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A Bayesian statistical framework for identifying strongly-lensed gravitational-wave signals

Lo, Rico K. L. and Magaña Hernandez, Ignacio (2021) A Bayesian statistical framework for identifying strongly-lensed gravitational-wave signals. . (Unpublished)

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It is expected that gravitational waves, similar to electromagnetic waves, can be gravitationally lensed by intervening matters, producing multiple instances of the same signal arriving at different times from different apparent luminosity distances with different phase shifts compared to the un-lensed signal due to lensing. If unaccounted for, these lensed signals will masquerade as separate systems with higher mass and lower redshift. Here we present a Bayesian statistical framework for identifying strongly-lensed gravitational-wave signals that incorporates astrophysical information and accounts for selection effects. We also propose a two-step hierarchical analysis for more efficient computations of the probabilities and inferences of source parameters free from bias introduced by lensing. We show with examples on how changing the astrophysical models could shift one's interpretation on the origin of the observed gravitational waves, and possibly lead to indisputable evidence of strong lensing of the observed waves. In addition, we demonstrate the improvement in the sky localization of the source of the lensed signals, and in some cases the identification of the Morse indices of the lensed signals. If confirmed, lensed gravitational waves will allow us to probe the Universe at higher redshift, and to constrain the polarization contents of the waves with fewer detectors.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Lo, Rico K. L.0000-0003-1561-6716
Magaña Hernandez, Ignacio0000-0003-2362-0459
Additional Information:Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) The authors would like to thank Will Farr, Masamune Oguri, Alan Weinstein, Yanbei Chen, Katerina Chatziioannou, Colm Talbot, and Ken K. Y. Ng for the discussion and the help when preparing this paper. RKLL acknowledges support from the Croucher Foundation. IMH is supported by the NSF Graduate Research Fellowship Program under grant DGE-17247915. The computations presented here were conducted on the Caltech High Performance Cluster partially supported by a grant from the Gordon and Betty Moore Foundation. IMH also acknowledges support from NSF awards PHY-1607585, PHY-1912649, and PHY-1806990. The authors are also grateful for computational resources provided by the LIGO Laboratory and supported by National Science Foundation Grants PHY-0757058 and PHY-0823459. Figures 1, 2, 4, and 5 were generated using BayesNet. Figures 6, 7, and 10 were generated using [47]. This is LIGO document number P1900058.
Funding AgencyGrant Number
Croucher FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-17247915
Gordon and Betty Moore FoundationUNSPECIFIED
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Other Numbering System NameOther Numbering System ID
LIGO DocumentP1900058
Record Number:CaltechAUTHORS:20210809-205949295
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110181
Deposited By: George Porter
Deposited On:09 Aug 2021 23:03
Last Modified:09 Aug 2021 23:03

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