Kuiper Belt: Dynamics 601
00.10.20.30.40102030 35 40 45 50050100150a (AU)4:3 3:2 5:3 2:1 FIGURE 9 Final distribution of the Kuiper
Belt bodies according to a simulation of the
sweeping resonances scenario by R. Malhotra.
The simulation is done by numerical
integrating, over a 200 million year timespan,
the evolution of 800 test particles on initial
quasi-circular and coplanar orbits. The planets
are forced to migrate (Jupiter,−0.2 AU; Saturn,
0.8 AU; Uranus, 3 AU; Neptune, 7 AU) and
reach their current orbits on an exponential
timescale of 4 million years. Large solid dots
represent “surviving” particles (i.e., those that
have not suffered any planetary close
encounters during the integration time); small
dots represent the “removed” particles at the
time of their close encounter with a planet. In
the lowest panel, the solid line is the histogram
of semimajor axis of the surviving particles; the
dotted line is the initial distribution. Most of the
initial mass of the Kuiper Belt is simply
relocated from the classical belt to the resonant
populations. The mass lost is only a small
fraction of the total mass.classical belt to the resonances, and only a minority of them
are lost, which cannot explain the mass depletion of the
belt. Finally, the region beyond the 1:2 mean-motion reso-
nance is unaffected by planet migration, and therefore the
existence of an outer edge requires a different explanation.
Four plausible models have been proposed so far to
explain the formation of an outer edge: (1) the outer
part of the disk was destroyed by the passage of a star;
(2) it was photoevaporated by the radiation emitted by
massive stars originally in the neighborhood of the Sun;
(3) planetesimals beyond some threshold distance could not
grow because of the enhanced turbulence in the outer disk
which prevented the accumulation of solid material; and
(4) distant dust particles and/or planetesimals migrated to
smaller heliocentric distance during their growth, as a con-
sequence of gas drag, thus forming sizeable objects only
within some threshold distance from the Sun. The first two
scenarios require that the Sun formed in a dense stellar
environment, consistent with recent observations showing
that stars tend to form in clusters which typically disperse in
about 100 million years. The entire protoplanetary disk—
both the gas and the planetesimal components—would be
truncated by these mechanisms. However, the protoplan-
etary disks that we see around other stars, even in dense
stellar associations, are typically much larger than 50 AU.
Thus, the history of our proto–solar system disk was not
typical. The third and the fourth scenarios, conversely, form
a truncated planetesimal disk out of an extended gaseous
disk. Therefore, they are more consistent with observations,
which are sensitive only to the gas and dust components,
and do not detect the location of planetesimals.
Whatever mechanism formed the edge, it is intriguing
that the latter is now at the location of a resonance with
Neptune, despite the fact that Neptune did not play any
role in the edge formation. Is this a coincidence? Probably
not. It may suggest that originally the outer edge of the plan-
etesimal disk was well inside 48 AU, and that the migration
of Neptune pushed somehow a small fraction of the disk
planetesimals beyond the disk’s original boundary. These
pushed-out planetesimals are now identified with the cur-
rent members of the Kuiper Belt. The fact that the Kuiper
Belt is mass deficient all over its radial extent (36–48 AU),
in addition suggests that the original edge was inside 36 AU.
In fact, if the original edge had been somewhere in the 36–
48 AU range, we would see a discontinuity in the current
radial mass distribution of the Kuiper Belt, which is not the
case. An edge of the planetesimal disk close to 30 AU also
helps to explain why Neptune stopped there and did not
continue its outer migration beyond this limit.
Several mechanisms have been identified to push be-
yond the original disk edge a small fraction (of order 0.1%)
of the disk’s planetesimals, and to implant them on stable
Kuiper Belt orbits. They are described next. More mecha-
nisms might be identified in the future.