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Chaos and the Formation of Binary objects in the Kuiper-belt

    Last October 24th, Professor David Farrelly from Utah State University, gave a seminar at Fundación Imdea Matemáticas, titled “Chaos and the formation of binary objects in the Kuiper-belt”. In order to share the conclusions that were presented during the seminar of such an interesting subject, Professor Farrelly wrote the following abstract.

    The discovery that many trans-Neptunian objects exist as binaries is invaluable for shedding light on the formation, evolution and structure of the outer Solar system, e.g., the nature of the dynamics in debris disks. So far a total of 21 Kuiper-belt binaries (KBBs) are known plus the Pluto-Charon-P1-P2 quartet. Most KBBs contain partners having similar masses which follow large and eccentric mutual orbits. In this talk we briefly review current KBB formation models, all of which point to a primordial origin. We further propose a common dynamical explanation for the unusual compositional and orbital properties of KBBs based on four-body simulations in the Hill approximation.

    Our calculations suggest that binaries are produced through the following chain of events. Initially, long-lived quasi-bound binaries form by two bodies getting entangled in thin layers of dynamical chaos produced by solar tides within the Hill sphere (i.e., chaos-assisted capture). Next, energy transfer through gravitational scattering with a low-mass intruder elbows the binary into a nearby non-chaotic (stable) zone of phase space. Finally, the binary hardens (loses energy) through a series of relatively gentle gravitational scattering encounters with further, low-mass, intruders. This produces binary orbits that are well fitted by Kepler ellipses. Dynamically, the overall process is strongly favoured if the original quasi-bound binary contains comparable masses.

    Unexpectedly, chaos plays a twin role in the stabilization and destabilization of nascent binaries; it provides a mechanism for the formation of transient binaries but selectively destabilizes binaries containing partners having very unequal masses. This suggests that the observed preponderance of roughly equal-mass ratio binaries is a real effect and not simply an artefact of an observational bias for widely separated, comparably bright objects. Nevertheless, we predict that a sizeable population of very unequal-mass Kuiper-belt binaries is probably awaiting discovery.

    Extensions of this mechanism to other problems of interest in the outer Solar System, as well as problems in atomic and molecular physics will be briefly discussed.


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