Planetary magnetic fields

As a consequence of the smallness of the electronic fine structure constant, the characteristic time scale for the free diffusive decay of a magnetic field in a planetary core is much less than the age of the Solar System, but the characteristic time scale for thermal diffusion is greater than the age of the Solar System. Consequently, primordial fields and permanent magnetism are small and the only means of providing a substantial planetary magnetic field is the dynamo process. This requires a large region which is fluid, electrically conducting and maintained in a non-uniform motion that includes a substantial RMS vertical component. The attributes of fluidity and conductivity are readily provided in the deep interiors of all planets and most satellites, either in the form of an Fe alloy with a low eutectic temperature (e.g. Fe-S-O in terrestrial bodies and satellites) or by the occupation of conduction states in fluid hydrogen or 'ice' (H2O-NH3-CH4) in giant planets. It is argued that planetary dynamos are almost certainly maintained by convection (compositional and/or thermal)

Mass distributions in a variational model

The time-dependent Hartree-Fock approach may be derived from a variational principle and a Slater Determinant wavefunction Ansatz. It gives a good description of nuclear processes in which one-body collisions dominate and has been applied with success to giant resonances and collisions around the barrier. It is inherently unable to give a good description of two-body observables. A variational principle, due to Balian and Veneroni has been proposed which can be geared to good reproduction of two-body observables. Keeping the Slater Determinant Ansatz, and restricting the two-body observables to be the squares of one-body observables, the procedure can be implemented as a modification of the time-dependent Hartree-Fock procedure. Applications, using the Skyrme effective interaction, are presented for the mass distributions of fragments following de-excitation of the giant dipole resonance in S-32. An illustration of the method's use in collisions is given.Comment: 5 pages, proceedings of XXXII Symposium on Nuclear Physics, Cocoyoc, Mexic

Volcanism by melt-driven Rayleigh-Taylor instabilities and possible consequences of melting for admittance ratios on Venus

A large number of volcanic features exist on Venus, ranging from tens of thousands of small domes to large shields and coronae. It is difficult to reconcile all these with an explanation involving deep mantle plumes, since a number of separate arguments lead to the conclusion that deep mantle plumes reaching the base of the lithosphere must exceed a certain size. In addition, the fraction of basal heating in Venus' mantle may be significantly lower than in Earth's mantle reducing the number of strong plumes from the core-mantle boundary. In three-dimensional convection simulations with mainly internal heating, weak, distributed upwellings are usually observed. We present an alternative mechanism for such volcanism, originally proposed for the Earth and for Venus, involving Rayleigh-Taylor instabilities driven by melt buoyancy, occurring spontaneously in partially or incipiently molten regions

Condensed matter physics of planets: Puzzles, progress and predictions

Despite recent advances in observations, experiment and theory, there are many major unresolved issues concerning planetary interiors. This paper is not a comprehensive review but seeks to highlight these issues. Emphasis is on the cosmically most abundant materials, the dominant constituents of the giant planets. The important issues include: (1) What are the atomic and electronic degrees of freedom in hydrogen at high pressure and temperature and how do they behave? (2) To what extent does helium dissolve in hydrogen? (3) What is the behavior of water at megabar pressures and what is the H_2-H_2O phase diagram? (4) How does carbon behave at high pressures, in the presence of oxygen and hydrogen? (5) What happens to clathrates (e.g. CH_4·5-3/4H_2O) at high pressure? (6) How does the volatile ice assemblage expected in Titan H_2O- NH_3-CH_4-N_2-CO?) behave at P ~ 20-40 kbar? (7) What is the nature of the core alloy in the Earth and the core-mantle phase boundary? (8) What are the electrical conductivities of all of the above

Thermodynamics and phase separation of dense fully ionized hydrogen-helium fluid mixtures

The free energy of a hydrogen-helium fluid mixture is evaluated for the temperatures and densities appropriate to the deep interior of a giant planet such as Jupiter. The electrons are assumed to be fully pressure ionized and degenerate. In this regime, an appropriate first approximation to the ionic distribution functions can be found by assuming hard-sphere interactions. Corrections to this approximation are incorporated by means of the perturbation theory of Anderson and Chandler. Approximations for the three-body interactions and the nonlinear response of the electron gas to the ions are included. We predict that a hydrogen-helium mixture, containing 10% by number of helium ions, separates into hydrogen-rich and helium-rich phases below about 8000°K, at the pressures relevant to Jupiter (4-40 Mbar). We also predict that the alloy occupies less volume per ion than the separated phases. The equation of state and other thermodynamic derivatives are tabulated. The implications of these results are mentioned

Semiconvection as the occasional breaking of weakly amplified internal waves

An analysis is made of the semiconvective zones which arise in the evolution of many stars. Despite the presence of a strongly stabilizing solute gradient, growing overstable modes are possible for a slightly superadiabatic temperature gradient, because heat diffusion greatly exceeds solute diffusion or molecular viscosity. These modes are essentially identical to weakly amplified internal waves (or hydromagnetic waves if rotation and magnetic field are present). Their amplification is balanced by a cascade to higher wavevectors (caused in part by subharmonic parametric instabilities) leading to infrequent wavebreaking 'events' which provide the required redistribution of solute. Detailed quantification of this model is impractical, but a simplified analysis indicates that the ratio of the superadiabaticity to the solute gradient is at most of order (D_e/K)^(1/2) where D_e is the solute 'eddy' diffusivity and K is the thermal diffusivity. Evolutionary models require D_e << K, so the Schwarzschild-Härm criterion for semiconvection is essentially correct. A field in excess of about 10^4 gauss modifies the model somewhat, but does not invalidate it. Propagation of the waves out into the radiative envelope of the star is unimportant. The related phenomenon to semiconvection which occurs in differentiating black dwarfs (e.g. Jupiter, Saturn) is also briefly discussed