594 Encyclopedia of the Solar System
must have excited the eccentricities, making them grow
from almost zero to the current values.
The same is true, and even more striking, for the incli-
nations (top panel of Fig. 2). The inclinations are related
to the relative encounter velocities among the objects, so
that the Kuiper Belt bodies had to grow in a razor-thin
disk. Despite this, the current inclinations range up to 30–
40 ◦. Figure 2 gives the impression that large inclination
bodies are a modest fraction among the classical objects.
However, one should take into account that the discovery
surveys have been concentrated near the ecliptic plane, so
that large inclination bodies have a lower probability of be-
ing discovered than low inclination ones. Accounting for
this selection effect, astronomers have computed that the
real inclination distribution of the classical objects is bi-
modal (Fig. 3). There is a cluster of objects with inclination
smaller than 4◦and a second group of objects with a very
distended inclination distribution. The former constitute
what is now usually called the cold population and the lat-
ter the hot population. The adjectives “hot” and “cold” do
not refer to physical temperature (it is always very cold out
there) but to the encounter velocities inside each popula-
tion, in an analogy with gas kinetic theory. The cold and the
hot populations should contain roughly the same number
of objects.
The last striking property of the Kuiper Belt is its outer
edge. Figure 2 shows that the belt ends at the location of
the 1:2 mean motion resonance with Neptune. For several
years, the astronomers suspected that this edge is only ap-
parent, due to the fact that more distant objects are more
difficult to discover. However, with an increasing statistical
FIGURE 3 The inclination distribution (in deg) of the classical
Kuiper Belt after observational biases have been subtracted,
according to the work of M. Brown. The points with error bars
show the model-independent estimate constructed from a
limited subset of confirmed classical belt bodies, while the
smooth line shows a best fit bimodal population model. In this
model∼60% of the objects havei> 4 ◦.
sample, it turned out that this is not true. It has been shown
that more distant objects should have been discovered by
now, unless either (1) the Kuiper Belt population steeply
decays in number beyond 48–50 AU or (2) the maximal
size of the objects beyond this limit is much smaller than
that in the observed Kuiper Belt. For various reasons, as-
tronomers tend to favor hypothesis (1): the existence of a
physical outer edge of the Kuiper Belt.
An important issue is to understand which of the or-
bital properties discussed earlier is due to the dynamical
processes that are still occurring in the Kuiper Belt or
not. For instance, do the eccentricities and the inclina-
tions slowly grow due to some dynamical phenomenon?
Are the low eccentricity objects beyond 48 AU unstable?
If these are the cases, then the existence of large eccen-
tricities and inclinations, as well as the outer edge of the
Kuiper Belt could be simply explained. In the opposite case,
these properties—like the existence of theextended scat-
tered disk—reveal that the solar system was different in the
past.
Dynamical astronomers have studied in great detail the
dynamics beyond Neptune, using numerical simulations
and semianalytic models. Figures 4 and 5 show maps of
the dynamical lifetime of trans-Neptunian bodies on a wide
range of initial semimajor axes, eccentricities, and inclina-
tions. These maps have been computed numerically, by sim-
ulating the evolution of thousands of massless particles un-
der the gravitational perturbations of the giant planets. The
latter have been assumed to be initially on their current
orbits. Each particle was followed until it suffered a close
encounter with Neptune. Objects encountering Neptune,
would then evolve in the scattered disk for a time of order
∼ 108 years, until they are transported by planetary encoun-
ters into the inner planets region, or are ejected to the Oort
cloud or to interstellar space. This issue is described in more
detail in Section 6.
In Fig. 4, the colored strips indicate the length of time
required for a particle to encounter Neptune as a function
of its initial semimajor axis and eccentricity. The initial in-
clination of the particles was set equal to 1◦. Strips that are
colored yellow represent objects that survive for the length
of the simulation, 4× 109 years, the approximate age of
the solar system. As can be seen in the figure, the Kuiper
Belt can be expected to have a complex structure, although
the general trends are readily explained. Objects with per-
ihelion distances less than∼35 AU (shown as a red curve)
are unstable, unless they are near, and presumably librating
about, a mean-motion resonance with Neptune (Section 2).
Indeed, the results in Fig. 4 show that many of the Nep-
tunian mean-motion resonances (shown in blue) are stable
for the age of the solar system. Objects with semimajor axes
between 40 and 42 AU are unstable. This is presumably due
to the presence of three overlapping secular resonances that
occur in this region of the solar system: two with Neptune
and one with Uranus.