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arXiv · 1311.4457

Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals

Maarten van de Meent
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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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Maarten van de Meent. 2013-11-18. Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals. https://doi.org/10.1103/physrevd.89.084033

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