Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field toy model

Abstract

The computational cost of inspiral and merger simulations for black-hole binaries increases in inverse proportion to the square of the mass ratio $q:=m_2/m_1\le 1$. One factor of $q$ comes from the number of orbital cycles, which is proportional to $1/q$, and another is associated with the required number of time steps per orbit, constrained (via the Courant-Friedrich-Lewy condition) by the need to resolve the two disparate length scales. This problematic scaling makes simulations progressively less tractable at smaller $q$. Here we propose and explore a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range ($10^{-4}\lesssim q\lesssim 10^{-2}$), where purely perturbative methods may not be adequate. A region of radius much larger than $m_2$ around the smaller object is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. The analytical model involves certain a priori unknown parameters, associated with unknown bits of physics together with gauge-adjustment terms; these are dynamically determined by matching to the numerical solution outside the excision region. In this paper we develop the basic idea and apply it to a toy model of a scalar charge in a circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in a 1+1D framework. Our main goal here is to explore the utility and properties of different matching strategies, and to this end we develop two independent implementations, a finite-difference one and a spectral one. We discuss the extension of our method to a full 3D numerical evolution and to gravity.

24 pages, 18 figures

References in corpus (10)

• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• GW190814: Gravitational Waves from the Coalescence of a 23 M${}_{\odot }$ Black Hole with a 2.6 M${}_{\odot }$ Compact Object
• GW190521: A Binary Black Hole Merger with a Total Mass of $150M_{\odot }$
• Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis
• Tidal Love Numbers of Kerr Black Holes
• Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Black hole mergers from dwarf to massive galaxies with the NewHorizon and Horizon-AGN simulations
• Nonrotating black hole in a post-Newtonian tidal environment
• Adapted gauge to small mass ratio binary black hole evolutions

Cited by in corpus (1)

• Redshift factor and the small mass-ratio limit in binary black hole simulations