Tidally-induced nonlinear resonances in EMRIs with an analogue model

Abstract

One of the important targets for the future space-based gravitational wave observatory LISA is extreme mass ratio inspirals (EMRIs), where long and accurate waveform modeling is necessary for detection and characterization. Modeling EMRI dynamics requires accounting for effects such as the ones induced by an external tidal field, which can break integrability at resonances and cause significant dephasing. In this paper, we use a Newtonian analogue of a Kerr black hole to study the effect of an external tidal field on the dynamics and the gravitational waveform. We have developed a numerical framework that takes advantage of the integrability of the background system to evolve it with a symplectic splitting integrator, and compute approximate gravitational waveforms to estimate the timescale over which the perturbation affects the dynamics. Comparing this timescale with the characteristic time under radiation reaction at resonance, we introduce a tool for quantifying the regime in which tidal effects might be included when modeling EMRI gravitational waves. As an application of this framework, we perform a detailed analysis of the dynamics at one resonance to show how different entry points into the resonance in phase-space can produce substantially different dynamics, and how one can estimate bounds for the parameter space where tidal effects may become dominant. Such bounds will scale as $\epsilon \gtrsim Cq$, where $\epsilon$ measures the strength of the external tidal field, $q$ is the mass ratio, and $C$ is a number which depends on the resonance and the shape of the tide. We demonstrate how to estimate $C$ using our framework for the 2:3 radial to polar frequency resonance in our model system. This framework can serve as a proxy for proper modeling of the tidal perturbation in the fully relativistic case.

arXiv commentV2. Updated to match published version

References in corpus (44)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?
• Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• Prospects for Fundamental Physics with LISA
• Perturbative Approach to an orbital evolution around a Supermassive black hole
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field
• Observation of Dirac Monopoles in a Synthetic Magnetic Field
• Measuring gravitational waves from binary black hole coalescences: II. the waves' information and its extraction, with and without templates
• "Kludge" gravitational waveforms for a test-body orbiting a Kerr black hole
• Observation of superradiance in a vortex flow
• Celestial mechanics in Kerr spacetime
• Extreme- and Intermediate-Mass Ratio Inspirals in Dynamical Chern-Simons Modified Gravity
• The Fast and the Fiducial: Augmented kludge waveforms for detecting extreme-mass-ratio inspirals
• Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
• Tidal Love Numbers of Kerr Black Holes
• Rotating black hole orbit functionals in the frequency domain
• Improved approximate inspirals of test-bodies into Kerr black holes
• Transient resonances in the inspirals of point particles into black holes
• An observable signature of a background deviating from Kerr
• Tidal resonance in extreme mass-ratio inspirals
• Gravitational-wave glitches in chaotic extreme-mass-ratio inspirals
• Forced motion near black holes
• Fast Self-forced Inspirals
• Importance of transient resonances in extreme-mass-ratio inspirals
• Visualization and comparison of classical structures and quantum states of 4D maps
• Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals
• Assessing the impact of transient orbital resonances
• A census of transient orbital resonances encountered during binary inspiral
• Importance of tidal resonances in extreme-mass-ratio inspirals
• General Relativistic Dynamics of an Extreme Mass-Ratio Binary interacting with an External Body
• Modeling transient resonances in extreme-mass-ratio inspirals
• Carter-like constants of the motion in Newtonian gravity and electrodynamics
• The dynamics of a spinning particle in a linear in spin Hamiltonian approximation
• The exact dynamical Chern Simons metric for a spinning black hole possesses a fourth constant of motion: A Dynamical-Systems-Based Conjecture
• The structure of phase space close to fixed points in a 4D symplectic map
• A Newtonian analogue of Kerr black hole
• Detectability of Gravitational Wave from a population of Inspiralling Black Holes in Milky Way Mass Galaxies
• The separable analogue of Kerr in Newtonian gravity
• Analyses on a Relativistic Hierarchical Resonance with the Hamiltonian Approach
• Revised event rates for extreme and extremely large mass-ratio inspirals