Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational Waves
A small fraction of the gravitational-wave (GW) signals from binary black holes observable by ground-based detectors will be strongly lensed by intervening objects such as galaxies and clusters. Strong lensing will produce nearly identical copies of the GW signals separated in time. These lensed sig...
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2025-01-01
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| Online Access: | https://doi.org/10.3847/1538-4357/adae10 |
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| author | Ankur Barsode Srashti Goyal Parameswaran Ajith |
| author_facet | Ankur Barsode Srashti Goyal Parameswaran Ajith |
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| description | A small fraction of the gravitational-wave (GW) signals from binary black holes observable by ground-based detectors will be strongly lensed by intervening objects such as galaxies and clusters. Strong lensing will produce nearly identical copies of the GW signals separated in time. These lensed signals must be identified against a background of unlensed pairs GW events, some of which may appear similar by accident. This is usually done using fast, but approximate methods that, for example, check for the overlap between the posterior distributions of a subset of binary parameters, or using slow, but accurate joint Bayesian parameter estimation. In this work, we present a modified version of the posterior overlap method dubbed “PO2.0” that is mathematically equivalent to joint parameter estimation while still remaining fast. We achieve a significant gain in efficiency by incorporating informative priors about the binary and lensing populations, selection effects, and all the inferred parameters of the binary. For binary black hole signals lensed by galaxies, our improved method can detect 65% lensed events at a pairwise false alarm probability of ∼2 × 10 ^−6 . Consequently, we have a 13% probability of detecting a strongly lensed event above 2.25 σ significance during 18 months of observation by the LIGO-Virgo detectors at their current sensitivity. We also show how we can compute the joint posteriors of the lens and source parameters from a pair of lensed events by reweighting the posteriors of individual events in a computationally inexpensive way. |
| format | Article |
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| spelling | doaj-art-997ac09a1f7e49b08423cc751d420b4d2025-08-20T03:05:03ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-01980225810.3847/1538-4357/adae10Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational WavesAnkur Barsode0https://orcid.org/0009-0002-3054-7237Srashti Goyal1https://orcid.org/0000-0002-4225-010XParameswaran Ajith2https://orcid.org/0000-0001-7519-2439International Centre for Theoretical Sciences, Tata Institute of Fundamental Research , Bangalore 560089, India ; ankur.barsode@icts.res.in, srashti.goyal@aei.mpg.de, ajith@icts.res.inInternational Centre for Theoretical Sciences, Tata Institute of Fundamental Research , Bangalore 560089, India ; ankur.barsode@icts.res.in, srashti.goyal@aei.mpg.de, ajith@icts.res.in; Max Planck Institute for Gravitational Physics (Albert Einstein Institute) , Am Mühlenberg 1, D-14476 Potsdam-Golm, GermanyInternational Centre for Theoretical Sciences, Tata Institute of Fundamental Research , Bangalore 560089, India ; ankur.barsode@icts.res.in, srashti.goyal@aei.mpg.de, ajith@icts.res.in; Canadian Institute for Advanced Research , CIFAR Azrieli Global Scholar, MaRS Centre, West Tower, 661 University Avenue, Suite 505, Toronto, ON M5G 1M1, CanadaA small fraction of the gravitational-wave (GW) signals from binary black holes observable by ground-based detectors will be strongly lensed by intervening objects such as galaxies and clusters. Strong lensing will produce nearly identical copies of the GW signals separated in time. These lensed signals must be identified against a background of unlensed pairs GW events, some of which may appear similar by accident. This is usually done using fast, but approximate methods that, for example, check for the overlap between the posterior distributions of a subset of binary parameters, or using slow, but accurate joint Bayesian parameter estimation. In this work, we present a modified version of the posterior overlap method dubbed “PO2.0” that is mathematically equivalent to joint parameter estimation while still remaining fast. We achieve a significant gain in efficiency by incorporating informative priors about the binary and lensing populations, selection effects, and all the inferred parameters of the binary. For binary black hole signals lensed by galaxies, our improved method can detect 65% lensed events at a pairwise false alarm probability of ∼2 × 10 ^−6 . Consequently, we have a 13% probability of detecting a strongly lensed event above 2.25 σ significance during 18 months of observation by the LIGO-Virgo detectors at their current sensitivity. We also show how we can compute the joint posteriors of the lens and source parameters from a pair of lensed events by reweighting the posteriors of individual events in a computationally inexpensive way.https://doi.org/10.3847/1538-4357/adae10Strong gravitational lensingGravitational wavesBayesian statisticsPosterior distribution |
| spellingShingle | Ankur Barsode Srashti Goyal Parameswaran Ajith Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational Waves The Astrophysical Journal Strong gravitational lensing Gravitational waves Bayesian statistics Posterior distribution |
| title | Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational Waves |
| title_full | Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational Waves |
| title_fullStr | Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational Waves |
| title_full_unstemmed | Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational Waves |
| title_short | Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational Waves |
| title_sort | fast and efficient bayesian method to search for strongly lensed gravitational waves |
| topic | Strong gravitational lensing Gravitational waves Bayesian statistics Posterior distribution |
| url | https://doi.org/10.3847/1538-4357/adae10 |
| work_keys_str_mv | AT ankurbarsode fastandefficientbayesianmethodtosearchforstronglylensedgravitationalwaves AT srashtigoyal fastandefficientbayesianmethodtosearchforstronglylensedgravitationalwaves AT parameswaranajith fastandefficientbayesianmethodtosearchforstronglylensedgravitationalwaves |