Abstract
Extreme mass ratio inspirals (EMRIs) occur when a compact object orbits a much larger one, like a solar-mass black hole around a supermassive black hole. The orbit has 3 frequencies which evolve through the inspiral. If the orbital radial frequency and polar frequency become commensurate, the system passes through a transient resonance. Evolving through resonance causes a jump in the evolution of the orbital parameters. We study these jumps and their impact on EMRI gravitational-wave detection. Jumps are smaller for lower eccentricity orbits; since most EMRIs have small eccentricities when passing through resonances, we expect that the impact on detection will be small. Neglecting the effects of transient resonances leads to a loss of ∼ 4% of detectable signals for an astrophysically motivated population of EMRIs.
Highlights
Flanagan and Hinderer [4] highlighted a previously overlooked phenomenon that complicates Extreme mass ratio inspirals (EMRIs) waveform modelling, that of transient resonances
The orbital phase can be expressed as φ ∼ t +
Adiabatic waveforms quickly dephase from true EMRI waveforms if passing through resonance causes a jump in the orbital parameters
Summary
Flanagan and Hinderer [4] highlighted a previously overlooked phenomenon that complicates EMRI waveform modelling, that of transient resonances. The evolving Laser Interferometer Space Antenna (eLISA) provides the chance to observe gravitational waves from stellar-mass black holes orbiting supermassive black holes [2]. These extreme mass ratio inspirals (EMRIs) emit ∼ 104–105 gravitational-wave cycles in eLISA’s frequency band, allowing exquisite measurements to be made [3]. The orbit does not cover the whole allowed r–θ plane, but cycles over a single loop [5].
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