Interiors of the Giant Planets 407
composition of the remaining planetary atmospheres is in-
ferred from spectroscopy. In planetary science, composi-
tions are often stated relative to “solar” abundances. Solar
abundances are the relative quantities of elements present
in the solar nebula at the time of planetary formation. The
solar abundances of hydrogen and helium are about 70%
and 28% by mass, respectively. Oxygen, carbon, nitrogen,
and the other elements make up the remainder. These el-
ements are collectively called theheavy elementsto dis-
tinguish them from hydrogen and helium. Measurements
of the rate at which the atmospheric pressure decreases
with height in these atmospheres require that hydrogen
and helium must be the dominant components of the at-
mospheres of all four jovian planets. Spectroscopy supports
this conclusion and gives the relative abundance of hydro-
gen and helium. The helium mass fraction of each atmo-
sphere,Y, is listed in Table 1. The heavier elements are
generally enriched in the jovian atmospheres over their so-
lar abundances, which must be explained by any formation
scenario for these planets.
2.3 Magnetic Field
All four jovian planets possess a magnetic field. Jupiter’s
is large and complex; Saturn’s is less complex and smaller.
The magnetic fields of both Uranus and Neptune are very
complex: They deviate substantially from a dipole, and their
field axes are tilted strongly with respect to their rotation
axes. The only known mechanism for producing global plan-
etary magnetic fields, the hydromagnetic dynamo process,
requires nonuniform motion of a large electrically conduc-
tive region. Convection in the highly conductive interior of
the jovian planets is presumed responsible for formation of
their fields. The level of complexity of each field plausibly
relates to the depth of the electrically conducting region.
Magnetic fields formed by relatively small, deep sources
may be simpler and smaller than fields formed by large,
shallow dynamos. [SeePlanetaryMagnetospheres.]
3. Equations of State
3.1 Overview
Beyond observations of the planets themselves, a second
major ingredient in interior models is anequation of state,
or EOS. An EOS is a group of equations—derived from lab-
oratory observations and theory—that relate the pressure
(P) of a mixture of materials to its temperature (T), compo-
sition (x), and density (ρ). Any attempt to model the interior
structure of a giant planet must rely on an EOS. The con-
struction of accurate equations of state is a primary activity
in planetary interior modeling.
For an ideal gas, the well-known EOS isP=nkT. Here
kis Boltzman’s constant, andnis the number density of the
gas. The composition of an ideal gas does not affect the pres-
sure; only the number of molecules and atoms in a given
volume,n, enters the equation. Under the conditions of high
temperature and pressure found in the interiors of the gi-
ant planets, atoms and molecules interact strongly with one
another, thus violating the conditions under which the ideal
gas EOS holds. Additionally, the typical pressures reached
in the interiors of the giant planets (tens to hundreds of
megabars) are also sufficient to modify the electronic struc-
ture of individual atoms and molecules. This further adds
to the challenge of understanding the EOS. In short, the
properties of planetary materials at high pressures will differ
substantially from those encountered in their low-pressure,
and more familiar, forms. In practice, the behavior of plan-
etary materials must be understood from both experiments
and theory.
For pressures less than about 1–3 Mbar, depending on
the material, shock wave experiments provide guidance in
the construction of equations of state. In these experiments,
a high-velocity projectile is fired into a container hold-
ing a sample of the material under study. The thermody-
namically irreversible nature of shock compression causes
both high temperatures and high pressures in the sam-
ple. Alternatively, this shock compression can be achieved
with powerful lasers. High-speed measuring devices record
the temperatures, pressures, and densities achieved during
the brief experiments. A photograph of a shock tube at
Lawrence Livermore National Laboratory, used extensively
for planetary work, is shown in Fig. 3.FIGURE 3 The 60-foot-long, two-stage light-gas gun at
Lawrence Livermore National Laboratory. This apparatus is
used to obtain equation of state, shock temperature, and
electrical conductivity data for planetary liquids (H 2 , He, H 2 O,
NH 3 , and various mixtures). An experiment begins when a
projectile is fired from the gun on the left side of the photo and
ends with the impact of a second projectile, accelerated by gas
compressed by the first, on the target sample at the extreme
right. (Photo courtesy William Nellis, LLNL.)