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\newpage{Peter Goldreich's Research Interests}
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	Peter Goldreich is a general purpose theoretician whose recent
	research interests include planetary rings, helioseismology and
	neutron stars. \p
	
	\h{4}{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. \p
	
	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. \p
	
	\h{4}{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. \p
	
	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. \p
	
	\h{4}{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. \p
	
	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. \p
	
	\hr
	
	Some recent references: \p
	
	Goldreich, P. and Kumar, P., \i{Ap. J.}, in press (1990) \p
	
	Goldreich, P., Murray, N., Kumar, P. and Willette, G., \i{Ap.
	J.}, submitted (1990) \p
	
	Goldreich, P. and Porco, C., \i{A. J.}, \b{93}, p. 724 (1987) \p
	
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