Gravitational lensing aided luminosity distance estimation for compact binary coalescences

The luminosity distance is a key observable of gravitational-wave observations. We demonstrate how one can correctly retrieve the luminosity distance of compact binary coalescences if the gravitational-wave signal is strongly lensed. We perform a proof-of-concept parameter estimation for the luminosity distance supposing (i) strong lensing produces two lensed gravitational-wave signals, (ii) the advanced LIGO-Virgo network detects both lensed signals as independent events, and (iii) the two events are identified as strongly lensed signals originated from a single compact binary coalescence. Focusing on the maximum magnification allowed in the given lensing scenario, we find that the strong lensing can improve the precision of the distance estimation by up to a factor of two compared to that can be expected for the signal experiencing no lensing. Our results imply that strong lensing of gravitational waves can be helpful for better constraining the distance to the source, and furthermore, the Hubble constant.Comment: 7 pages, 4 figures, 2 table

Improving Detection of Gravitational wave Microlensing Using Repeated Signals Induced by Strong Lensing

Microlensing imprints by typical stellar mass lenses on gravitational waves are challenging to identify in the LIGO and Virgo frequency band because such effects are weak. However, stellar mass lenses are generally embedded in lens galaxies such that strong lensing accompanies microlensing. Therefore, events that are strongly lensed in addition to being microlensed may significantly improve the inference of the latter. We present a proof of principle demonstration of how one can use parameter estimation results from one strongly lensed signal to enhance the inference of the microlensing effects of the other signal with the Bayesian inference method currently used in gravitational wave astronomy. We expect this to significantly enhance our future ability to detect the weak imprints from stellar mass objects on gravitational-wave signals from colliding compact objects.Comment: 8 pages, 5 figures, presented at TAUP 202

Inferring properties of dark galactic halos using strongly lensed gravitational waves

Gravitational waves (GWs) can be deflected, similarly to electromagnetic (EM) waves, by massive objects through the phenomenon of gravitational lensing. The importance of GW lensing for GW astronomy is becoming increasingly apparent in the GW detection era, in which nearly 100 events have already been detected. As current ground-based interferometers reach their design sensitivities, it is anticipated that these detectors may observe a few GW signals that are strongly lensed by the dark halos of intervening galaxies or galaxy clusters. Analyzing the strong lensing effects on GW signals is, thus, becoming important to understand the lens' properties and correctly infer the intrinsic GW source parameters. However, one cannot accurately infer lens parameters for complex lens models with only GW observations because there are strong degeneracies between the parameters of lensed waveforms. In this paper, we discuss how to conduct parameter estimation of strongly lensed GW signals and infer the lens parameters using additional EM information, including the lens galaxy's axis ratio and the GW source-hosting galaxy's lensed images. We find that for simple spherically symmetric lens models, the lens parameters can be well recovered using only GW information. On the other hand, recovering the lens parameters requires systems in which four or more GW images are detected with additional EM observations for nonaxially symmetric lens models. Combinations of GW and EM observations can further improve the inference of the lens parameters

Improving detection of gravitational-wave microlensing using repeated signals induced by strong lensing

Microlensing imprints by typical stellar-mass lenses on gravitational waves are challenging to identify in the LIGO–Virgo frequency band because such effects are weak. However, stellar-mass lenses are generally embedded in lens galaxies such that strong lensing accompanies microlensing. Therefore, events that are strongly lensed in addition to being microlensed may significantly improve the inference of the latter. We present a proof-of-principle demonstration of how one can use parameter estimation results from one strongly lensed signal to enhance the inference of the microlensing effects of the other signal with the Bayesian inference method currently used in gravitational-wave astronomy. We expect this to significantly enhance our future ability to detect the weak imprints from stellar-mass objects on gravitational-wave signals from colliding compact objects

On the identification of individual gravitational-wave image types of a lensed system using higher-order modes

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 analyze 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 identification of individual image types for the observed gravitational-wave events when two lensed images are detected, which would lead to unambiguous confirmation of lensing. In addition, we show that higher-order mode content can be analyzed more accurately with strongly lensed gravitational-wave events

Inferring the intermediate-mass black hole number density from gravitational-wave lensing statistics

The population properties of intermediate-mass black holes remain largely unknown, and understanding their distribution could provide a missing link in the formation of supermassive black holes and galaxies. Gravitational-wave observations can help fill in the gap from stellar mass black holes to supermassive black holes with masses between ∼100–104 M⊙. In our work, we propose a new method for examining lens populations through lensing statistics of gravitational waves, here focusing on inferring the number density of intermediate-mass black holes through hierarchical Bayesian inference. Simulating ∼200 lensed gravitational-wave signals, we find that existing gravitational-wave observatories at their design sensitivity could either constrain the number density of 106 Mpc−3 within a factor of 10, or place an upper bound of ≲104 Mpc−3 if the true number density is 103 Mpc−3. More broadly, our method leaves room for incorporation of additional lens populations, providing a general framework for probing the population properties of lenses in the universe

Follow-up analyses to the O3 LIGO-Virgo-KAGRA lensing searches

Along their path from source to observer, gravitational waves may be gravitationally lensed by massive objects. This results in distortions of the observed signal which can be used to extract new information about fundamental physics, astrophysics, and cosmology. Searches for these distortions amongst the observed signals from the current detector network have already been carried out, though there have as yet been no confident detections. However, predictions of the observation rate of lensing suggest detection in the future is a realistic possibility. Therefore, preparations need to be made to thoroughly investigate the candidate lensed signals. In this work, we present some of the follow-up analyses and strategies that could be applied to assess the significance of such events and ascertain what information may be extracted about the lens-source system from such candidate signals by applying them to a number of O3 candidate events, even if these signals did not yield a high significance for any of the lensing hypotheses. For strongly-lensed candidates, we verify their significance using a background of simulated unlensed events and statistics computed from lensing catalogs. We also look for potential electromagnetic counterparts. In addition, we analyse in detail a candidate for a strongly-lensed sub-threshold counterpart that is identified by a new method. For microlensing candidates, we perform model selection using a number of lens models to investigate our ability to determine the mass density profile of the lens and constrain the lens parameters. We also look for millilensing signatures in one of the lensed candidates. Applying these additional analyses does not lead to any additional evidence for lensing in the candidates that have been examined. However, it does provide important insight into potential avenues to deal with high-significance candidates in future observations.Comment: 34 pages, 27 figure

Follow-up analyses to the O3 LIGO–Virgo–KAGRA lensing searches

Along their path from source to observer, gravitational waves may be gravitationally lensed by massive objects leading to distortion in the signals. Searches for these distortions amongst the observed signals from the current detector network have already been carried out, though there have as yet been no confident detections. However, predictions of the observation rate of lensing suggest detection in the future is a realistic possibility. Therefore, preparations need to be made to thoroughly investigate the candidate lensed signals. In this work, we present some follow-up analyses that could be applied to assess the significance of such events and ascertain what information may be extracted about the lens-source system by applying these analyses to a number of O3 candidate events, even if these signals did not yield a high significance for any of the lensing hypotheses. These analyses cover the strong lensing, millilensing, and microlensing regimes. Applying these additional analyses does not lead to any additional evidence for lensing in the candidates that have been examined. However, it does provide important insight into potential avenues to deal with high-significance candidates in future observations

Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass M>70 M⊙) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities 0<e≤0.3 at 0.33 Gpc−3 yr−1 at 90\% confidence level