MIGRATION TIMESCALES FOR RESONANT CAPTURE
IN THE PLUTINO PROBLEM
L. Friedland, Astrophys. J. Lett. 547, L75-L79 (2001).  PDF.

    Most planets in our solar system move approximately in one plane (the ecliptic) on almost circular (small eccentricity) orbits.  Notable exception is Pluto with orbit inclined relative to the ecliptic plane and having eccentricity of ~0.3 (on the scale between 0 and 1). Similarly, many transneptunian objects (KBOs) in the Kuiper Belt (a belt consisting of estimated ~100,000 bodies with radii ranging between 100-1000m) have large eccentricities. Furthermore, Pluto and estimated 30% of the observed KBOs move in 3:2 resonance with Neptune. In other words, when Neptune completes 3 rotations around the Sun, Pluto and other KBO's (so called Plutinos) complete nearly 2 rotations. What is the reason for this persisting phenomenon? Why there are almost no KBOs in the 2:1 resonance? How eccentricity was created in the solar system?



    In an attempt to answer these questions, R. Malhotra suggested to use migrating Neptune idea. According to this idea, Neptune's orbit radius increased slowly in the early stage of evolution of the solar system. In the process of migration Neptune passed 3:2 resonance with Pluto (and other KBOs) which originally had circular orbits and captured it into resonance. The 3:2 synchronization in the system persisted as Neptune's orbit continued to expand reaching its present size. According to the autoresonance theory such adiabatic synchronization can only be achieved if Pluto develops sizable eccentricity of the orbit.  The only problem remained was why there were almost no observed KBOs trapped into 2:1 resonance (this resonance with a large fraction of KBOs was also passed through by the migrating Neptune)

    We have suggested the following answer to this last remaining question. The capture of a Plutino into resonance and continuing synchronization at later times required the migration rate be below a threshold. This threshold phenomenon was explained only recently and plays an important role in nonlinear synchronization theory. We found that in the Plutino problem the threshold migration time scale for resonant capture into 3:2 resonance was by one order of magnitude smaller than for capture into 2:1 resonance. The phenomenon was due to the effect of Sun's motion around the common center of mass, affecting primarily 2:1 resonance. The study of thresholds allowed us to  explain the observed difference between 3:2 and 2:1 resonance, and estimate how long did it take Neptune to migrate for creating the observed distribution of Plutinos in various resonances.