48 Encyclopedia of the Solar System
and argon, compared to the Sun. It is thought likely that
these enrichments extend deep into the planets’ interiors,
but this remains uncertain.
Giant planets may form directly by the contraction and
collapse of gravitationally unstable regions of a protoplan-
etary disk. This disk instability is analogous to the gravita-
tional instabilities that may have formed planetesimals, but
instead the instability takes place in nebula gas rather than
the solid component of the disk. Instabilities will occur if
the Toomre stability criterionQbecomes close to or lower
than 1, where
Q=Msuncs
πa^2 vkep(15)wherevkepis the Keplerian velocity,csis the sound speed,
andis the local surface density of gas in the disk. Gas in
an unstable region quickly becomes much denser than the
surrounding material. Disk instability requires high surface
densities and low sound speeds (cold gas), so it is most likely
to occur in the outer regions of a massive protoplanetary
disk. Numerical calculations suggest instabilities will occur
beyond about 5 AU in a nebula a few times more massive
than the minimum-mass solar nebula. What happens to an
unstable region depends on how quickly the gas cools as it
contracts, and this is the subject of much debate. If the gas
remains hot, the dense regions will quickly become sheared
out and destroyed by the differential rotation of the disk.
If cooling is efficient, simulations show that gravitationally
bound clumps will form in a few hundred years, and these
may ultimately contract to form giant planets. Initially, such
planets would be homogeneous and have the same compo-
sition as the nebula. Their structure and composition may
change subsequently due to gravitational settling of heavier
elements to the center and capture of rocky or icy bodies
such as comets.
The evidence for dense cores at the centers of Jupiter
and Saturn suggests to many scientists that giant planets
form by core accretion rather than disk instability. In this
model, the early stages of giant-planet formation mirror the
growth of rocky planets, beginning with the formation of
planetesimals, followed by runaway and oligarchic growth.
However, planetary embryos would have grown larger in
the outer solar system for two reasons. First, feeding zones
here are larger because the Sun’s gravity is weaker, so each
embryo gravitationally holds sway over a larger region of
the nebula. Second, temperatures here were cold enough
for volatile materials such as tars, water ice, and other ices
to condense, so more solid material was available to build
large embryos.
In the outer solar system, bodies roughly ten times more
massive than Earth would have formed via oligarchic growth
in a million years, provided the disk was a few times more
massive than the minimum-mass solar nebula. Bodies that
grew larger than Mars would have captured substantial
atmospheres of gas from the nebula. Such atmospheres
remain in equilibrium due to a balance between an em-
bryo’s gravity and an outward pressure gradient. However,
there is a critical core mass above which an embryo can no
longer support a static atmosphere. Above this limit, the
atmosphere begins to collapse onto the planet forming a
massive gas envelope that increases in mass over time as
more gas is captured from the nebula. As gas falls toward
the planet, it heats up as gravitational potential energy is
released. The rate at which a planet grows depends on how
fast this heat can be radiated away. The critical core mass
depends on the opacity of the envelope and the rate at which
planetesimals collide with the core, but calculations suggest
it is in the range 3–20 Earth masses. The growth of the en-
velope is slow at first, but speeds up rapidly once an embryo
reaches 20–30 Earth masses. Numerical simulations show
that Jupiter-mass planets can form this way in 1–5 Ma. Such
planets are mostly composed of hydrogen-rich nebular gas,
but are also enriched in heavier elements due to the pres-
ence of a solid core. As with the disk instability, the planet’s
envelope may be further enriched in heavy elements by
collisions with comets.
Measurements by theGalileospacecraft showed that
Jupiter’s upper atmosphere is enriched in carbon, nitrogen,
sulfur, and the noble gases argon, krypton, and xenon by fac-
tors of 2–3 compared to the Sun. If these enrichments are
typical of Jupiter’s envelope as a whole, it suggests the planet
captured a huge number of comets. Argon can be trapped
in cometary ices but only if these ices form at temperatures
below about 30 K. Temperatures at Jupiter’s current dis-
tance from the Sun were probably quite a lot higher than
this. This suggests either that the comets came from colder
regions of the nebula or that Jupiter itself migrated inward
over a large distance. However, the fact that relatively re-
fractory elements such as sulfur are present in the same
enrichment as the noble gases suggests these elements may
all have been captured as gases from the nebula along with
hydrogen and helium. If so, Jupiter’s envelope must be non-
homogeneous, with the lower layers depleted in heavy ele-
ments, perhaps due to exclusion from high pressure phases
of hydrogen, while the upper layers are enriched.
It is unclear why Jupiter and Saturn stopped growing
when they reached their current masses. These planets are
sufficiently massive that they would continue to grow very
rapidly if a supply of gas was available nearby. It is possible,
but unlikely, that they stopped growing because the nebula
happened to disperse at this point. A more likely explana-
tion is that the growth of these planets slowed because they
each became massive enough to clear an annular gap in
the nebula around their orbit. Gap clearing happens when
a planet’s Hill radius becomes comparable to the vertical
thickness of the gas disk, which would have been the case
for Jupiter and Saturn. Gas orbiting a little further from the
Sun than Jupiter would have been sped up by the planet’s
gravitational pull, moving the gas away from the Sun. Gas
orbiting closer to the Sun than Jupiter was slowed down,
causing it to move inward. These forces open up a gap in