Caudill, Sarah and Field, Scott E. and Galley, Chad R. and Herrmann, Frank and Tiglio, Manuel (2012) Reduced basis representations of multi-mode black hole ringdown gravitational waves. Classical and Quantum Gravity, 29 (9). Art. No. 095016. ISSN 0264-9381 http://resolver.caltech.edu/CaltechAUTHORS:20120925-113646346
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We construct compact and high-accuracy reduced basis (RB) representations of single and multiple quasinormal modes (QNMs). The RB method determines a hierarchical and relatively small set of the most relevant waveforms. We find that the exponential convergence of the method allows for a dramatic compression of template banks used for ringdown searches. Compressing a catalog with a minimal match MM = 0.99, we find that the selected RB waveforms are able to represent any QNM, including those not in the original bank, with extremely high accuracy, typically less than 10^(−13). We then extend our studies to two-mode QNMs. Inclusion of a second mode is expected to help with detection, and might make it possible to infer details of the progenitor of the final black hole. We find that the number of RB waveforms needed to represent any two-mode ringdown waveform with the above high accuracy is smaller than the number of metric-based, one-mode templates with MM = 0.99. For unconstrained two modes, which would allow for consistency tests of general relativity, our high accuracy RB has around 10^4 fewer waveforms than the number of metric-based templates for MM = 0.99. The number of RB elements grows only linearly with the number of multipole modes versus exponentially with the standard approach, resulting in very compact representations even for many multiple modes. The results of this paper open the possibility of searches of multi-mode ringdown gravitational waves.
|Additional Information:||© 2012 IOP Publishing Ltd. Received 27 September 2011; in final form 18 March 2012; published 16 April 2012. We are especially grateful to Emanuele Berti and Vitor Cardoso for very valuable discussions (which motivated this work), feedback, assistance and suggestions. We also thank Evan Ochsner, Duncan Brown, Nickolas Fotopoulos, Ajith Parameswaran, Ulrich Sperhake and Bernard Whiting for very useful discussions and feedback on the manuscript. This work has been supported by NSF Grants NSF PHY-0905 184 to Louisiana State University, PHY1005 632 and PHY0801 213 to the University of Maryland, and NSF DMS 0554 377 and OSD/AFOSR FA9550-09-1-0613 to Brown University. CRG has been supported by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory through a contract with NASA, administered by the Oak Ridge Associated Universities. MT thanks Tryst DC Coffeehouse Bar and Lounge, where parts of this work were done, for its hospitality.|
|Subject Keywords:||Gravitation and cosmology; Astrophysics and astroparticles|
|Classification Code:||PACS: 04.80.Nn; 04.25.dg; 04.70.−s; 04.80.Cc. MSC: 83C35; 83C57.|
|Official Citation:||Reduced basis representations of multi-mode black hole ringdown gravitational waves Sarah Caudill et al 2012 Class. Quantum Grav. 29 095016|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Aucoeur Ngo|
|Deposited On:||25 Sep 2012 18:52|
|Last Modified:||27 Dec 2012 02:43|
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