August 6, 2004 | David F. Coppedge

“Toy Model” of Planetary Migration Partially Explains Neptune, but Not Uranus

When we last saw Hal Levison (Southwest Research Institute), the genius-at-work was going crazy in fairyland over the difficulties of explaining Uranus and Neptune (see 05/30/2002 headline).  He’s been recovering sanity slowly; he thinks he has a working hypothesis for why Neptune stopped migrating at 30 AU (astronomical unit = sun-earth distance).  Uranus, though, is still enough to drive a sane man nuts.
    Levison concluded last time that the two blue water giants could not have formed where they are; the protoplanetary disk would have been too sparse.  This fact and observations of Jupiter-class extrasolar planets orbiting very close in has raised consciousness of the need to consider a wild and crazy idea: planetary migration.
    Classical (i.e., simplistic) nebular/planetesimal hypotheses considered primarily orbital motion, the around-the-racetrack vector.  These days, planetary physicists have to add the radial vector, the inward vs. outward component.  They suspect a planet forms at one radius, then somehow moves closer in or farther out from the parent star.  There are some physical laws to support these notions: gravitational interactions between two large bodies can perturb orbits, gas drag and disk instabilities can cause angular momentum exchange, and asymmetric collisions with minor bodies can produce net motions in certain directions.  But migration has multiplied the complexities of explaining planets from a rotating disk.  Even a three-body problem is notoriously difficult to solve, to say nothing of one involving billions of objects ranging from dust particles to gas giants.  Of necessity, planetary scientists use models to simulate what might have happened.  Typically, when the simulation solves one condition, others fly off the chart.  Then there is always the tedious necessity of having to match one’s pet idealized model against the hard, cold realities of the observed planets.  Planetary migration models are new; how are they coming along?
    “Despite the importance of planetary migration,” he says, “not much work has been done up to now to study the migration process per se.”  In a new paper in the August issue of Icarus,1 Levison and two colleagues try a “back-of-the-envelope analytic ‘theory’ for migration in planetesimal disks,” which they describe as “an intuitive, easy to understand toy model, intended to be a guide for interpreting the range of behaviors observed in our numerical simulations.”  It must be a tinker toy model.  The authors tinker with pirouettes around Jupiter, square dances with Kuiper Belt Objects and other fancy footwork, with some hand waving along the way.  One excerpt:

We have not been able to identify any dynamical reason for why, in some cases, Neptune sometimes reverses direction.  Thus, we believe it is a matter of chance.  If so, this whole effect may be the result of the fact that our simulations contain a relatively small number of massive bodies compared to the real early Solar System.  Perhaps an ideal system with a nearly infinite number of planetesimals with infinitesimal mass would behave differently.  We will address this issue again in future work….

They get Neptune all the way out to 120 AU, but then the simulation reveals a runaway inward migration, so they try various ways to get it to stop at its observed radial distance without ejecting out all the KBOs and comets in the process.  Phrases like “not obvious” or “not clear exactly how” and “we cannot rule out the possibility” season the entree.  After examining many scenarios, they decide “Therefore, we believe that the current location of Neptune and the mass deficiency of the Kuiper belt imply that the proto-planetary disk possessed an edge at about 30 AU,” which is where Neptune stalled out in its migration.
    Uranus, however, is the stick in the mud that puts the simulation in doubt.  Clearly, explaining planets from a rotating work is, at best, a work in progress:

So far in this paper, we have focused on the evolution of Neptune.  Unfortunately, we find that we have a significant problem with Uranus.  In all simulations starting from a compact planetary configuration where Neptune is initially inside 20 AU, Uranus always stopped well before its current location at ~19 AU.  This is because in these cases the planetesimals scattered by Neptune interact with Saturn almost at the same time as they interact with Uranus, so that Uranus effectively ‘sees’ only a small portion of the total disk’s mass.  This may indicate that Uranus and Neptune formed at 17-18 and 23-25 AU, respectively (see Hahn and Malhotra, 1999), despite of the apparent difficulty of accreting planets at large heliocentric distances (Levison and Stewart, 2001 and Thommes et al., 2003).  Alternatively, it may indicate that the migration process was triggered by some instability in the originally compact planetary system, something similar to what was proposed by Thommes et al. (1999).  This will be the subject of future investigations.

Till next time, happy travails.


1Gomes, Morbidelli and Levison, “Planetary migration in a planetesimal disk: why did Neptune stop at 30 AU?”, Icarus, Volume 170, Issue 2, August 2004, Pages 492-507; doi:10.1016/j.icarus.2004.03.011.

The word planet is from the Greek root for “wanderer” because, to the ancients, the planets in their orbits appeared to wander against the fixed stars in mysterious ways.  Kepler’s and Newton’s laws only temporarily removed the mystery: once again, the planets wander in mysterious ways.  At least now we know the lyrics to the music of the spheres: The Happy WandererI love to go a-wandering along the radial track / And as I go, I love to fling the KBOs out back.
    Hal is fun because he is so brutally honest and able to laugh at himself.  (He looks like a biker or cowboy on the Science Channel Planets series, not your typical white-lab-coat science geek.)  Keeping a sense of humor is one way to keep your sanity: another is to keep working on the details and don’t let the big picture get you down.  Whether these strategies lead one to the truth is a different question.  For anyone having delusions about planetary scientists being able to explain the origin of our solar system through natural processes alone, papers like this should provide a reality check.  Everyone, sing!  Valderi, valdera, valderi, valdera-ha-ha-ha-ha-ha / Valderi, valdera / Beneath God’s clear blue sky.

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