416 Encyclopedia of the Solar System
observational error bars) of the transiting planets, as com-
pared to Jupiter and Saturn. The density of these planets
can be read from the dotted curves. There are already at
least 2 peculiar planets in this sample. One planet, HD
209458b, has a radius 20% larger than expected, and one,
HD 149026b, has a radius 20% smaller than expected for a
mostly hydrogen–helium composition. Small radii can rea-
sonably be attributed to a large fraction of the planet mass
(likely around two-thirds) being made up of rocks and ices.
Indeed, HD 149026b is the only extra-solar planet we know
for certain has a core. The planets that are more massive
than Jupiter, which one would assume would be denser than
Jupiter, due to larger self-compression, are modestly less
dense than Jupiter, showing that stellar irradiation indeed
does slow the contraction of these transiting planets.
However, the planet HD 209458b, the first transiting
planet discovered, is quite puzzling. Since it has by far
the largest radius of the planets discovered to date, itmay
uniquely have some additional internal energy source that
keeps it inflated. Most explanations invoke some sort of tidal
dissipation related the planet’s close orbit around the parent
star. Others involve the penetration of stellar energy to deep
regions of the atmosphere by dynamical processes. This is
still an open question that is a very active area of research.
6. Jovian Planet Evolution
The amount of energy radiated by each of the jovian planets,
except possibly for Uranus, is greater than the amount of
energy that they receive from the Sun (see Table 1). This
internal heat source is too large to be explained by decay
of radioactive elements in the rock cores of the planets.
Temperatures, even in the deep interior, are far below the
1,000,000 K required for thermonuclear fusion. The source
of the excess energy is gravitational potential energy that
was converted to heat during the planets’ formation and
stored in their interiors. [SeeTheOrigin of theSolar
System.]
The potential energy of gas and solids in the solar nebula
was converted to thermal energy when they were accreted
onto the forming planet. Over time, the planets radiated
energy into space and cooled, slowly losing their primordial
energy content. Thus, all four jovian planets were initially
warmer than they are now. During the early evolutionary
stages, the planets contracted as they cooled, thereby re-
leasing even more gravitational potential energy. Today, the
planets all cool at essentially constant radius because the
internal pressures depend only slightly on temperature.
The coupled contraction and cooling is known as Kelvin–
Helmholtz cooling.
Evolutionary models test whether Kelvin–Helmholtz
cooling can account for the current observed heat flows of
the jovian planets. In these calculations, a series of sequen-
tially cooler planetary interior models is created, with the
last model representing the present-day planet. The time
elapsed between each static model is calculated, and thus
the evolutionary age of the planet found.
Models predict that Jupiter should have cooled from an
initially hot state (accompanied by an atmospheric temper-
ature greater than about 600 K) to its current temperature
in about 4.5 billion years. This is about the age of the solar
system, so the Kelvin–Helmholtz model is judged a success
for Jupiter. For Saturn, however, the model is less success-
ful. The models suggest that Saturn, with its current heat
flow, should be about 2 billion years old. Because there is no
reason to believe that Saturn formed 2.5 billion years later
than Jupiter, another heat source must be adding to Saturn’s
Kelvin–Helmholtz luminosity. This leads to the hypothesis
that differentiation of helium in the interior provides addi-
tional thermal energy to the planet.
The helium depletion hypothesis holds that as Saturn
has cooled from an initially warmer state with the solar
abundance of helium throughout, its interior reached the
point (near 2 Mbar and 8000 K) at which hydrogen and
helium no longer mix in all proportions. Like oil and water
in salad dressing, the hydrogen and helium are separating
into different phases.
As the helium-rich drops form in Saturn’s envelope and
fall to deeper, warmer layers of its interior, the helium even-
tually again mixes with hydrogen. Over time, this rainfall
is depleting the supply of helium in the outer envelope
and visible atmosphere and enriching the helium content
deeper in the interior, close to the core. The overall plan-
etary inventory of helium remains constant. This model is
compatible with the observed depletion at Saturn. Jupiter,
with a warmer interior and with smaller helium depletion,
has apparently only recently begun this process.
This process of helium differentiation liberates grav-
itational potential energy as the drops fall. The helium
droplets in Saturn may be raining down very far into the
planet, possibly all the way down the core. No other pro-
cess can simultaneously explain Saturn’s anomalously high
heat flow and the observed atmospheric depletion of he-
lium. Observations from theCassinispacecraft will help
allow for a better determination of the helium abundance
(and the abundances of many other compounds) in Saturn’s
atmosphere.
The problem for Uranus and Neptune is somewhat dif-
ferent. The Kelvin–Helmholtz hypothesis predicts ages of
the correct order of magnitude for Uranus and Neptune,
but the ages are too large. In other words, the model pre-
dicts that these planets should have higher heat flows at the
current time than they are observed to have. The problem is
most severe for Uranus, which has no detectable heat flow.
There are several possible resolutions to this contradiction.
One possibility is that gradients in the composition of
Uranus with radius have served to impede convection in the
deep interior. Composition gradients, for example, a grad-
ual increase in the rock abundance with depth, can severely