Interiors of the Giant Planets 409
understood, the behavior of mixtures of these two con-
stituents is less well constrained. This is a serious theoretical
void because the hydrogen–helium mixture composes most
of the mass of Jupiter and Saturn and is an important com-
ponent at Uranus and Neptune.
Current calculations of the behavior of hydrogen and
helium mixtures show that helium is not soluble in hydrogen
at all mass fractions and temperatures. At the temperatures
predicted in the interior of Saturn, hydrogen and helium do
not mix. According to this model, droplets of helium-rich
material are constantly forming in the molecular to metallic
transition region of the planet. Because they are more dense
than their surroundings, the drops fall to deeper, warmer
levels of the envelope, where temperatures may be high
enough to again allow mixing. Thus, at certain depths in
Saturn’s interior, it is always raining helium. This remarkable
conclusion is discussed in Section 5.3 in the context of the
Saturn interior models.
3.4 Ices
The termicesis applied to mixtures of volatile elements
in the form of water (H 2 O), methane (CH 4 ), and ammo-
nia (NH 3 ) in solar proportions, not necessarily present as
intact molecules. Ices are a primary constituent of Uranus
and Neptune but are less abundant in Jupiter and Saturn. As
the planetary interior temperatures are over several thou-
sand Kelvin, they are present as liquids. Shock wave data
on a mixture of water, isopropanol, and ammonia (dubbed
“synthetic Uranus”) have helped establish the equation of
state of this material at pressures less than about 2 Mbar
and temperatures less than about 4000 K. These experi-
ments helped confirm that ices are a primary constituent of
Uranus and Neptune. The shock wave data on this mixture
show that, at pressures exceeding∼200 kbar, the planetary
ice constituents ionize to form an electrically conductive
fluid. At pressures≥1 Mbar, the ice constituents dissociate,
and the EOS becomes quite “stiff,” meaning the density is
not particularly sensitive to the pressure.
3.5 Rock
The remaining planetary constituents are lumped into the
categoryrock. Rock is presumed to consist of a solar mix-
ture of silicon, magnesium, and iron, with uncertain addi-
tions of oxygen and the remaining elements. Although the
rock equation of state is not well known, it is also expected
to be quite “stiff.” The lack of a detailed rock EOS is not a
serious limitation for planetary interior models because the
rock component is not a major fraction of the mass.
3.6 Mixtures
Because all the planetary components—including gas, ice,
and rock—are likely mixed throughout the interiors, equa-
tions of state of such mixtures are required for interior mod-
eling. Hydrogen–helium mixtures, considered earlier, may
not exist at all temperatures, pressures, and concentrations.
The solubility of other mixtures, for example, rock or oxy-
gen in metallic hydrogen, is less well known. From the lim-
ited data, it appears that the planetary constituents other
than hydrogen and helium do mix well under the temper-
ature and pressure conditions typically found in planetary
interiors. This is because delocalization of electrons at high
pressure diminishes the well-defined intermolecular bonds
present at lower pressures. Thus, the separation of planetary
materials into distinct layers of “pure” rock or ice is highly
unlikely. If correct, such considerations also have impor-
tant cosmogonic implications. For example, the rock cores
of the planets likely did not “settle” from an initially well-
mixed planet, but instead the gaseous components likely
collapsed onto a preexisting rocky nucleus that formed in
the protosolar nebula.
Since the EOS of all possible mixtures has not been stud-
ied, either experimentally or theoretically, approximations
must be employed. One approximation, the additive vol-
ume law, weights the volumes of individual components in
a mixture by their mass fraction. An implication of such ap-
proximations is that the computed densities of mixtures of
rock, ice, and gas can be similar to that of pure ice. Thus, it
is not currently possible to differentiate between models of
Uranus and Neptune with mantles of pure ice and models
with mantles of a mixture of rock, ice, and gas.4. Interior Modeling
In addition to an equation of state for the material in the
interior of a planet, two more components are required to
produce an interior model. The temperature and compo-
sition in the interior as a function of pressure,T(P) and
x(P), must also be known. (These quantities are described
as functions of pressure because the pressure increases
monotonically toward the center of the planet.) The first
of these ingredients,T(P), is not difficult to find. If the
jovian planets are fully convective in their interiors, trans-
porting internal heat to the surface by means of convection,
the relation between temperature and pressure in their in-
teriors is known as an adiabat. An adiabat has the property
that knowledge of a single temperature and pressure at any
point allows specification ofTas a function ofPat any
other point (assuming the material’s EOS is known). The
temperature and pressure in the convecting region of each
Jovian atmosphere have been measured so a uniqueT(P)
relation for each planet can be found.
More difficult to specify is the variation in composition
through each planet,x(P). The composition of each planet’s
atmosphere is known, but there is no guarantee that this
composition is constant throughout the planet. Earth’s core,
for example, has a very different composition from the crust.