Worldtube excision method for intermediate-mass-ratio inspirals: Scalar-field toy model
Worldtube excision method for intermediate-mass-ratio inspirals: Scalar-field toy model
The computational cost of inspiral and merger simulations for black hole binaries increases in inverse proportion to the square of the mass ratio q≔m2/m1≤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-Friedrichs-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≲q≲10-2), where purely perturbative methods may not be adequate. A region of radius much larger than m2 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 them 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+1)D 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.
Dhesi, Mekhi
e063fe53-2d75-4a7f-9480-88e2bb4d5943
Rueter, Hannes
a6361937-a5a1-4c69-91f5-96d3694d6871
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Barack, Leor
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Pfeiffer, Harald P.
b533faf1-143c-4e10-8189-f8dfde1c1fea
1 December 2021
Dhesi, Mekhi
e063fe53-2d75-4a7f-9480-88e2bb4d5943
Rueter, Hannes
a6361937-a5a1-4c69-91f5-96d3694d6871
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Pfeiffer, Harald P.
b533faf1-143c-4e10-8189-f8dfde1c1fea
Dhesi, Mekhi, Rueter, Hannes, Pound, Adam, Barack, Leor and Pfeiffer, Harald P.
(2021)
Worldtube excision method for intermediate-mass-ratio inspirals: Scalar-field toy model.
Physical Review D, 104 (12), [124002].
(doi:10.1103/PhysRevD.104.124002).
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≔m2/m1≤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-Friedrichs-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≲q≲10-2), where purely perturbative methods may not be adequate. A region of radius much larger than m2 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 them 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+1)D 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.
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Accepted/In Press date: 23 October 2021
e-pub ahead of print date: 1 December 2021
Published date: 1 December 2021
Additional Information:
Funding Information:
We thank Ian Hawke, Barry Wardell, and Nikolas Wittek for helpful discussions. Mekhi Dhesi acknowledges support from an STFC studentship, Project Reference No. 2283146 and Grant Reference No. ST/T506412/1. Adam Pound gratefully acknowledges the support of a Royal Society University Research Fellowship and a Research Fellows Enhancement Award. Leor Barack acknowledges support from STFC through Grant No. ST/R00045X/1.
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© 2021 American Physical Society.
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Local EPrints ID: 452613
URI: http://eprints.soton.ac.uk/id/eprint/452613
ISSN: 2470-0010
PURE UUID: b02d44a6-0ff2-4ba0-9032-ba43ca8cf0a1
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Date deposited: 11 Dec 2021 11:29
Last modified: 17 Mar 2024 03:27
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Author:
Hannes Rueter
Author:
Harald P. Pfeiffer
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