Gravitational lensing is a phenomenon where intervening objects bend and magnify light, first predicted by Einstein’s theory of general relativity in 1915. However, it wasn’t until the 1970s that the first observational evidence of gravitational lensing was discovered. Since then, scientists have made great strides in studying this phenomenon, which provides a unique way to study the distribution of matter in the universe.

In recent years, gravitational-wave lensing has become an area of intense interest. Gravitational-wave astronomy is a rapidly advancing field that allows us to study the cosmos by observing ripples in spacetime caused by massive objects. Gravitational waves were first detected in 2015 by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and have since opened up a new window to observe the universe.

Our CUHK gravitational-wave team, with Anna Liu, a PhD student at the Chinese University of Hong Kong, as the leading author, recently published a research article titled “Exploring the hidden Universe: A novel phenomenological approach for recovering arbitrary gravitational-wave millilensing configurations.” The article presents a new approach to study millilensing, a specific form of gravitational lensing that can split a gravitational wave signal into multiple copies.

The approach offers a more accurate and efficient tool for studying the distribution of matter in the universe using gravitational-wave signals. Current models for gravitational-wave millilensing are limited and cannot account for complex lensing scenarios. The approach is model-independent, meaning it can recover arbitrary lens configurations without the need for extensive computational modeling. It is also computationally efficient, making it suitable for large-scale studies.

The proposed approach has potential applications for studying complex lens configurations, such as dark matter subhalos and MACHOs. With gravitational-wave lensing observations becoming more feasible, this new method can provide a powerful tool for studying the distribution of matter in the universe and testing our understanding of gravity.

In conclusion, Anna Liu and our CUHK gravitational-wave team have developed a new approach for studying millilensing, a specific form of gravitational lensing that can split a gravitational wave signal into multiple copies. With this novel phenomenological approach, we can study complex lens configurations and potentially unlock new insights into the distribution of matter in the universe, including dark matter subhalos and MACHOs. This research builds upon the legacy of Einstein and we hope it will open up new possibilities for gravitational-wave astronomy. We are excited to see the future applications of this approach, as it might help uncover and the impact it will have on our understanding of the universe.

The research is now published in the Monthly Notices of Royal Astronomical Society (MNRAS)
Link: https://doi.org/10.1093/mnras/stad1302

Title: Lensing or luck? False alarm probabilities for gravitational lensing of gravitational waves
Link: https://arxiv.org/abs/2201.04619 (accepted to MNRAS)

Gravitational lensing is a fascinating phenomenon in which light from a distant object is bent and magnified by the gravity of an intervening massive object, allowing us to study objects that would otherwise be too faint or too distant to observe. This effect was first predicted by Albert Einstein’s theory of general relativity in 1915, and was famously confirmed during the solar eclipse of 1919 by the British astrophysicist Arthur Eddington (see Figure above).

Fast forward to today, and we’re now able to study gravitational lensing in a new way: using gravitational waves. These ripples in the fabric of spacetime are generated by some of the most energetic events in the universe, such as the merger of two black holes or neutron stars. As gravitational waves travel through space, they can be bent and distorted by massive objects just like light, creating a gravitational lensing effect that can magnify or even multiply the signal we receive on Earth.

However, as we report in our recently accepted publication in the Physical Review D, distinguishing genuine lensing events from chance coincidences can be a difficult task. The problem is that the parameters of a genuine lensed event – such as its chirp mass, sky location, and coalescence phase – can overlap with those of an unrelated event, making it difficult to tell them apart.

To investigate this issue, we constructed a mock catalog of lensed and unlensed gravitational wave events and calculated the false alarm probability (FAP) based on coincidental overlaps of the parameters. We found that the FAP based on chirp mass, sky location, and coalescence phase are approximately 9%, 1%, and 10% per pair, respectively. Combining all three, the overall FAP per pair is around one part in 10 thousand. This means that for sufficiently high numbers of events in the gravitational wave catalogs, false alarms will always dominate over the true lensing events.

To combat this problem, we proposed alternative identification criteria that go beyond simple waveform and sky location overlap. We also explored the possibility of using statistical modelling of strong lenses to help distinguish genuine lensing events from false alarms.

Our study, led by Mesut Çalışkan, a PhD student from Johns Hopkins, highlights the challenges of detecting and characterizing gravitational lensing of gravitational waves. But it also provides a roadmap for developing more sophisticated methods of identifying and studying these rare events. By improving our ability to detect and study gravitational lensing, we can unlock new insights into the nature of the universe and the physics of gravity itself.

Could any of the gravitational wave signals observed in the LVC observing run O3a be lensed by massive astrophysical objects, such as galaxies, galaxy clusters, black holes, or stars?

Like electromagnetic waves, gravitational waves can be gravitationally lensed. While the lensing of electromagnetic waves has had a rich observational history, we are still taking the first steps in the hunt for lensed gravitational waves. The theory behind light lensing and gravitational-wave lensing are similar, but the methodologies to detect these waves are entirely different — and so are the scientific goals.

If we observed lensed gravitational waves in practice, they would open the door to several exciting scientific pursuits. When the lens system is sufficiently unique, one could locate merging black holes, invisible to conventional telescopes, by combining gravitational-wave and electromagnetic lensing surveys. When an electromagnetic counterpart accompanies the lensed waves, precision cosmology studies may become feasible owing to the sub-millisecond lensing time-delay gravitational-wave measurements. By contrasting the time delays between lensed gravitational waves with their transient electromagnetic counterparts, one could measure the speed of gravity relative to light. As lensed gravitational waves allow us to observe the same event multiple times at different detector orientations, they can also probe the full polarization of the waves, testing general relativity and alternative theories. Microlensing, on the other hand, might help in studying populations of objects such as primordial and intermediate-mass black holes. Interestingly, the detection of lensed waves has been forecasted in the coming years by recent studies (e.g., ArXiv:2106.06303, ArXiv:2105.14390).

In a recent LVC study, we have looked for lensing signatures in the gravitational wave signals detected in the first half of the third LIGO-Virgo observing run.

Published in the Monthly Notices of Royal Astronomical Society.

Like electromagnetic waves, gravitational waves can be gravitationally lensed by intervening objects, such as stars, black holes, galaxies, and galaxy clusters. However, while the theory behind the lensing of gravitational waves is similar to that of light lensing, the methods to detect it are entirely different due to fundamentally different sources and detectors. In particular, we may detect lensing magnification as an overall amplification of the waves. This magnification would cause binary merger signals to appear as coming from closer and higher-mass sources than they really do. Multiple images would appear as “repeated” events: near-identical events appearing minutes to months (or sometimes years) apart. As the lens will typically produce image separations that are far too tiny to be resolved with the current detectors, the events appear to come from the same sky location.

If smaller objects such as stars reside near the trajectory of the waves, microlensing occurs. The microlensing produces tiny lensing time delays, which can cause multiple lensed waveforms to overlap at the detectors and produce waveform “beating patterns.”

It is generally difficult to account for these beating patterns due to what we refer to as the wave optics effects. These effects are known to suppress microlensing (pointed out previously by, e.g., Oguri). This suppression limits our ability to detect microlenses in the low-mass limit. It is, in this sense, a hindrance for microlensing searches. On the other hand, the suppression can be seen as an advantage for the science case: If gravitational waves are unaffected by microlensing, they can offer a clean probe of strong lensing. 

Here we have studied the effect of microlensing on gravitational waves in the presence of strong lensing and discussed the scientific implications.

Link to paper

As the current ground-based gravitational-wave detectors are upgraded and more detectors come online, we expect to access new scientific avenues. One such avenue is observations of gravitational-wave lensing, with recent forecasts predicting detections in the coming years. Before the first detection, it is essential to investigate, outline, and build upon the various science cases of gravitational-wave lensing.

In recent work, we show that strong lensing could be used to localize merging black holes at high precision, even though they do not emit light.

Suppose a gravitational wave from a merging black hole is strongly lensed. In that case, the light from the galaxy that hosts the black holes is also lensed. Thus, if we point electromagnetic telescopes in this direction, the host galaxy would appear as a lensed galaxy.

Locating this lensed host galaxy allows us to localize merging black holes and study the lens system using electromagnetic and gravitational-wave channels.

In our study, we demonstrated the proof-of-principle for the method. Specifically, we demonstrated how to combine the image properties of lensed gravitational waves with electromagnetic galaxy lens searches to locate the host galaxy of merging black holes. Furthermore, we show that follow-up lens modeling allows us to locate where the merger occurred within the galaxy at a sub-arcsecond precision. Finally, we demonstrate a simple example application for the localization: Studying the expansion of the Universe at high redshift.

Besides the fundamental interest, this could plausibly enable several scientific pursuits such as cross-verification of lensing claims, measuring the cosmological expansion at high redshift, studying the binary black hole-host galaxy connection and binary formation channels, improved lens modeling, and improved tests of gravitational-wave polarization. It could also extend the current gravitational-wave lensing studies onto a multi-messenger playground.

Link to the paper

We discuss the prospects for constraining dark matter models with an EMRI-based dark matter spike measurement. In particular, many of the standard dark matter models predict the destruction or smoothening of the dark matter spike. That is, these dark matter models could not produce a dark matter spike detection through an EMRI.

We turn the problem around: Given that we have detected a dark matter spike through an EMRI measurement, can we constrain the common dark matter models?

As a proof-of-principle, we show that detection of even a single dark matter spike from the EMRIs will severely constrain several popular dark matter candidates, such as ultralight bosons, keV fermions, MeV–TeV self-annihilating dark matter, and sub-solar mass primordial black holes, as these candidates would flatten the spikes through various mechanisms.

Link to paper

In this work, we demonstrate a smoking-gun method to detect lensed gravitational waves from binary neutron stars through a measurement of their “tidal effects.”

When a gravitational wave is lensed, it can undergo magnification. Usually, identifying lensing magnification from gravitational waves is not possible because it only introduces an overall shift in the gravitational wave’s amplitude. Due to the change in the gravitational-wave amplitude, the binary neutron star will simply appear more massive than it truly is, but no unique lensing signature can be extracted from such a “mass bias.”

However, gravitational-wave measurements combined with the so-called equation-of-state of neutron stars allow us to estimate the binary neutron star mass from the gravitational waves in a “secondary way,” which would render feasible a robust check for the lensing magnification.

By measuring the tidal effects of binary neuron stars, we can perform Bayesian analysis to estimate the source-frame masses that are not subjected to the above “mass bias.” We show that if the two mass measurements disagree with each other, then we can conclude that the event must be lensed. Indeed, a “lensed” binary neutron star would resemble an apparently massive binary neutron star merger with the tidal effects of a lower mass binary neutron star.

Using the methodologies we present in this paper, we can test if future gravitational-wave observations of neutron star mergers are lensed. The method could likely be applied in Einstein Telescope or LISA based on the current best models for the binary neutron star and lens populations. We also perform the lensing test on the GW190425, a LIGO/Virgo detection of a gravitational wave from a massive binary neutron star merger, finding no evidence favoring the lensed hypothesis, consistent with the expectation.

Link to paper

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General relativity postulates that massive objects curve space and time. Gravitational lensing occurs when these objects distort or bend light curves. Similarly to light, gravitational waves can be gravitationally lensed.

However, unlike in lensing of light where one detects particles, in gravitational-wave lensing we detect waves. Consequently, methods to detect and utilize gravitational-wave lensing are entirely different from that of light and are being actively developed.

Specifically, when a pair of gravitational waves travel through a galaxy, the gravity of the galaxy curves the trajectories of the waves, focusing them toward us. As we observe the waves, they will have been amplified due to the focusing by lensing and will arrive at different times due to having traveled different trajectories at the same speed. However, unlike in light lensing, where one has to classify incoming photons as lensed by their angular direction (as no signal templates exist), we can classify gravitational waves as lensed by statistically distinguishing them as identical events using gravitational-wave templates and Bayesian analysis. Moreover, if there are substructures on the lensing path, the galaxy will amplify their lensing effects, resulting in wave diffraction and “beating patterns”. The patterns occur at characteristic lensing time-scale and could potentially be resolved to infer the properties of the structures in LIGO/Virgo/LISA if the events occur. Such wave diffraction does not take place in light lensing.

In our recent work, we investigate if there are signatures of gravitational-wave lensing within the LIGO/Virgo ground-based gravitational-wave detectors. In particular, we look for three effects: 1) evidence of lensing magnification in the individual signals due to galaxy lenses, 2) evidence of multiple images due to strong lensing by galaxies, 3) evidence of wave optics effects due to point-mass lenses.

We find no compelling evidence of any of these signatures in the observed gravitational wave signals in our work. However, as the sensitivities of gravitational wave detectors improve in the future, detecting lensed events is estimated to become likely (see 1,2,3).

Link to our work published in the Astrophysical Journal Letters

Published in Nature Astronomy Letters (2019). See also accompanied blog-post.

Astroparticle physics, a field that has boomed since the 2000s, aims to learn about elementary particles through astrophysical observations. One focus of this field has been the study of bosons in very light mass regime — an exciting area of research that has seen rapid developments with the improved understanding of the coupling between long quantum wavelength and astrophysical systems.

Extremely light particles will have long quantum wavelengths, allowing them to exhibit quantum behaviour on a large scale that would not be possible for typical, more massive particles. These particles could potentially solve — for example — the core-cusp problem of galaxies, where they could explain observed galactic cores (as opposed to theoretical cusps) due to quantum smoothening of their density on the scale of their wavelengths. Other interesting light boson candidates such as dilatons and moduli, and types of axion-like particles, could offer potential solutions to various problems in fundamental physics and cosmology.

The first common challenge in astroparticle physics involves finding sources that produce measurable particle signatures. The second challenge usually requires discriminating these signatures from other astrophysical sources (e.g., pulsars could mimic gamma-ray signatures from WIMPs). However, it would appear that ultralight bosons may be able to overcome both these challenge.

Indeed, if these light bosons exist, then they spin down rotating black holes of sizes roughly equivalent to their quantum wavelengths and create highly dense “clouds” of matter around them. This happens through a well-understood process called “superradiance.” The shape of these clouds is related to the now spun-down black hole geometry, enabling us to predict the cloud profile theoretically.

When a smaller compact object inspirals the cloud within the gravitational geometry of the host, it emits gravitational waves. These waves allow us to not only predict the profile by extension of recording the host geometry but also to measure it directly. By obtaining both a prediction and a direct measurement, we can test if the direct measurement matches its theoretical prediction. By doing so, we could obtain stringent evidence for the existence of these bosons, rule out other sources that could mimic the signal and measure the boson mass.

We illustrate the methodology for such a test through model-selection by mapping our system to three independent measurements of the ultralight boson mass. We also show that this type of measurement is possible using observations of extreme mass-ratio inspirals (EMRIs) by the forthcoming Laser Interferometer Space Antenna (LISA).

Link to full paper with details.