Abstract
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.
Abstract
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.
Abstract
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.
Detectability of microlensed gravitational waves Yeung, Simon M C; Cheung, Mark H Y; Seo, Eungwang ...
Monthly notices of the Royal Astronomical Society,
09/2023, Volume:
526, Issue:
2
Journal Article
Peer reviewed
ABSTRACT
Gravitational lensing describes the bending of the trajectories of light and gravitational waves due to the gravitational potential of a massive object. Strong lensing by galaxies can create ...multiple images with different overall amplifications, arrival times, and image types. If, furthermore, the gravitational wave encounters a star along its trajectory, microlensing will take place. Previously, it has been shown that the effects of microlenses on strongly-lensed type-I images could be negligible in practice, at least in the low magnification regime. In this work, we study the same effect on type-II strongly-lensed images by computing the microlensing amplification factor. As opposed to being magnified, type-II images are typically demagnified. Moreover, microlensing on top of type-II images induces larger mismatches with un-microlensed waveforms than type-I images. These results are broadly consistent with recent literature and serve to confirm the findings. In addition, we investigate the possibility of detecting and analysing microlensed signals through Bayesian parameter estimation with an isolated point mass lens template, which has been adopted in recent parameter estimation literature. In particular, we simulate gravitational waves microlensed by a microlens embedded in a galaxy potential near moderately magnified type-I and II macroimages, with variable lens masses, source parameters and macromagnifcations. Generally, an isolated point mass model could be used as an effective template to detect a type-II microlensed image but not for type-I images, demonstrating the necessity for more realistic microlensing search templates.
Abstract
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 ∼100–10
4
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 10
6
Mpc
−3
within a factor of 10, or place an upper bound of ≲10
4
Mpc
−3
if the true number density is 10
3
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.
The luminosity distance is a key observable of gravitational-wave (GW) observations. We demonstrate how one can correctly retrieve the luminosity distance of compact binary coalescences (CBCs) if the ...GW signal is strongly lensed. We perform a proof-of-concept parameter estimation for the luminosity distance supposing (i) strong lensing produces two lensed GW signals emitted from a CBC, (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 the same source. Taking into account the maximum magnification allowed in two lensing scenarios and simulated GW signals emitted from four different binary black holes, we find that the strong lensing can improve the precision of the distance estimation of a CBC by up to a factor of a few compared to that can be expected without lensing.
Gravitational waves (GWs) can be deflected, similarly to electromagnetic (EM) waves, by massive objects through the phenomenon of gravitational lensing. The importance of gravitational 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. Analysing 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 non-axially symmetric lens models. Combinations of GW and EM observations can further improve the inference of the lens parameters.
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.
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. In our work, we propose a new method for probing lens populations through lensing statistics of gravitational waves, here focusing on inferring the number density of intermediate mass black holes. Using hierarchical Bayesian inference of injected lensed gravitational waves, we find that existing gravitational wave observatories at design sensitivity could either identify an injected number density of \(10^6 \mathrm{Mpc}^{-3}\) or place an upper bound of \(\lesssim 10^4 \mathrm{Mpc}^{-3}\) for an injected \(10^3 \mathrm{Mpc}^{-3}\). More broadly, our method could be applied to probe other forms of compact matter as well.
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