Localizing merging black holes with sub-arcsecond precision using gravitational-wave lensing

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 constrain the lensing galaxy's physical properties through both gravitational-wave and electromagnetic observations. We show that these simultaneous constraints allow one to localize quadruply lensed waves to one or at most a few galaxies with the LIGO/Virgo/Kagra network in typical scenarios. Once we identify the host, we can localize the binary to two sub-arcsec regions within the host galaxy. Moreover, we demonstrate how to use the system to measure the Hubble constant as a proof-of-principle application.Comment: 5 pages (main text) + 5 pages (methods+references), 5 figures. Accepted to MNRA

lensingGW: a Python package for lensing of gravitational waves

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 observable time delays at LIGO/Virgo frequencies. Therefore, gravitational waves could offer an exciting alternative probe of microlensing. However, currently, only a few lensing configurations have been worked out in the context of gravitational-wave lensing. In this paper, we present lensingGW, a Python package designed to handle both strong and microlensing of compact binaries and the related gravitational-wave signals. This synergy paves the way for systematic parameter space investigations and the detection of arbitrary lens configurations and compact sources. We demonstrate the working mechanism of lensingGW and its use to study microlenses embedded in galaxies.Comment: 11 pages, 10 figure

A fast and precise methodology to search for and analyse strongly lensed gravitational-wave events

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, analyze all viable combinations of individual events present in the gravitational-wave catalogs. An increasingly pressing problem is that the number of candidate pairs that we need to analyse grows rapidly with the increasing number of single-event detections. At design sensitivity, one may have as many as $\mathcal O(10^5)$ event pairs to consider. To meet the ever-increasing computational requirements, we develop a fast and precise Bayesian methodology to analyse strongly lensed event pairs, enabling future searches. The methodology works by replacing the prior used in the analysis of one strongly lensed gravitational-wave image by the posterior of another image; the computation is then further sped up by a pre-computed lookup table. We demonstrate how the methodology can be applied to any number of lensed images, enabling fast studies of strongly lensed quadruplets.Comment: 10 pages, 6 figure

Extreme Dark Matter Tests with Extreme Mass Ratio Inspirals

Future space-based laser interferometry experiments such as LISA are expected to detect $\cal O$(100--1000) stellar-mass compact objects (e.g., black holes, neutron stars) falling into massive black holes in the centers of galaxies, the so-called extreme-mass-ratio inspirals (EMRIs). If dark matter forms a "spike" due to the growth of the massive black hole, it will induce a gravitational drag on the inspiraling object, changing its orbit and gravitational-wave signal. 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. Future space gravitational wave experiments could thus have a significant impact on the particle identification of dark matter.Comment: 10 pages (main body: 5 pages), 2 figure

The return of GOLUM : improving distributed joint parameter estimation for strongly lensed gravitational waves

Owing to the forecasted improved sensitivity of ground-based gravitational-wave detectors, new research avenues will become accessible. This is the case for gravitational-wave strong lensing, predicted with a non-negligible observation rate in the coming years. However, because one needs to investigate all the event pairs in the data, searches for strongly lensed gravitational waves are often computationally heavy, and one faces high false-alarm rates. In this paper, we present upgrades made to the GOLUM software, making it more reliable while increasing its speed by re-casting the look-up table, imposing a sample control, and implementing symmetric runs on the two lensed images. We show how the recovered posteriors have improved coverage of the parameter space and how we increase the pipeline’s stability. Finally, we show the results obtained by performing a joint analysis of all the events reported until the GWTC-3 catalogue, finding similar conclusions to the ones presented in the literature

Reducing the Impact of Weak-lensing Errors on Gravitational-wave Standard Sirens

The mergers of supermassive black hole binaries (SMBHBs) can serve as standard sirens: the gravitational wave (GW) analog of standard candles. The upcoming space-borne GW detectors will be able to discover such systems and estimate their luminosity distances precisely. Unfortunately, weak gravitational lensing can induce significant errors in the measured distance of these standard sirens at high redshift, severely limiting their usefulness as precise distance probes. The uncertainty due to weak lensing can be reduced if the lensing magnification of the siren can be estimated independently, a procedure called 'delensing'. With the help of up-to-date numerical simulations, here we investigate how much the weak-lensing errors can be reduced using convergence maps reconstructed from shear measurements. We also evaluate the impact of delensing on cosmological parameter estimation with bright standard sirens. We find that the weak-lensing errors for sirens at $z_s = 2.9$ can be reduced by about a factor of two on average, but to achieve this would require expensive ultra-deep field observations for every siren. Such an approach is likely to be practical in only limited cases, and the reduction in the weak-lensing error is therefore likely to be insufficient to significantly improve the cosmological parameter estimation. We conclude that performing delensing corrections is unlikely to be worthwhile, in contrast to the more positive expectations presented in previous studies. For delensing to become more practicable and useful in the future will require significant improvements in the resolution/depth of the weak-lensing surveys themselves and/or the accuracy of the methods to reconstruct convergence maps from these surveys.Comment: 19 pages, 22 figures, preparing for submitting to MNRA

Searching for ultralight bosons within spin measurements of a population of binary black hole mergers

Ultralight bosons can form clouds around rotating black holes if their Compton wavelength is comparable to the black hole size. The boson cloud spins down the black hole through a process called superradiance, lowering the black hole spin to a characteristic value. It has been suggested that spin measurements of the black holes detected by ground-based gravitational-wave detectors can be used to constrain the mass of ultralight bosons. Unfortunately, a measurement of the \emph{individual} black hole spins is often uncertain, resulting in inconclusive results. Instead, we use hierarchical Bayesian inference to \emph{combine} information from multiple gravitational-wave sources and obtain stronger constraints. We show that hundreds of high signal-to-noise ratio gravitational-wave detections are enough to exclude (confirm) the existence of non-interacting bosons in the mass range $\left[10^{-13},3\times 10^{-12}\right]$~eV $\left([10^{-13},10^{-12}]~\rm{eV}\right)$. The precise number depends on the distribution of black hole spins at formation and the mass of the boson. From the few uninformative spin measurements of binary black hole mergers detected by LIGO and Virgo in their first two observing runs, we cannot draw statistically significant conclusions.Comment: 10 pages, 4 figures, revised version after resubmissio

Lensed or not lensed: Determining lensing magnifications for binary neutron star mergers from a single detection

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 intrinsically high-mass sources. In this work, we show how to recognize lensed and unlensed binary neutron star systems through the measurement of their tidal effects for highly magnified sources as a proof-of-principle. The proposed method could be used to identify lensed binary neutron stars, which are the chief candidate for lensing cosmography studies. We apply our method on GW190425, finding no evidence in favor of lensing, mainly due to the poor measurement of the event's tidal effects. However, we expect that future detections with better tidal measurements can yield better constraints.Comment: 12 pages, 7 figure

Beyond the Detector Horizon:Forecasting Gravitational-Wave Strong Lensing

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 Voyager and briefly comment on potential improvements due to the inclusion of sub-threshold triggers. We find that most galaxy-lensed events originate from redshifts $z \sim 1-4$ and report the expected distribution of lensing parameters for the observed events. Besides forecasts, we investigate the role of lensing forecasts in strong lensing searches, which explore repeated event pairs. One problem associated with the searches is the rising number of event pairs, which leads to a rapidly increasing false alarm probability. We show how knowledge of the expected galaxy lensing time delays in our searches allow us to tackle this problem. Once the time delays are included, the false alarm probability increases linearly (similar to non-lensed searches) instead of quadratically with time, significantly improving the search. For galaxy cluster lenses, the improvement is less significant. The main uncertainty associated with these forecasts are the merger-rate density estimates at high redshift, which may be better resolved in the future