1. Tidal Synchronization of the Rotation of Early Main Sequence Stars in Close Binaries. 2. The Rings of Uranus: Results of the 1978 April 10 Occultation. 3. On the Resonance Theory of the Rings of Uranus

Citation

Nicholson, Philip David (1979) 1. Tidal Synchronization of the Rotation of Early Main Sequence Stars in Close Binaries. 2. The Rings of Uranus: Results of the 1978 April 10 Occultation. 3. On the Resonance Theory of the Rings of Uranus. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xtcv-p562. https://resolver.caltech.edu/CaltechETD:etd-03032006-160754

Abstract

Part 1:

The rotational synchronization of an early type main sequence star in a close binary system has been attributed to radiative damping of the dynamical component of the tide raised in the star by its companion (Zahn, 1975, 1977). An investigation of the dynamical tide is presented here, which includes the heretofore neglected effects of stellar rotation. Foremost among these effects is the splitting of the tidal response into a set of modes whose latitudinal structures are controlled by the solutions of Laplace's tidal equation.

An approximate analytic expression is derived for the rate of tidal energy dissipation associated with each of these modes, which in turn determines the rate of synchronization of the star's rotation with its orbital motion. This analytic result is supported by a numerical analysis of the dynamical tide raised in a 5 M_⊙ star. Combination of analytic and numerical results yields synchronization timescales for stars in the mass range 2 M_⊙ - 10 M_⊙. These timescales are a factor of 10 shorter than those obtained by Zahn, and are in good agreement with the observational data concerning synchronism among early type stars in close binaries. It is suggested, however, that the final stages of synchronization are controlled by another mechanism: the slow stellar expansion which accompanies the later stages of main sequence evolution.

Part 2:

Observations of the 1978 April 10 stellar occultation by the rings of Uranus are presented. Nine rings were observed and their radii and widths are calculated. Rings η, γ, and δ are found to be most likely circular and coplanar, in agreement with previous analyses; the remaining rings are either non-circular or slightly inclined. The width of the ϵ ring is a linear function of its radius from the center of Uranus, projected onto the satellites' orbital plane; this suggests that it forms one continuous non-circular ring. The optical depth profile of the ϵ ring has not changed significantly since 1977 March. A model of this ring which fits all available observations adequately is that of a uniformly precessing Keplerian ellipse coplanar with the satellites' orbits. This model permits predictions of the radius and width of the ϵ ring for future occultations. The precession rate is used to determine J₂ for Uranus, on the assumption that precession is caused solely by the planetary oblateness and not by satellite-ring interactions.

Part 3:

A three-body resonance model proposed to account for the rings of Uranus is quantitatively analyzed and found to be unacceptable on several grounds. Calculation of the strengths of two-body and three-body resonances involving all known satellites of Uranus, and which fall in the neighborhood of the rings, reveals that the strongest resonances are the 4:1 and 5:1 resonances with Miranda, and the three-body resonances involving Miranda and Ariel. Resonances invoked by the proposed model are much weaker. Despite the fact that four of these relatively strong resonances approximately coincide with rings 5, α, γ, and ϵ, they are too weak to explain the observed widths of the rings. Finally, the simple ring model of densely packed particles librating about a resonance is shown to be secularly unstable.

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