Motivated by the preponderance of so-called "heavy black holes" in the binary black hole (BBH) gravitational wave (GW) detections to date, and the role that gravitational lensing continues to play in discovering new galaxy populations, we explore the possibility that the GWs are strongly-lensed by massive galaxy clusters. For example, if one of the GW sources were actually located at $z=1$, then the rest-frame mass of the associated BHs would be reduced by a factor $\sim2$. Based on the known populations of BBH GW sources and strong-lensing clusters, we estimate a conservative lower limit on the number of BBH mergers detected per detector year at LIGO/Virgo's current sensitivity that are multiply-imaged, of $R_{\rm detect}\simeq10^{-5}{\rm yr}^{-1}$. This is equivalent to rejecting the hypothesis that one of the BBH GWs detected to date was multiply-imaged at $<\sim4σ$. It is therefore unlikely but not impossible that one of the GWs is multiply-imaged. We identify three spectroscopically confirmed strong-lensing clusters with well constrained mass models within the $90\%$ credible sky localisations of the BBH GWs from LIGO's first observing run. In the event that one of these clusters multiply-imaged one of the BBH GWs, we predict that $20-60\%$ of the putative next appearances of the GWs would be detectable by LIGO, and that they would arrive at Earth within three years of first detection.
We search for gravitational wave (GW) events from LIGO-Virgo's third run that may have been affected by gravitational lensing. Gravitational lensing delays the arrival of GWs, and alters their amplitude -- thus biasing the inferred progenitor masses. This would provide a physically well-understood interpretation of GW detections in the ''mass gap'' between neutron stars and black holes, as gravitationally lensed binary neutron star (BNS) mergers. We selected three GW detections in LIGO-Virgo's third run for which the probability of at least one of the constituent compact objects being in the m…
Microlenses with typical stellar masses (a few ${\rm M}_{\odot}$) have traditionally been disregarded as potential sources of gravitational lensing effects at LIGO/Virgo frequencies, since the time delays are often much smaller than the inverse of the frequencies probed by LIGO/Virgo, resulting in negligible interference effects at LIGO/Virgo frequencies. While this is true for isolated microlenses in this mass regime, we show how, under certain circumstances and for realistic scenarios, a population of microlenses (for instance stars and remnants from a galaxy halo or from the intracluster me…
The Proper Motion of Strongly Lensed Binary Neutron Star Mergers in LIGO/Virgo/Kagra can be Constrained by Measuring Doppler Induced Gravitational Wave Dephasing
Strong gravitational lensing can produce multiple images of the same gravitational-wave signal, each arriving at different times and with different magnification. Previous work has explored if lensed pairs exist among the known high-significance events and found no evidence of this. However, the possibility remains that weaker counterparts of these events are present in the data, unrecovered by previous searches. We conduct a targeted search specifically looking for sub-threshold lensed images of known binary black hole (BBH) observations. We recover candidates matching three of the additional…
Strong lensing of gravitational waves is more likely for distant sources but predicted event rates are highly uncertain with many astrophysical origins proposed. Here we open a new avenue to estimate the event rate of strongly lensed systems by exploring the amplitude of the stochastic gravitational wave background (SGWB). This method can provide a direct upper bound on the high redshift binary coalescing rates, which can be translated into an upper bound on the expected rate of strongly lensed systems. We show that from the ongoing analysis of the Laser Interferometer Gravitational-wave Obser…
Gravitational lensing allows the detection of binary black holes (BBH) at cosmological distances with chirp masses that appear to be enhanced by $1+z$ in the range $1<z<4$, in good agreement with the reported BBH masses. We propose this effect also accounts for the puzzling "mass gap" events (MG) newly reported by LIGO/Virgo, as distant, lensed NSBH events with $1<z<4$. The fitted mass of the neutron star member becomes $(1+z)\times 1.4M_\odot$, and is therefore misclassified as a low mass black hole. In this way, we derive a redshift of $z\simeq 3.5$ and $z\simeq 1.0$ for two newly reported "…
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…
Advanced LIGO and Advanced Virgo could observe the first lensed gravitational waves in the coming years, while the future Einstein Telescope could observe hundreds of lensed events. Ground-based gravitational-wave detectors can resolve arrival time differences of the order of the inverse of the observed frequencies. As LIGO/Virgo frequency band spans from a few $\rm Hz$ to a few $ \rm kHz$, the typical time resolution of current interferometers is of the order of milliseconds. When microlenses are embedded in galaxies or galaxy clusters, lensing can become more prominent and result in observab…
We study gravitational lensing of gravitational waves from compact object binaries as a probe of compact dark matter (DM) objects such as primordial black holes. Assuming a point mass lens, we perform parameter estimation of lensed gravitational wave signals from compact object binaries to determine the detectability of the lens with ground based laser interferometers. Then, considering binary populations that LIGO-Virgo has been probing, we derive a constraint on the abundance of compact DM from non-observation of lensed events. We find that the LIGO-Virgo observations imply that compact obje…
Time-Domain Deep Learning for Pairwise Identification of Strongly Lensed Gravitational-Wave Candidates
Zhejiang University（浙江大学）；Massachusetts Institute of Technology（麻省理工学院）；Wuhan University（武汉大学）；Jiangsu Sungo Intelligent Technology Research Center Co., Ltd.（江苏舜智智能科技有限公司）；Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所）
Advanced LIGO and Advanced Virgo could observe the first lensed gravitational wave sources in the coming years, while the future Einstein Telescope could observe hundreds of lensed events. It is, therefore, crucial to develop methodologies to distinguish between lensed from unlensed gravitational-wave observations. A lensed signal not identified as such will lead to biases during the interpretation of the source. In particular, sources will appear to have intrinsically higher masses. No robust method currently exists to distinguish between the magnification bias caused by lensing and intrinsic…
Similarly to light, gravitational waves can be gravitationally lensed as they propagate near massive astrophysical objects such as galaxies, stars, or black holes. In recent years, forecasts have suggested a reasonable chance of strong gravitational-wave lensing detections with the LIGO-Virgo-KAGRA detector network at design sensitivity. As a consequence, methods to analyse lensed detections have seen rapid development. However, the impact of higher-order modes on the lensing analyses is still under investigation. In this work, we show that the presence of higher-order modes enables the identi…
The expected event rate of lensed gravitational wave sources scales with the merger rate at redshift $z\geq 1$, where the optical depth for lensing is high. It is commonly assumed that the merger rate of the astrophysical compact objects is closely connected with the star formation rate, which peaks around redshift $z\sim 2$. However, a major source of uncertainty is the delay time between the formation and merger of compact objects. We explore the impact of delay time on the lensing event rate. We show that as the delay time increases, the peak of the merger rate of gravitational wave sources…
We study the prospects of detecting continuous gravitational waves (CGWs) from spinning neutron stars (NSs), gravitationally lensed by the galactic supermassive black hole. Assuming various astrophysically motivated spatial distributions of galactic NSs, we find that CGW signals from a few ($\sim 0-6$) neutron stars should be strongly lensed. Lensing will produce two copies of the signal (with time delays of seconds to minutes) that will interfere with each other. The relative motion of the NS with respect to the lensing optical axis will change the interference pattern, which will help us to …
When gravitational waves pass near massive astrophysical objects, they can be gravitationally lensed. The lensing can split them into multiple wave-fronts, magnify them, or imprint beating patterns on the waves. Here we focus on the multiple images produced by strong lensing. In particular, we investigate strong lensing forecasts, the rate of lensing, and the role of lensing statistics in strong lensing searches. Overall, we find a reasonable rate of lensed detections for double, triple, and quadruple images at the LIGO--Virgo--KAGRA design sensitivity. We also report the rates for A+ and LIGO…
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…
Associating binary black holes with galactic centres using lensed gravitational waves
The Chinese University of Hong Kong（香港中文大学）；Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）；University of Portsmouth（朴茨茅斯大学）；Royal Observatory of Belgium（比利时皇家天文台）
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…
We search for strongly lensed and multiply imaged gravitational wave signals in the second observing run of Advanced LIGO and Advanced Virgo (O2). We exploit a new source of information, the so-called Morse phase, which further mitigates the search background and constrains viable lenses. The best candidate we find is consistent with a strongly lensed signal from a massive binary black hole (BBH) merger, with three detected images consisting of the previously catalogued events GW170104 and GW170814, and a subthreshold trigger, GWC170620. Given the number of BBH events detected so far, we estim…
The Chinese University of Hong Kong（香港中文大学）；The Inter-University Centre for Astronomy and Astrophysics (IUCAA)（天文学与天体物理学大学间中心）；Kavli Institute for the Physics and Mathematics of the Universe (IPMU)（宇宙物理与数学系卡尔费利研究所）；Utrecht University（乌得勒支大学）；Nikhef – National Institute for Subatomic Physics（荷兰亚原子物理国家研究所）；Pennsylvania State University（宾夕法尼亚州立大学）；Universit'e Catholique de Louvain（天主教鲁汶大学）；Royal Observatory of Belgium（比利时皇家天文台）；Universitat de les Illes Balears（巴利阿里群岛大学）
We present observations of two strong-lensing galaxy clusters located within the $90$ per cent credible sky localization maps released following LIGO-Virgo's discovery of the binary black hole (BH-BH) gravitational wave (GW) source GW170814. Our objectives were (1) to search for candidate electromagnetic (EM) counterparts to GW170814 under the hypothesis that it was strongly-lensed, and thus more distant and less massive than inferred by LIGO-Virgo, and (2) to demonstrate the feasibility of rapid target of opportunity observations to search for faint lensed transient point sources in crowded c…
LSST's wide-field of view and sensitivity will revolutionize studies of the transient sky by finding extraordinary numbers of new transients every night. The recent discovery of a kilonova counterpart to LIGO/Virgo's first detection of gravitational waves (GWs) from a double neutron star (NS-NS) merger also creates an exciting opportunity for LSST to offer a Target of Opportunity (ToO) mode of observing. We have been exploring the possibility of detecting strongly lensed GWs, that would enable new tests of GR, extend multi-messenger astronomy out to $z\gtrsim1$, and deliver a new class of sub-…
Pre-merger gravitational-wave (GW) sky-localisation of binary neutron star (BNS) and neutron star black hole (NSBH) coalescence events, would enable telescopes to capture precursors and electromagnetic (EM) emissions around the time of the merger. We propose a novel astrophysical scenario that could provide early-warning times of hours to days before coalescence with sub-arcsecond localisation, provided that these events are gravitationally lensed. The key idea is that if the BNS/NSBH is lensed, then so must the host galaxy identified via the EM counterpart. From the angular separation of the …
It is commonly assumed that ground-based gravitational wave (GW) instruments will not be sensitive to supermassive black holes (SMBHs) because the characteristic GW frequencies are far below the ~ 10 - 1000 Hz sensitivity bands of terrestrial detectors. Here, however, we explore the possibility of SMBH gravitational waves to leak to higher frequencies. In particular, if the high frequency spectral tail asymptotes to h(f) ~ f^{-alpha}, where alpha<=2, then the spectral amplitude is a constant or increasing function of the mass M at a fixed frequency f>>c^3/GM. This will happen if the time domai…
We analyze the event GW 150914 announced by the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) as the gravitational-wave emission of a black-hole binary merger. We show that the parameters of the coalescing system and of the newly formed Kerr black-hole can be extracted from basic results of the gravitational-wave emission during the inspiraling and merger phases without sophisticated numerical simulations. Our strikingly accurate estimates are based on textbook formulas describing two different regimes: 1) the binary inspiraling analysis treated in Landau and Lifshitz tex…
What is the nature of GW230529? An exploration of the gravitational lensing hypothesis
Université Catholique de Louvain（天主教鲁汶大学）；Royal Observatory of Belgium（比利时皇家天文台）；Utrecht University（乌得勒支大学）；Nikhef（尼赫夫国家粒子物理研究所）；Universitat de les Illes Balears（巴利阿里群岛大学）；University of Portsmouth（朴茨茅斯大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）；The Chinese University of Hong Kong（香港中文大学）；California Institute of Technology（加州理工学院）；The University of Tokyo（东京大学）
When gravitational waves pass through the nuclear star clusters of galactic lenses, they may be microlensed by the stars. Such microlensing can cause potentially observable beating patterns on the waveform due to waveform superposition and magnify the signal. On the one hand, the beating patterns and magnification could lead to the first detection of a microlensed gravitational wave. On the other hand, microlensing introduces a systematic error in strong lensing use-cases, such as localization and cosmography studies. We show that diffraction effects are important when we consider GWs in the L…
In a recent letter we have outlined some issues on GW 150914, we hereby give additional details. We analyze the event GW 150914 announced by the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) as the gravitational-wave emission of a black-hole binary merger. We show that the parameters of the coalescing system and of the newly formed Kerr black-hole can be extracted from basic results of the gravitational-wave emission during the inspiraling and merger phases without sophisticate numerical simulations. Our strikingly accurate estimates are based on textbook formulas describ…
Primordial black holes (PBHs) have been proposed to explain at least a portion of dark matter. Observations have put strong constraints on PBHs in terms of the fraction of dark matter which they can represent, $f_{\rm PBH}$, across a wide mass range -- apart from the stellar-mass range of $20M_\odot\lesssim M_{\rm PBH}\lesssim 100M_\odot$. In this paper, we explore the possibility that such PBHs could serve as point-mass lenses capable of altering the gravitational-wave (GW) signals observed from binary black hole (BBH) mergers along their line-of-sight. We find that careful GW data analysis c…
Our understanding of the formation and evolution of binary black holes (BBHs) is significantly impacted by the recent discoveries made by the LIGO/Virgo collaboration. Of utmost importance is the detection of the most massive BBH system, GW190521. Here we investigate what it takes for field massive stellar binaries to account for the formation of such massive BBHs. Whether the high mass end of the BH mass function is populated by remnants of massive stars that either formed at extremely low metallicities and avoid the pair-instability mass gap or increase their birth mass beyond the pair-insta…
The light from distant supernovae (SNe) can be magnified through gravitational lensing when a foreground galaxy is located along the line of sight. This line-up allows for detailed studies of SNe at high redshift that otherwise would not be possible. Spectroscopic observations of lensed high-redshift Type Ia supernovae (SNe Ia) are of particular interest since they can be used to test for evolution of their intrinsic properties. The use of SNe Ia for probing the cosmic expansion history has proven to be an extremely powerful method for measuring cosmological parameters. However, if systematic …
Gravitational wave (GW) transients from binary neutron star (BNS) coalescences can, in principle, be subject to gravitational lensing thereby increasing the amplitude and signal-to-noise ratio. We estimate the rate of lensed BNS events resolvable by LIGO and Virgo and find that it is constrained by the current non-detection of a stochastic GW background. Following closely the formalism we developed (10.1103/PhysRevLett.125.141102) in the context of binary black hole lensing, we show that at current sensitivities the fraction of BNS coalescences with lensing magnifications $μ> 1.02$ is less tha…
Several past searches for gravitational waves from a selection of known pulsars have been performed with data from the science runs of the Laser Inferometer Gravitational-wave Observatory (LIGO) gravitational wave detectors. So far these have lead to no detection, but upper limits on the gravitational wave amplitudes have been set. Here we study our intrinsic ability to detect, and estimate the gravitational wave amplitude for non-accreting pulsars. Using spin-down limits on emission as a guide we examine amplitudes that would be required to observe known pulsars with future detectors (Advance…
Joint population and strong-lensing inference for resolved gravitational-wave events probes the black-hole merger rate beyond the peak of star formation
Nottingham Centre of Gravity & School of Mathematical Sciences, University of Nottingham（诺丁汉大学引力中心与数学科学学院）
Gravitational waves from binary black holes have the potential to yield information on both of the intrinsic parameters that characterize the compact objects: their masses and spins. While the component masses are usually resolvable, the component spins have proven difficult to measure. This limitation stems in great part from our choice to inquire about the spins of the most and least massive objects in each binary, a question that becomes ill-defined when the masses are equal. In this paper we show that one can ask a different question of the data: what are the spins of the objects with the …
We present a thorough observational investigation of the heuristic quantised ringdown model presented in Foit & Kleban (2019). This model is based on the Bekenstein-Mukhanov conjecture, stating that the area of a black hole horizon is an integer multiple of the Planck area $l_P^2$ multiplied by a phenomenological constant, $α$, which can be viewed as an additional black hole intrinsic parameter. Our approach is based on a time-domain analysis of the gravitational wave signals produced by the ringdown phase of binary black hole mergers detected by the LIGO and Virgo collaboration. Employing a f…
LIGO's detection of gravitational waves from binary black hole mergers was an unexpected surprise that immediately raised the question - what is the origin of these black hole binaries? The "simplest" scenario is evolution of field massive stellar binaries. However, other possibilities involving capture have been proposed. We explore here one of the more interesting clues on this puzzle: the relatively modest spins of the resulting black holes that imply that the progenitor black holes were not spinning rapidly. More specifically we consider the implication of observed distribution of, $χ_{\rm…
In August 2017, the first detection of a binary neutron star merger, GW170817, made it possible to study neutron stars in compact binary systems using gravitational waves. Despite being the loudest gravitational wave event detected to date (in terms of signal-to-noise ratio), it was not possible to unequivocally determine that GW170817 was caused by the merger of two neutron stars instead of two black holes from the gravitational-wave data alone. That distinction was primarily due to the accompanying electromagnetic counterpart. This raises the question: under what circumstances can gravitatio…
Strong gravitational lensing of gravitational wave sources offers a novel probe of both the lens galaxy and the binary source population. In particular, the strong lensing event rate and the time delay distribution of multiply-imaged gravitational-wave binary coalescence events can be used to constrain the mass distribution of the lenses as well as the intrinsic properties of the source population. We calculate the strong lensing event rate for a range of second (2G) and third generation (3G) detectors, including Advanced LIGO/Virgo, A+, Einstein Telescope (ET), and Cosmic Explorer (CE). For 3…
Gravitational wave science should transform in this decade from a study of what has not been seen to a full-fledged field of astronomy in which detected signals reveal the nature of cataclysmic events and exotic objects. The LIGO Scientific Collaboration and Virgo Collaboration have recently completed joint data runs of unprecedented sensitivities to gravitational waves. So far, no gravitational radiation has been seen (although data mining continues). It seems likely that the first detection will come from 2nd-generation LIGO and Virgo interferometers now being installed. These new detectors …
The recent announcement of the detection of gravitational waves by the LIGO/Virgo collaboration has opened a new window to test the nature of astrophysical black holes. Konoplya & Zhidenko have shown how the LIGO data of GW 150914 can constrain possible deviations from the Kerr metric. In this letter, we compare their constraints with those that can be obtained from accreting black holes by fitting their reflected X-ray spectrum, the so-called iron line method. We simulate observations with eXTP, a next generation X-ray mission, finding constraints much stronger than those obtained by Konoplya…
