Conditions for sustained orbital resonances in extreme mass ratio inspirals
Conditions for sustained orbital resonances in extreme mass ratio inspirals
We investigate the possibility of sustained orbital resonances in extreme mass ratio inspirals. Using a near-identity averaging transformation, we reduce the equations of motion for a particle moving in Kerr spacetime with self-force corrections in the neighbourhood of a resonant geodesic to a one dimensional equation for a particle moving in an effective potential. From this effective equation we obtain the necessary and sufficient conditions that the self-force needs to satisfy to allow inspiralling orbits to be captured in sustained resonance. Along the way we also obtain the full non-linear expression for the jump in the adiabatic constants of motion incurred as an inspiral transiently evolves through a strong resonance to first-order in the mass ratio. Finally, we find that if the resonance is strong enough to allow capture in sustained resonance, only a small fraction (order of the square root of mass-ratio) of all inspirals will indeed be captured. This makes observation of sustained resonances in EMRIs---if they exist---very unlikely for space based observatories like eLisa.
084033-[15pp]
van de Meent, Maarten
c06e1d53-18af-4ef1-8671-ff99b1a1df22
15 April 2014
van de Meent, Maarten
c06e1d53-18af-4ef1-8671-ff99b1a1df22
van de Meent, Maarten
(2014)
Conditions for sustained orbital resonances in extreme mass ratio inspirals.
Physical Review D, 89 (8), .
(doi:10.1103/PhysRevD.89.084033).
Abstract
We investigate the possibility of sustained orbital resonances in extreme mass ratio inspirals. Using a near-identity averaging transformation, we reduce the equations of motion for a particle moving in Kerr spacetime with self-force corrections in the neighbourhood of a resonant geodesic to a one dimensional equation for a particle moving in an effective potential. From this effective equation we obtain the necessary and sufficient conditions that the self-force needs to satisfy to allow inspiralling orbits to be captured in sustained resonance. Along the way we also obtain the full non-linear expression for the jump in the adiabatic constants of motion incurred as an inspiral transiently evolves through a strong resonance to first-order in the mass ratio. Finally, we find that if the resonance is strong enough to allow capture in sustained resonance, only a small fraction (order of the square root of mass-ratio) of all inspirals will indeed be captured. This makes observation of sustained resonances in EMRIs---if they exist---very unlikely for space based observatories like eLisa.
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Published date: 15 April 2014
Organisations:
Applied Mathematics
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Local EPrints ID: 379376
URI: http://eprints.soton.ac.uk/id/eprint/379376
ISSN: 1550-7998
PURE UUID: 75d685f9-1a39-4a41-ac9f-887176faea2d
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Date deposited: 28 Jul 2015 08:50
Last modified: 14 Mar 2024 20:40
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Author:
Maarten van de Meent
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