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Resonant Excitation of White Dwarf Oscillations in Compact Object Binaries


Rathore, Yasser (2005) Resonant Excitation of White Dwarf Oscillations in Compact Object Binaries. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0726-4X92.


White dwarfs are ubiquitous in the known Universe. They are frequently found in binary systems with ordinary stars, giants, or compact objects as companions. Depending upon their histories, such systems may have significantly eccentric orbits. Because of gravitational radiation, a white dwarf-compact object binary will shrink and circularize with time. If the system is initially close enough, then the inspiral will occur on a time-scale shorter than a Hubble time. As an eccentric system inspirals, it will pass through resonances when harmonics of the orbital period match one of the white dwarf's normal mode eigenfrequencies. At these tidal resonances, energy can be transferred from the orbit to the white dwarf normal modes, and the system will pass through a sequence of such resonances for each mode. If the amplitude of a mode is driven high enough, the modes may damp due to non-linear processes and heat the white dwarf. If the temperature of the white dwarf can be raised in this way to a critical value, then the star may undergo a thermonuclear detonation that results in a Type Ia supernova. In order to determine whether such a scenario is possible, and what other observable consequences of tidal resonances may be, it is necessary to understand the resonant energy transfer and the non-linear evolution of modes on a white dwarf in some detail.

A variational approach to the excitation of dynamical tides is presented. This is then used to study the energy transfer in the resonant excitation of tides. The energy transfer problem is complicated by the fact that a mode perturbs the orbit as it is resonantly excited, effectively creating a non-linear feedback loop. We call this effect 'back reaction.' In the present work, the problem is considered both in the approximation when back reaction is neglected, and when it is included. It is found that back reaction changes the resonant energy transfer both qualitatively and quantitatively. In particular, unlike the no back reaction case, the energy transfer with back reaction is shown to be always positive to lowest order in the rate of dissipation by gravitational radiation, and any initial energy in the mode before resonance is shown to increase the energy transfer.

Numerical simulations of resonant mode excitation and non-linear evolution of white dwarf oscillations are also considered. An adiabatic, parallel hydrodynamic code is described for this. Results from several test problems and preliminary simulations of resonant tidal excitation are presented.

The formalism developed for resonant tidal excitation is applied to studying the feasibility of a tidally triggered supernova via resonant excitation of quadrupolar f-modes. It is found that a 1.4 solar mass companion to the white dwarf is not viable, which rules out double degenerates and white dwarf-neutron star binaries as potential progenitors. However, it is found that with a companion mass of ten to hundred thousand solar masses, there exist regions in the parameter space where the white dwarf can be detonated before tidal disruption. It is calculated that the ejecta from such a detonation would remain trapped in orbit around the companion for the majority of cases, and would presumably be accreted eventually.

A preliminary calculation of the importance of tidal effects for gravitational wave observations of capture sources with central masses of about a million solar masses is also presented. The resonant excitation of f-modes is found to be unimportant because of the long orbital periods at the last stable orbits. It is, however, found that the excitation of g-modes could introduce significant errors in the parameter estimation for such systems, though it would probably not affect detection capability. The exact magnitude of the errors depends upon the density of resonances during the period of observation, and therefore depends upon details of the white dwarf model.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Hamiltonian methods; non-linear dynamics; numerical fluid dynamics; supernovae
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Blandford, Roger D.
Thesis Committee:
  • Blandford, Roger D. (chair)
  • Libbrecht, Kenneth George
  • Kamionkowski, Marc P.
  • Sari, Re'em
Defense Date:18 May 2005
Record Number:CaltechETD:etd-05272005-160411
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2159
Deposited By: Imported from ETD-db
Deposited On:31 May 2005
Last Modified:22 May 2020 21:53

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