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Title: The dynamics of eccentric discs in binary systems
Author: Goodchild, S. G.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2008
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This thesis concerns the behaviour of eccentricity in accretion discs in binary systems, both stellar binaries and systems with a single planet. Linear equations are derived which describe the precision of eccentric discs and growth of eccentricity in two-dimensional and three-dimensional discs, with adiabatic or locally isothermal thermodynamics. The gravitational interaction of the binary companion with the disc and of the disc particles with each other is also included in the equation. These equations are analysed by looking for normal modes, with eigenvalues which contain the precession and growth rates for eccentricity. It is shown that the eigenvalue can be written in terms of integrals which describe the separate contributions of the different fluid and dynamical terms to precession and growth. It is also described how simple forms of the eccentricity equation can be interpreted by rewriting them as time-dependent Schrödinger equations. They are applied to explain the behaviour of real systems, firstly superhump systems in which a resonant tidal instability is thought to cause strong outbursts. It is shown that the presence of a strong delta-function resonance creates a cusp in the eccentricity distribution and results in suppression of eccentricity at the resonance leading to low growth rates or stability. A more careful treatment of the resonance results in the resonance causing precession of the disc as well as eccentricity growth and that this leads to a strong eccentric instability in the disc. When the calculated precession rates are compared with observation it is found that a simple 2D disc without a resonance provides the best fit for the expected system parameters. The eccentricity equations are then applied to the interaction of a single planet, large enough to clear a gap, with a protoplanetary disc. It is shown that the width of the gap cleared by a planet is the critical parameter for determining whether the eccentricity can grow, and that a wider gap is needed to excite the planet’s eccentricity than the disc’s. Both eccentric Lindblad and eccentric corotation resonances need to be considered to explain eccentricity growth. This may lead to a new model for the formation of eccentrically orbiting planets in which the disc’s eccentricity is excited first and feedback processes than cause the planet to become eccentric.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available