| As an eccentric white dwarf-compact object binary shrinks and circularizes because of gravitational radiation, it will pass through resonances when harmonics of the orbital frequency match one of the white dwarf's normal mode eigenfrequencies. A formalism for calculating the resonant energy transfer is presented, both when the when the perturbation of the orbit by the excited mode is neglected (resonances without back reaction), and when the perturbation is included (resonances with back reaction). It is found that back reaction changes the resonant energy transfer both qualitatively and quantitatively. In particular, the energy transfer with back reaction is shown to be always positive, to lowest order in the rate of dissipation by gravitational radiation.; Numerical simulations of resonant mode excitation and non-linear evolution of white dwarf oscillations are also considered. A hydrodynamics code for studying this is described. Results from several test problems and simulations of resonant tidal excitation are presented.; If the amplitude of an excited mode is driven high enough, the mode may damp non-linearly and heat the white dwarf. If the temperature of the star can be raised to a critical value, then the star may undergo a thermonuclear detonation that results in a Type Ia supernova. The feasibility of such a detonation via excitation of quadrupolar ƒ-modes is studied. It is found that a system with a 1.4 M⊙ companion is not viable, but, for companion masses of ∼ 10--10 5 M⊙ , there exist regions in the parameter space where the white dwarf can be detonated. The ejecta from such a detonation are expected to remain trapped in orbit around the companion in most cases.; A preliminary evaluation of the importance of tidal resonances for gravitational wave observations of capture sources with central masses of ∼ 10 6 M⊙ is also presented. The excitation of ƒ-modes is found to be unimportant, however, but g-mode are shown to potentially introduce significant errors in parameter estimation for such systems. The exact magnitude of the errors depends upon the density of resonances during the period of observation, and therefore upon details of the white dwarf model. |
