The Astrophysics Spectator
The Astrophysics Spectator
The two giant gaseous planets of our solar system, Jupiter and Saturn, are distinguished from the other planets in the Solar System by their composition and size. They have the same composition as the Sun, as is reflected in their densities, and they are two orders of magnitude more massive than Earth. But as large as they are, they are simply runt stars, too small to fuse hydrogen, too small even to fuse deuterium, condemned to grow colder and colder through the ages.
Jupiter and Saturn have identical ages and compositions, with an age of about 4.5 billion years and a solar composition that by mass is three-quarters hydrogen and one-quarter helium, plus a small trace of heavier elements such as nitrogen, oxygen, and carbon. Both planets are rapidly rotating with a period of roughly 10 hours. The two principle differences between them are their masses, with Saturn 0.30 times the mass of Jupiter, and their distance from the Sun, with Saturn 1.8 times more distant than Jupiter. A third difference, the presence of a large ring around Saturn, produces atmospheric effects on Saturn that are not seen on any other planet.
The study of gaseous giants is the study of hydrogen at extreme pressures and temperatures. The conditions at the core of a gaseous giant are unattainable in the laboratory, even in those experiments employing nuclear bombs to compress hydrogen to high density. Research on the structure of gaseous planets therefore makes heavy use of computer simulations to carry the laboratory measurements into the relevant regimes (a recent review is Hubbard et al. [2002]).1
Data about the interior structure of these planets is equally difficulty to obtain. Unlike Earth's interior, which can be studied by watching waves generated by earthquake propagate, or the Sun's interior, which can be studied by watching oscillations of the Sun's photosphere, waves on Jupiter and Saturn have never been observed. The primary information about how mass is distributed within these planets is found by measuring the variation of the gravitational field around each planet. This is done by precisely measurement of the motion of satellites around each. Because few spacecraft have visited either planet, the information on their gravitational fields is limited.
The first point to make about the interior of the gaseous giants is that the pressure and temperature are so high that one is above the critical point of the phase transition from molecular hydrogen (H2) to metallic hydrogen.2 This means that as the phase of hydrogen changes with a change in temperature and pressure, one transitions from one state to the other gradually. The second point is that in either state the hydrogen is always a fluid.
An important and uncertain characteristic of metallic hydrogen is its ability to absorb helium. This is a critical question because of the large fraction of helium in gaseous giants; if metallic hydrogen cannot carry helium at the solar abundance level, then helium will precipitate out, which has implications for the structure and energy release in these planets. Unfortunately, different studies come to radically different conclusions: early work suggested that helium at the solar abundance level could be carried in the metallic hydrogen layer of Jupiter, but not of Saturn; a later study concluded that helium could not be carried in this layer of either Jupiter or Saturn; and a third study concluded that helium could be carried in this layer of both Jupiter and Saturn. This problem has a direct impact on the ability of current computer codes to correctly simulate the evolution of the gaseous giants.
The general picture of the structure of Jupiter and Saturn starts with the conjecture, which is based on theories for the formation of the planets, that these planets have a core of iron, nickel, and silicates. This conjecture need not be right, because model calculations of Jupiter find that a Jupiter without this core is consistent with the data. Around the core is a thick layer of metallic hydrogen that gradually transitions with radius to a layer of molecular hydrogen.
As implied by its name, metallic hydrogen is a conductor. This conductor is thought to be the source of these planets' magnetic field. For the temperature at the center of a gaseous giant, the electrons in this conductor are degenerate.3 Any fluid that is degenerate, whether it is the degeneracy of the electrons at the cores of Jupiters, or the degeneracy of the neutrons and protons at the cores of neutron stars, exerts a degeneracy pressure. This pressure is in addition to the coulomb pressure exerted by the hydrogen nuclei. For gaseous planets, the effect of the degeneracy pressure is to make the planet's radius almost independent of mass. This is why, despite having 0.3 times the mass of Jupiter, Saturn has a volumetric mean radius that is 0.833 time Jupiter's radius.
Parts, and perhaps all, of the hydrogen fluid of these planets is unstable to convection. The convection is the primary mechanism for transporting energy from the core to the surface. It also ensures that the hydrogen layers remain uniform in composition. The precise nature of the convection is uncertain, but the winds in the atmospheres of Jupiter and Saturn are consistent with convection occurring along cylinders oriented parallel to the rotation axis; in this theory, the planets are differentially rotating.
A striking feature of both Jupiter and Saturn is their thick cloud layers. The clouds are formed by trace-element chemicals, and they form for the same reason that they form in Earth's atmosphere: gas convectively carried from low altitude to high altitude becomes supersaturated with these chemicals, which condense into droplets. The lowest-altitude clouds are composed of silicate compounds. As one goes to higher altitude, where the temperatures are lower, one passes through cloud layers of hydrosulfide, water, and ammonia. The clouds play a critical role in the solar heating and the radiative cooling of a gaseous giant.
In the early stages of their lives, gaseous planets contract, converting their gravitational potential energy into thermal energy. A planet's luminosity decreases slightly faster than the inverse of the planet's age. Jupiter and Saturn were not much less luminous than main-sequence stars at their birth; Jupiter radiated 10-5 as much power as the Sun, and Saturn radiated at one-tenth of this rate. As a consequence, at the current distance of the moon Ganymede from Jupiter, fifteen times as much energy flux came from Jupiter as came from the Sun, and at the current distance of the moon Titan from Saturn (about the same as the distance of Ganymede from Jupiter), three times as much energy flux came from Saturn as from the Sun. The early radiation from these planets therefore modified the surrounding environment, which should affect the formation and evolution of the moons.
Today, about half of the power emitted by Jupiter and Saturn comes from internal sources; the remaining half is the solar energy they absorb. For Jupiter, this is consistent with the model simulations for the composition and structure outlined above. For Saturn, this is inconsistent with the model simulations, which produce a much cooler planet. This suggests that there is an additional power source for Saturn other than the gravitational contraction. A hypothesis is that this energy is produced by the precipitation of helium out of the hydrogen; as the droplets of helium fall to the core of Saturn, additional gravitational potential energy is releases.
Astronomers have found over one hundred gaseous giant planets orbiting other stars over the past decade, so Saturn and Jupiter are the best-studied objects of a very large collection of objects. Saturn sets the minimum size of a gaseous giant. The two examples we have of giant planets that are smaller than Saturn?Uranus and Neptune?have structures that are much different than Saturn, being composed of ice. The maximum size of a gaseous giant is 0.012 solar masses (13 times the mass of Jupiter), which is set by the onset of deuterium fusion; an object larger than this mass is called a brown dwarf. From a practical standpoint, brown dwarfs and Jupiters belong in the same class, because the same physics describes them. Unlike a star, the composition of a brown dwarf does not change appreciably through deuterium fusion, so once all of the deuterium is converted into helium, the brown dwarf continues to cool like a gaseous giant. The superclass of brown dwarfs and Jupiters is separated from the class of stars by the threshold for hydrogen fusion at 0.075 solar masses (80 times the mass of Jupiter).
1 Hubbard, W.B., Burrows, A., and Lunine, J.I. ?Theory of Giant Planets.? In Annual Review of Astronomy and Astrophysics, edited by G. Burbidge, A. Sandage, and F.H. Shu, vol. 40. Palo Alto, California: Annual Reviews, 2002: 103?136.
2 A phase transition between two states occurs when a material absorbs or releases energy without changing its temperature. The evaporation or condensation of water is an example of this phenomena. As one changes the pressure of a material, one finds that both the temperature at which the phase transition occurs and the amount of energy absorbed or released in a phase transition changes. Normally, the energy in a phase transition decreases at the temperature increases. At a sufficiently-high pressure for some phase transitions, the energy associated with the phase transition goes to zero. This point is the critical point. For example, by increasing the pressure to so that water is above the critical point, it can transition from a fluid to a gas without having both present simultaneously.
3 Degeneracy pressure is an effect of quantum mechanics. Under quantum mechanics, the type of particle called a fermion?among which are electrons, protons, and neutrons?cannot exist in the same energy state as another fermion of the same species. For example, in an atom, an electron cannot exist in the same energy state as another electron. For free electrons this rule becomes a limitation on the density of electrons that can exist in a given energy interval. If the free electrons are cool enough, all of the lowest energy levels will be occupied by electrons. Such a state is termed degenerate. If one applies pressure to a degenerate gas of electrons, the gas will not compress unless the pressure is sufficient to raise the energy of some of the electrons so that they fill higher unoccupied energy levels. The pressure exerted in opposition by the electrons in this instance is called degeneracy pressure.
