598 Encyclopedia of the Solar System
FIGURE 7 The cumulative magnitude distribution of
the cold population (red) and of the hot population
and scattered disk (green) according to a recent
analysis by G. Bernstein and collaborators. A turnover
of the magnitude distribution is detected around
H∼10. The slope of the magnitude distribution is
very uncertain beyond this limit.small compared to the amount of energy holding the ob-
jects together. In this case, the objects merge to form a
larger object. If two small, weak objects collide at high ve-
locities, then the energy in the collision overpowers the
gravitational and material binding energies. In this case,
the objects break apart, forming a large number of much
smaller objects. In realistic models of the Kuiper Belt with
a range of sizes and velocities, we expect small objects to
fragment and large objects to grow. This produces a size
distribution witha∼ 0. 4 − 0 .5 at small sizes and a much
steeper slope at large sizes where accretion is important.
Statistics of discoveries of Kuiper Belt objects (Fig. 7)
suggest that the absolute magnitude distribution is indeed
very steep forH<9 (approximately equivalent to a diam-
eterD>100 km), witha∼ 0. 6 − 0 .7, and then turns over
toward a significantly shallower slope. Interestingly, the hot
and the cold classical population seems to have two differ-
ent values ofain the steep part. More precisely, the hot
population and the scattered disk have a shallower magni-
tude distribution than the cold population (Fig. 7). This is
consistent with the fact that the largest bodies are all in the
hot population, and yet the hot and cold populations and the
scattered disk contain roughly the same number of bodies
bigger than 100 km.
The value ofain the shallow part of the magnitude distri-
bution beyondH∼10 is very uncertain. Only few surveys
with the most powerful telescopes could probe this region,
but they have discovered very few objects. The results are
therefore affected by small number statistics. It is possi-
ble thata< 0 .5 in some magnitude range. In fact, in the
Asteroid Belt, the magnitude distribution is wavy, and the
canonical values of 0.4–0.5 ofais only a mean value. It
is possible that the magnitude distribution in the Kuiper
Belt is wavy as well, and that the range 10<H<14 cor-
responds to the very shallow part of one of these waves.
It is possible to integrate under the magnitude distribu-
tion shown in Fig. 7 in order to estimate the total mass in
the Kuiper Belt between 30 and 50 AU. Such an integration
with limits betweenR=1 km and 1200 km (the approxi-
mate radius of Pluto) and assuming a density of 1 g cm−^3 ,
shows that the total mass is a few hundredths of an Earth
mass. Given the uncertainties, it is possible that the mass is
of order of 0.1M⊕, but not significantly larger.
As with many scientific endeavors, the discovery of
new information tends to raise more questions than it an-
swers. Such is the case with the preceding mass estimate.
Edgeworth’s and Kuiper’s original arguments for the exis-
tence of the Kuiper Belt were based on the idea that it
seemed unlikely that the disk of planetesimals that formed
the planets would have abruptly ended at the current loca-
tion of the outermost known planet. An extrapolation into
the Kuiper Belt (between 30 and 50 AU) of the current
surface density of nonvolatile material in the outer planets
region predicts that there should originally have been about
30 M⊕of material there. However, as stated previously, our
best estimate is over 200 times less than that figure!
Edgeworth’s and Kuiper’s argument is not the only in-
dication that the mass of the primordial Kuiper Belt had
to be significantly larger in the past. Models of collisional
accretion show that it is not possible for objects with radii