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Resonant excitation of white dwarf oscillations in compact object binaries - I. The no back reaction approximation

Rathore, Yasser and Blandford, Roger D. and Broderick, Avery E. (2005) Resonant excitation of white dwarf oscillations in compact object binaries - I. The no back reaction approximation. Monthly Notices of the Royal Astronomical Society, 357 (3). pp. 834-846. ISSN 0035-8711. https://resolver.caltech.edu/CaltechAUTHORS:20180413-162135097

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Abstract

We consider the evolution of white dwarfs with compact object companions (specifically black holes with masses up to ∼10^6 M_⊙, neutron stars, and other white dwarfs). We suppose that the orbits are initially quite elliptical and then shrink and circularize under the action of gravitational radiation. During this evolution, the white dwarfs will pass through resonances when harmonics of the orbital frequency match the stellar oscillation eigenfrequencies. As a star passes through these resonances, the associated modes will be excited and can be driven to amplitudes that are so large that there is a back reaction on the orbit which, in turn, limits the growth of the modes. A formalism is presented for describing this dynamical interaction for a non-rotating star in the linear approximation when the orbit can be treated as non-relativistic. A semi-analytical expression is found for computing the resonant energy transfer as a function of stellar and orbital parameters for the regime where back reaction may be neglected. This is used to calculate the Results of passage through a sequence of resonances for several hypothetical systems. It is found that the amplitude of the ℓ = m = 2f-mode can be driven into the non-linear regime for appropriate initial conditions. We also discuss where the no back reaction approximation is expected to fail, and the qualitative effects of back reaction.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1111/j.1365-2966.2004.08459.xDOIArticle
https://arxiv.org/abs/astro-ph/0406102arXivDiscussion Paper
ORCID:
AuthorORCID
Blandford, Roger D.0000-0002-1854-5506
Broderick, Avery E.0000-0002-3351-760X
Additional Information:© 2005 RAS. Accepted 2004 September 28. Received 2004 September 21; in original form 2004 June 3. RDB thanks J. P. Ostriker, K. S. Thorne, P. Goldreich, Y. Wu, and M. L. Aizenmann for useful discussions and encouragement. The authors acknowledge support under NASA grant 5-12032.
Group:TAPIR
Funders:
Funding AgencyGrant Number
NASA5-12032
Subject Keywords:methods: analytical, binaries: general, stars: white dwarfs
Issue or Number:3
Record Number:CaltechAUTHORS:20180413-162135097
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180413-162135097
Official Citation:Yasser Rathore, Roger D. Blandford, Avery E. Broderick; Resonant excitation of white dwarf oscillations in compact object binaries – I. The no back reaction approximation, Monthly Notices of the Royal Astronomical Society, Volume 357, Issue 3, 1 March 2005, Pages 834–846, https://doi.org/10.1111/j.1365-2966.2004.08459.x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85863
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:16 Apr 2018 15:20
Last Modified:03 Oct 2019 19:36

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