Primary Surface Particle Motion and YORP-Driven Expansion of Asteroid Binaries

1. Primary Surface Particle Motion and YORP-Driven Expansion of Asteroid Binaries Eugene G. Fahnestock Dept. Aerospace Engineering, The University of Michigan efahnest@umich.edu

2. Our Systems of Interest… • ≈15±4% of NEOs are binary systems (and ≈2-3% MBAs) • Large class of close “asynchronous” binary systems: • Most abundant binary population • Found among NEOs, MCs, smaller MBAs • Primary diameter D1 typically <10 km, D2/D1 typically 0.2-0.5 • Large spheroidal / oblate roughly axisymmetric primary (Alpha), rotating faster than orbit rate, spin rate near surface disruption rate • Smaller elongated / ellipsoidal secondary (Beta), on-average synchronous rotation • Typified by (66391) 1999 KW4 system • Fission or mass-shedding due to spin-up by YORP implicated for their formation • What about evolution of this type of system after that?

3. Solid-body tidal evolution Asymmetric sunlight absorption and thermal re-radiation on Beta YORP spin-up of Alpha  surface particle motion (“lofting”) To work out details of this mechanism and confirm hypothesis… Precise dynamic simulation and approx. probabilistic simulation Evolution Mechanisms, Hypothesis

4. Precise Dynamic Simulation • First propagate the motion of the binary itself : F2BP • Polyhedral body representation: flexible in shape & resolution • Single polyhedral body and point mass potential Werner & Scheeres, CMDA, 1997 • Mutual potential between two polyhedral bodies  Werner & Scheeres, CMDA, 2005 • Gradients of polyhedral mutual potential, use in general integration of continuous F2BP EOM  Fahnestock & Scheeres, CMDA, 2006 • Parallel implementation and Lie Group Variational Integrator (LGVI) discrete EOM Lee, et. al., CMAME, 2006 , Fahnestock & Scheeres, Icarus, 2008 • Propagate non-interacting particles in binary system: RF3BP • Face, edge dependent dyads and dimensionless scalars are calculated from Alpha and Beta shape models • Impact detection with Laplacian:

5. KW4 as Demonstration System, Setup For RF3BP, batches of particles tiled on facets: F2BP runs and RF3BP batches propagated for pole offsets, , same and opposite sides for facet, different spin rates, {6.51444x10-4, 6.41444x10-4, 6.40444x10-4}rad/s Beta 0.57x0.46x0.35 km ~2.8 g/cm3 density 17.42 hr rotation period Mutual Orbit 2.55 km semi-major axis 17.42 hr orbit period Mass fraction = 0.054 Alpha 1.53x1.49x1.35 km 2.0 g/cm3 density 2.76 hr rotation period Alpha spin rate = 6.31343x10-4 rad/s

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7. Choice of Primary Spin Rate for Lofting Effort made to identify exact location, binary system parameters for which lofting likely first occurs: Facet 4113 chosen location, others nearby possible ≈1×10−6 rad/s difference in minima for everywhere-lofting spin rate between opposite side & same side (lower) Minimum in everywhere-lofting rate at

8. Approximate Probabilistic Simulation Hence choice of {6.51444x10-4,6.41444x10-4, 6.40444x10-4} rad/s Obtain probability matrix for RF3BP output data at thresholdrates, mapping to locations in re-impact longitude and time of flight, or to other outcomes (allows for transfer to Beta, escape) Precise Dynamic Simulation was for “test” particles  no influence on motion of binary components Instead use probability matrices & associated statistical representation of impact velocity to map particles forward in time  track changes to binary component states w/ particle motion Changes with lofting:

9. Approximate Probabilistic Simulation Similar changes across a particle’s impact … … and for a particle’s gravitational interaction during flight:  trajectory endpoints from prob. matrix

10. Approximate Probabilistic Simulation N particles uniformly distributed on surface around Alpha’s equator Test current spin rate against thresholds, Alpha radius bound  if passing, particles in longitude bin at same/opposite side loft  where they go is generated from probability matrix Lofted particles re-impacting later are buffered until impact time step Apply changes to binary states with each piece of particle motion Update states for time step passage Externally applied (YORP) ang. acceleration included in this update Time step length & buffer adjusted with changes in Alpha spin rate We find transient lofting episodes separated by long spin-up times  Adjustment to skip over most of long spin up times, for speedup Grounded in precise dynamic simulation, but can reach long durations, out to O(104)+ years.

11. Results for Nominal Case Case with = 3.0×10−11 rad/s/yr = 9.5129×10−19 rad/s2 10 Mt of surface material (≈0.43% of Alpha mass) modeled For all cases with small , linear fit to algorithm output at right is almost exactly equivalent to

12. Results for Nominal Case Primary spin rate regulated, doesn’t exceed the imposed threshold at which lofting starts Alpha inertia dyad Z-element doesn’t change through lofting episodes

13. Results for Nominal Case (time-integral of plot at right )/duration gives average mass aloft (Accumulated mass lofted)/ duration gives average mass lofting rate For nominal case, have Episodic nature of lofting  these #’s are activity level metrics only

14. vs. Angular Acceleration, Mass Parameters Eventual phase shift to different behavior occurs with vastly increased applied angular acceleration of primary, Greatdependence of on above, little dependence on variation of total mass available to loft, varied thru particle size or N

15. Results for Extreme Acceleration Case Case with = 1.5×10−13 rad/s2 , still 10 Mt surface material Interesting hypothetical scenario, as with propelled spin-up

16. Results for Extreme Acceleration Case Above ≈ 1×10−14 rad/s2, damping effect of same-side particle lofting on Alpha spin rate is overwhelmed Alpha spin rate increases 10−6 rad/s, until opposite-side lofting begins  runaway spin rate growth, use of same probability matrices not OK

17. Results for Extreme Acceleration Case • Shift to near-continuous lofting with sustained mass loss from Alpha, and sustained changes to inertia dyad… • Second shift occurs once opposite-side lofting also picks up

18. Implications for System Evolution Simple formula for semi-major axis growth in response to YORP or other angular acceleration: For KW4 and nominal case, gives expansion rate of ≈0.881 m/kyr Timescale for orbit growth by factor of over : Yields This evolution mechanism is several times faster than tidal evolution Orbit expansion accelerates as long as mechanism is sustained Bodies evolve toward separation rapidly  but at some point mechanism must break down Then Alpha overspin, large mass loss, possible formation of new component interior to old one?

19. Suggestive Observations… Many (≈60) related pairs of bodies, formerly binaries? Vokrouhlicky,Nesvorny Triple system (153591) 2001 SN263  Feb 12, 2008 Feb 13, 2008  Feb 14, 2008 

20. Conclusions and Questions Combination of precise dynamic simulation and statistical simulation confirms hypothesized evolution mechanism Maintains primary near surface disruption spin rate, while producing acceleration orbit expansion to separation Mechanism operates faster than tidal evolution Applies to large class of close asynchronous binary systems Need to better characterize exact conditions for lofting onset? particle physical size distribution (not just mass) accounting for contact, friction forces Inter-particle interaction? Particle-particle collision Electrostatic and gravitational interaction

21. Acknowledgements Thanks to: Al Harris, Petr Pravec, Mike Nolan & Steve Ostro Facilities and Support: JPL Supercomputing and Visualization Facility, JPL/Caltech, NASA ; E.G.F.’s work supported by a National Science Foundation Graduate Research Fellowship ; D.J.S. acknowledges support by a grant from the NASA Planetary Geology and Geophysics Program.

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