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.
Based on the rate of gravitational-wave (GW) detections by Advanced LIGO and Virgo, we expect these detectors to observe hundreds of binary black hole mergers as they achieve their design sensitivities (within a few years). A small fraction of them can undergo strong gravitational lensing by intervening galaxies, resulting in multiple images of the same signal. To a very good approximation, the lensing magnifies/de-magnifies these GW signals without affecting their frequency profiles. We develop a Bayesian inference technique to identify pairs of strongly lensed images among hundreds of binary…
A small fraction of the gravitational-wave (GW) signals that will be detected by second and third generation detectors are expected to be strongly lensed by galaxies and clusters, producing multiple observable copies. While optimal Bayesian model selection methods are developed to identify lensed signals, processing tens of thousands (billions) of possible pairs of events detected with second (third) generation detectors is both computationally intensive and time consuming. To mitigate this problem, we propose to use machine learning to rapidly rule out a vast majority of candidate lensed pair…
Strong gravitational lensing is a gravitational wave (GW) propagation effect that influences the inferred GW source parameters and the cosmological environment. Identifying strongly-lensed GW images is challenging as waveform amplitude magnification is degenerate with a shift in the source intrinsic mass and redshift. However, even in the geometric-optics limit, type II strongly-lensed images cannot be fully matched by type I (or unlensed) waveform templates, especially with large binary mass ratios and orbital inclination angles. We propose to use this mismatch to distinguish individual type …
We perform Bayesian model selection with parameter estimation to identify potentially lensed gravitational-wave images from the second observing run (O2) of Advanced LIGO and Advanced Virgo. Specifically, we compute the Bayesian evidence for a pair of events being lensed or not lensed (unlensed) using nested sampling. We consider the discrete coalescence phase shifts that can be induced if the gravitational-wave signal interacts with the lens caustics in the model selection. We find that the pair of events, GW170104 and GW170814 with a $π/2$ coalescence phase shift, has a significant Bayes fac…
Similar to light, gravitational waves (GWs) can be lensed. Such lensing phenomena can magnify the waves, create multiple images observable as repeated events, and superpose several waveforms together, inducing potentially discernible patterns on the waves. In particular, when the lens is small, $\lesssim 10^5 M_\odot$, it can produce lensed images with time delays shorter than the typical gravitational-wave signal length that conspire together to form ``beating patterns''. We present a proof-of-principle study utilizing deep learning for identification of such a lensing signature. We bring the…
Gravitational waves, like light, can be gravitationally lensed by massive astrophysical objects such as galaxies and galaxy clusters. Strong gravitational-wave lensing, forecasted at a reasonable rate in ground-based gravitational-wave detectors such as Advanced LIGO, Advanced Virgo, and KAGRA, produces multiple images separated in time by minutes to months. These images appear as repeated events in the detectors: gravitational-wave pairs, triplets, or quadruplets with identical frequency evolution originating from the same sky location. To search for these images, we need to, in principle, an…
A tiny fraction of observed gamma-ray bursts (GRBs) may be lensed. The time delays induced by the gravitational lensing are milliseconds to seconds if the point lenses are intermediate-mass black holes. The prompt emission of the lensed GRBs, in principle, should have repeated pulses with identical light curves and spectra but different fluxes and slightly offset positions. In this work, we search for such candidates within the GRBs detected by Fermi/GBM, Swift/BAT, and HXMT/HE and report the identification of an attractive event GRB 200716C that consists of two pulses. Both the autocorrelatio…
Gravitational-wave (GW) observations by a network of ground-based laser interferometric detectors allow us to probe the nature of GW polarizations. This would be an interesting test of general relativity (GR), since GR predicts only two polarization modes while there are theories of gravity that predict up to six polarization modes. The ability of GW observations to probe the nature of polarizations is limited by the available number of linearly independent detectors in the network. (To extract all polarization modes, there should be at least as many detectors as the polarization modes.) Stron…
The current gravitational-wave localization methods rely mainly on sources with electromagnetic counterparts. Unfortunately, a binary black hole does not emit light. Due to this, it is generally not possible to localize these objects precisely. However, strongly lensed gravitational waves, which are forecasted in this decade, could allow us to localize the binary by locating its lensed host galaxy. Identifying the correct host galaxy is challenging because there are hundreds to thousands of other lensed galaxies within the sky area spanned by the gravitational-wave observation. However, we can…
Recently, the LIGO-Virgo Collaboration (LVC) concluded that there is no evidence for lensed gravitational waves (GW) in the first half of the O3 run, claiming "We find the observation of lensed events to be unlikely, with the fractional rate at $μ>2$ being $3.3\times 10^{-4}$". While we agree that the chance of an individual GW event being lensed at $μ>2$ is smaller than $10^{-3}$, the number of observed events depends on the product of this small probability times the rate of mergers at high redshift. Observational constraints from the stochastic GW background indicate that the rate of conven…
The Proper Motion of Strongly Lensed Binary Neutron Star Mergers in LIGO/Virgo/Kagra can be Constrained by Measuring Doppler Induced Gravitational Wave Dephasing
Accelerated inference of microlensed gravitational waves with machine learning
Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；School of Mathematical Sciences, University of Nottingham（诺丁汉大学数学科学学院）
