Planetary Rings
All of the outer planets, from Jupiter to Neptune, are encircled by belts of small particles organized into rings. Goldreich has focused his attention on the morphology of these rings. Although the different ring systems are morphologically quite distinct, they are all shaped by a few common processes. These are the outward transport of angular momentum by particle collisions and by gravitational interactions between satellites and ring material. Orbital resonances between satellites and ring particles play an important role in enhancing the influence of satellites. The consequences of these resonant interactions are beautifully illustrated by the shepherd satellites that straddle the epsilon ring of Uranus, as predicted by Goldreich and Tremaine.The processes that take place in planetary rings have striking parallels to those that occur in more remote disk systems such as galactic disks, and accretion disks about stars and black holes.
Helioseismology
Observational helioseismology is carried out at Caltech's Big Bear Solar Observatory under the leadership of Professor Libbrecht. Goldreich provides theoretical support. His major effort has been directed toward identifying the mechanisms responsible for the excitation and damping of the modes. Current evidence suggests that the modes are stochastically excited by turbulence in the upper layers of the convection zone, as suggested by Goldreich and Keeley. In recent months Goldreich, Murray, Kumar and Willette have explored the implications of the solar cycle dependent frequency shifts discovered by Libbrecht and Woodard. They demonstrate that these signal an increase in the magnitude of the rms photospheric magnetic field to a value of order 200 Gauss at solar maximum.Over the coming decade Goldreich intends to extend his studies of helioseismology to asteroseismolgy, since the Keck telescope should make it possible to observed stochastically excited oscillations of other stars.
Neutron Stars
Goldreich's current work on neutron stars is directed toward understanding the origin and evolution of their magnetic fields. Surface magnetic fields of neutron stars are deduced from the spin down rates of radio pulsars under the assumption that the braking torque results from magnetic stress. For ordinary pulsars these fields cluster in the range 10^12 - 10^13 G. The weakening of the braking torque with age is most commonly attributed to decay of the dipole component of the magnetic field on a timescale ~ 5 x 10^6 y. The narrow range of the surface fields is an important clue to the mode of origin.Protons in the interior of neutron stars form a type II superconductor, so the magnetic field is concentrated in quantized flux tubes. Goldreich and Reisenegger are exploring different aspects of magnetic buoyancy that may limit initial magnetic field strengths or contribute to field decay. Previous studies have focused on the behavior of single quantized flux tubes. The correct approach is to consider collective motions of macroscopic bundles of flux tubes, since neighboring tubes are strongly coupled by electrons and protons whose orbits are much larger than the tubes' separations. Flux tubes have two distinct modes of collective motion. The first involves the buoyant rise of the field along with the entire fluid in which it is embedded. This motion is inhibited by the stable stratification of the neutron star interior. The stratification is due to the variation with depth of the ratio of the number densities of the charged components, electrons and protons, to the dominant neutrons The speed of buoyant rise of magnetic bubbles is limited by the rate at which weak interactions act to adjust this ratio as fluid elements change their depth. Phase space constraints make these rates very slow, even at the high densities inside neutron stars. The second mode is a quantum version of ambipolar diffusion and involves the motion of field and plasma relative to the neutrons. Its speed is limited by collisions between the charged particles and the neutrons.
Some recent references:
Goldreich, P. and Kumar, P., Ap. J., in press (1990)
Goldreich, P., Murray, N., Kumar, P. and Willette, G., Ap. J., submitted (1990)
Goldreich, P. and Porco, C., A. J., 93, p. 724 (1987)