Hydromagnetic convective instability of a rotating, self-gravitating fluid sphere containing a uniform distribution of heat sources

Abstract

Jupiter, the largest planet, and Saturn, the second largest, contain nine-tenths of the material of the solar system outside the Sun and most of the angular momentum of the solar system is associated with their orbital motion. Both planets rotate very rapidly (rotation periods $\sim $ 10 h) and possess rich satellite systems. Owing to their strong gravitational fields and low surface temperatures, Jupiter and Saturn may, unlike the 'terrestrial' planets, be fairly close in chemical composition to the primordial material out of which the solar system originally formed; they consist mainly of hydrogen, much of which is compressed to a metallic form. Jupiter is the only planet other than Earth showing evidence of a general magnetic field. Absorption of incident solar energy accounts for less than one-half the estimated total thermal (infrared) radiation emitted by Jupiter and Saturn. The balance is probably due to internal heat sources and could be accounted for in terms of a gravitational contraction at about 0.1 cm/year. The outward flow of heat should maintain the atmospheric temperature gradients close to their adiabatic values, which is a significant result for theories of atmospheric motions (see appendix A). These theories are largely concerned with explaining the rough alinement of clouds in bands parallel to the equator, the presence of strong eastward equatorial currents, the occurrence of transient spots and other irregular markings and, in the case of Jupiter, the nature of the enigmatic Great Red Spot. Jupiter, unlike Saturn, is a strong emitter of non-thermal radio noise on decametre and decimetre wavelengths. Plausible theories of this radio emission invoke a strong Jovian dipole magnetic field and an associated system of van Allen-type 'radiation' belts of electrically-charged particles extending beyond and interacting with the first Galilean satellite Io. The most likely source of the Jovian magnetic field - which theories of Jupiter's internal constitution must now take properly into account - is a hydromagnetic dynamo (see appendix B) associated with fluid motions in the electrically-conducting parts of Jupiter's interior. The absence of a non-thermal component in Saturn's radio spectrum implies that radiation belts cannot form around that planet, possibly because Saturn is non-magnetic or, if it is magnetic, because charged particles in the vicinity of Saturn are rapidly removed through interactions with Saturn's rings. Modern research on Jupiter and Saturn is based on a rich variety of data, soon to be augmented by observations from space-craft. Future progress with the theoretical interpretation of these data in terms of improved models of the structure and evolution of the giant planets will involve not only the further application of a wide range of established knowledge but also the development of new ideas in several areas of basic science. The paper ends with two appendices, on the dynamics of rapidly rotating non-homogeneous fluids and on hydromagnetic dynamos.