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Title: Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

Abstract

We study the inspiral, merger, and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M{sub 2}/M{sub 1}=1 to q=4). We compare numerical and post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the post-Newtonian series to the numerical results is nonmonotonic. To leading order, the total energy emitted in the merger phase scales like {eta}{sup 2} and the spin of the final black hole scales like {eta}, where {eta}=q/(1+q){sup 2} is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear-estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross correlating information from different multipoles, wemore » show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.« less

Authors:
; ; ; ; ; ;  [1]
  1. McDonnell Center for the Space Sciences, Department of Physics, Washington University, Saint Louis, Missouri 63130 (United States)
Publication Date:
OSTI Identifier:
21032264
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 76; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.76.064034; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; BLACK HOLES; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CONVERGENCE; COSMOLOGY; DISTRIBUTION; EMISSION; INDEXES; MASS; MULTIPOLES; PRONY METHOD; RESOLUTION; SPHERICAL HARMONICS; SPIN; WAVE FORMS

Citation Formats

Berti, Emanuele, Cardoso, Vitor, Gonzalez, Jose A, Sperhake, Ulrich, Hannam, Mark, Husa, Sascha, Bruegmann, Bernd, Department of Physics and Astronomy, University of Mississippi, University, Mississippi 38677-1848, and Theoretical Physics Institute, University of Jena, Max-Wien-Platz 1, 07743, Jena. Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.76.064034.
Berti, Emanuele, Cardoso, Vitor, Gonzalez, Jose A, Sperhake, Ulrich, Hannam, Mark, Husa, Sascha, Bruegmann, Bernd, Department of Physics and Astronomy, University of Mississippi, University, Mississippi 38677-1848, & Theoretical Physics Institute, University of Jena, Max-Wien-Platz 1, 07743, Jena. Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis. United States. https://doi.org/10.1103/PHYSREVD.76.064034
Berti, Emanuele, Cardoso, Vitor, Gonzalez, Jose A, Sperhake, Ulrich, Hannam, Mark, Husa, Sascha, Bruegmann, Bernd, Department of Physics and Astronomy, University of Mississippi, University, Mississippi 38677-1848, and Theoretical Physics Institute, University of Jena, Max-Wien-Platz 1, 07743, Jena. Sat . "Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis". United States. https://doi.org/10.1103/PHYSREVD.76.064034.
@article{osti_21032264,
title = {Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis},
author = {Berti, Emanuele and Cardoso, Vitor and Gonzalez, Jose A and Sperhake, Ulrich and Hannam, Mark and Husa, Sascha and Bruegmann, Bernd and Department of Physics and Astronomy, University of Mississippi, University, Mississippi 38677-1848 and Theoretical Physics Institute, University of Jena, Max-Wien-Platz 1, 07743, Jena},
abstractNote = {We study the inspiral, merger, and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M{sub 2}/M{sub 1}=1 to q=4). We compare numerical and post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the post-Newtonian series to the numerical results is nonmonotonic. To leading order, the total energy emitted in the merger phase scales like {eta}{sup 2} and the spin of the final black hole scales like {eta}, where {eta}=q/(1+q){sup 2} is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear-estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross correlating information from different multipoles, we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.},
doi = {10.1103/PHYSREVD.76.064034},
url = {https://www.osti.gov/biblio/21032264}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 76,
place = {United States},
year = {2007},
month = {9}
}