412 Encyclopedia of the Solar System
curve for hydrogen, thus revealing an appreciable compo-
nent of heavier elements in their interiors. In Section 5.5,
we will discuss giant planets around other stars, where the
only planetary properties we can determine are radii and
masses. For these planets, we can get a good estimate of
the percentage of their mass that is made of hydrogen and
helium, compared to the heavy elements.
Though the mass–radius relations clearly reveal the bulk
composition of Jupiter and Saturn, they do not reveal infor-
mation about the distribution of material inside the planet.
It is here that the shape and gravitational harmonics enter
the calculation. The response coefficient 2 measures the
response of the planet to its own rotation. For a uniform,
hydrogen-rich material, 2 =0.17. Values smaller than 0.17
indicate a reduced gravitational response to rotation com-
pared with that of the uniform composition hydrogen-rich
planet. Such a reduced response results when more of the
mass of the planet is concentrated in a dense core. Thus,
smaller values of 2 imply greater degrees of central con-
densation.
2 varies (see Table 1) from 0.16 for Jupiter to 0.11
for Saturn. The mass–radius relations show that the jovian
planets are not pure hydrogen, and their 2 values sug-
gest that they are more centrally condensed than a solar–
composition hydrogen–helium object. Hence the heavier
constituents are not uniformly distributed in the radius but
are concentrated toward the center of each planet. Jupiter
exhibits the least central condensation; Saturn and Uranus
are most centrally condensed. Thus, we begin to construct
an elementary interior model.
Finally, the gravitational harmonics,J 2 ,J 4 , andJ 6 , probe
the detailed variation of the various planetary constituents.
To simplify the interpretation of these harmonics, early in-
terior models tended to employ three distinct compositional
zones: an inner rocky core, an icy core surrounding the rock
one, and a hydrogen/helium envelope. More modern mod-
els allow the composition of various zones to vary gradually
between layers and allow the outer envelopes to be enriched
over solar abundance. The primary unknowns to be found
from interior modeling are the size of the rocky/icy core
and the abundance of helium and heavy elements in the
envelope.
5.2 Jupiter
Jupiter contains more mass than that of all the other plan-
ets combined. Because Jupiter’s gravitational harmonics
are also best known, it serves as a test bed for theoreti-
cal understanding of jovian interiors. The observed physical
characteristics of Jupiter are listed in Table 1. FromGalileo
Entry Probe data, abundance of methane in Jupiter’s at-
mosphere is about 3.5 times the solar abundance and the
abundance of ammonia is about three times solar. Water
does not show such enrichment, but it has been argued that
theGalileoEntry Probe fell into an anomalously dry region
of Jupiter’s atmosphere.
The general structure of Jupiter’s interior was briefly de-
scribed in Section 1. Modern interior models attempt to
determine specifically the degree of enrichment of heavy
elements in the hydrogen/helium envelope of the planet.
The atmospheric enrichment of methane and ammonia pro-
vides some indication that heavy element enrichment in the
deeper interior may be expected. Jupiter’s 2 implies that
Jupiter is not homogeneous but is slightly centrally con-
densed. Indeed, detailed modeling has shown that Jupiter’s
current core is less than 10 Earth masses and that there
may not be a core at all. The size and composition of jovian
planet cores and the amount of heavy element enrichment
in the envelopes have bearing on the scenarios by which
they are supposed to have formed.
The variations of density with a radius for two typical
Jupiter models are shown in Fig. 7. It should be empha-
sized that these are two Jupiter models that are consistent
with all available constraints. Other, equally valid interior
models exist. Figure 8 shows the mass of heavy elements
in the cores and hydrogen–helium envelopes for a large
number of Jupiter and Saturn models. Any model within
the solid red line is a valid interior model for Jupiter, given
the current uncertainties in the EOS of hydrogen. Models
within the hashed line area are tentatively preferred, given
the most recent experimental EOS data. The majority of
Jupiter’s heavy elements are found within the hydrogen–
helium envelope, not within the core. The models also ac-
count for uncertainty related to the unknown composition
of the core, which is likely some mixture of ice and rock.FIGURE 7 Density as a function of normalized radius for
Jupiter and Saturn models. A helium deficit in molecular
hydrogen regions and corresponding helium enrichment in
metallic regions is responsible for the small density change near
0.55r/Ris Saturn. For Jupiter, a model with and without a core
is shown. For the models with a core, the core is assumed to be
ices overlying rock.