ~equal mass binaries undergo rapid intruder scattering Circular or very elliptical binary orbits destabilized FLI MAPS

Capture of Neptune’s retrograde moon Triton

Binary-Planet Scattering Agnor & Hamilton – capture in a 3-body binary-Neptune exchange encounter: Nature, 441, 192 (2006). Triton approaches Neptune as part of a binary. Neptune then “exchanges” with one of the binary partners leaving Triton in an elliptical orbit with close approach distance q ~ 0.5 a Triton ~ 0.15% r Hill ~ 7 R Neptune Keplerization through tidal interactions Doesn’t consider Sun-Neptune Hill sphere Binary has to surmount Lagrange points

Binary-Neptune scattering + solar tides

Approach speeds

Outcomes – 3Dim orbits projected on to x-y plane Capture of one binary partner Temporary trapping of both binary partners as intact binary Escape of both binary partners Split-up of binary and temporary trapping of both binary partners (rare) Collisions with planet Numerous close encounters with planet – implies collisions with satellites may be probable X Y Hill Sphere

R min R max

Summary Small binary semi-major axes (a b ~ 10R N ) – hard binaries – and low relative velocities (few km/s): binary behaves as a composite and exchange is rare Binary partner collisions Softer binaries: long-term trapping and capture Opportunity for collisions with inner moons abab

Conclusions Chaos is important in providing the glue to allow otherwise improbable events to occur Likely that all proposed KBB capture mechanisms play some role, perhaps in combination Capture of moons in binary-planet encounters is possible but very complex dynamics inside Hill sphere results

Acknowledgements Andrew Burbanks, University of Portsmouth, U.K. Funding: National Science Foundation