A note on the conversion of orbital angles for extreme mass ratio inspirals
arXiv:2411.04955 · doi:10.1088/1361-6382/adf02b
Abstract
We outline a practical scheme for converting between three commonly used sets of phases to describe the trajectories of extreme mass ratio inspirals; quasi-Keplerian angles, Mino time action-angles, and Boyer-Lindquist time action-angles (as utilised by the FastEMRIWaveform package). Conversion between Boyer-Lindquist time action angles and quasi-Keplerian angles is essential for the construction of a source frame for adiabatic inspirals that can be related to the source frames used by other gravitational wave source modelling techniques. While converting from quasi-Keplerian angles to Boyer-Lindquist time action angles via Mino time action-angles can be done analytically, the same does not hold for the converse, and so we make use of an efficient numerical root-finding method. We demonstrate the efficacy of our scheme by comparing two calculations for an eccentric and inclined geodesic orbit in Kerr spacetime using two different sets of orbital angles. We have made our implementations available in Mathematica, C, and Python.
arXiv comment20 pages, 6 figures. Published in CQG
References in corpus (42)
- Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
- Intermediate and Extreme Mass-Ratio Inspirals -- Astrophysics, Science Applications and Detection using LISA
- Self-force and radiation reaction in general relativity
- Perturbative Approach to an orbital evolution around a Supermassive black hole
- The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission
- Zoom & Whirl: Eccentric equatorial orbits around spinning black holes and their evolution under gravitational radiation reaction
- Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
- Event rate estimates for LISA extreme mass ratio capture sources
- Gravitational wave snapshots of generic extreme mass ratio inspirals
- Evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission: II. Inspiral trajectories and gravitational waveforms
- Celestial mechanics in Kerr spacetime
- FastEMRIWaveforms: New tools for millihertz gravitational-wave data analysis
- Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
- Gravitational waveforms for compact binaries from second-order self-force theory
- Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis
- Second-order gravitational self-force
- Second-order self-force calculation of the gravitational binding energy in compact binaries
- Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
- Evolution of inspiral orbits around a Schwarzschild black hole
- Rotating black hole orbit functionals in the frequency domain
- Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
- Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
- Gravitational-wave energy flux for compact binaries through second order in the mass ratio
- Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime
- Highly eccentric inspirals into a black hole
- Black hole perturbation theory and gravitational self-force
- The adiabatic evolution of orbital parameters in the Kerr spacetime
- Forced motion near black holes
- Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach
- Evolution of small-mass-ratio binaries with a spinning secondary
- Fast Self-forced Inspirals
- Analytic solutions for parallel transport along generic bound geodesics in Kerr spacetime
- Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain
- "Flux-balance formulae" for extreme mass-ratio inspirals
- Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations
- Constraining the spin parameter of near-extremal black holes using LISA
- Self-forced inspirals with spin-orbit precession
- Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
- Fast inspirals and the treatment of orbital resonances
- Highly eccentric EMRI waveforms via fast self-forced inspirals
- BHPWAVE: An adiabatic gravitational waveform model for compact objects undergoing quasi-circular inspirals into rotating massive black holes
- Action-Angle formalism for extreme mass ratio inspirals in Kerr spacetime