skip to main content

Title: Improved statistic to identify strongly lensed gravitational wave events

As the number of detected gravitational wave sources increases with increased sensitivity of the gravitational wave observatories, observing strongly lensed pairs of events will become a real possibility. Lensed gravitational wave (GW) events will have very accurately measured time delays and magnification ratios. Suppose we identify the lens system corresponding to a GW event in the electromagnetic domain and also measure the redshifts of the lens and the host galaxy; in that case, we can use the GW event to constrain important astrophysical parameters of the lens system. As most lensing events have image separations that are significantly smaller than the GW event localization uncertainties, we must develop diagnostics that will aid in the robust identification of such lensed events. We define a new statistic based on the joint probability of lensing observables that can be used to discriminate lensed pairs of events from the unlensed ones. To this end, we carry out simulations of lensed GW events to infer the distribution of the relative time delays and relative magnifications subdivided by the type of lensed images. We compare this distribution to a similar one obtained for random unlensed event pairs. Our statistic can improve the search pipelines’ existing ranking approach to down-select event pairs for joint parameter estimates. The distributions we obtain can further be used to define more informative priors in joint parameter estimation analyses for candidate lensed events.

more » « less
Author(s) / Creator(s):
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Monthly Notices of the Royal Astronomical Society
Page Range / eLocation ID:
p. 1044-1051
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract 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 3G detectors, we find that ∼0.1% of observed events are expected to be strongly lensed. We predict detections of ∼1 lensing pair per year with A+, and ∼50 pairs per year with ET/CE. These rates are highly sensitive to the characteristic galaxy velocity dispersion, σ * , implying that observations of the rates will be a sensitive probe of lens properties. We explore using the time-delay distribution between multiply imaged gravitational-wave sources to constrain properties of the lenses. We find that 3G detectors would constrain σ * to ∼21% after 5 yr. Finally, we show that the presence or absence of strong lensing within the detected population provides useful insights into the source redshift and mass distribution out to redshifts beyond the peak of the star formation rate, which can be used to constrain formation channels and their relation to the star formation rate and delay-time distributions for these systems. 
    more » « less

    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.

    more » « less
  3. Abstract

    Supermassive black hole binary systems (SMBHBs) should be the most powerful sources of gravitational waves (GWs) in the universe. Once pulsar timing arrays (PTAs) detect the stochastic GW background from their cosmic merger history, searching for individually resolvable binaries will take on new importance. Since these individual SMBHBs are expected to be rare, here we explore how strong gravitational lensing can act as a tool for increasing their detection prospects by magnifying fainter sources and bringing them into view. Unlike for electromagnetic waves, when the geometric optics limit is nearly always valid, for GWs the wave-diffraction-interference effects can become important when the wavelength of the GWs is larger than the Schwarzchild radius of the lens, i.e.,Mlens108fmHz1M. For the GW frequency range explored in this work, the geometric optics limit holds. We investigate GW signals from SMBHBs that might be detectable with current and future PTAs under the assumption that quasars serve as bright beacons that signal a recent merger. Using the black hole mass function derived from quasars and a physically motivated magnification distribution, we expect to detect a few strongly lensed binary systems out toz≈ 2. Additionally, for a range of fixed magnifications 2 ≤μ≤ 100, strong lensing adds up to ∼30 more detectable binaries for PTAs. Finally, we investigate the possibility of observing both time-delayed electromagnetic signals and GW signals from these strongly lensed binary systems—that will provide us with unprecedented multi-messenger insights into their orbital evolution.

    more » « less

    Gravitational lensing deflects the paths of photons, altering the statistics of cosmic backgrounds and distorting their information content. We take the cosmic infrared background (CIB), which provides plentiful information about galaxy formation and evolution, as an example to probe the effect of lensing on non-Gaussian statistics. Using the Websky simulations, we first quantify the non-Gaussianity of the CIB, revealing additional detail on top of its well-measured power spectrum. To achieve this, we use needlet-like multipole-band filters to calculate the variance and higher-point correlations. Using our simulations, we show the two-, three- and four-point spectra, and compare our calculated power spectra and bispectra to Planck values. We then lens the CIB, shell-by-shell with corresponding convergence maps, to capture the broad redshift extent of both the CIB and its lensing convergence. The lensing of the CIB changes the three- and four-point functions by a few tens of per cent at large scales, unlike with the power spectrum, which changes by less than two per cent. We expand our analyses to encompass the full intensity probability distribution functions (PDFs) involving all n-point correlations as a function of scale. In particular, we use the relative entropy between lensed and unlensed PDFs to create a spectrum of templates that can allow estimation of lensing. The underlying CIB model is missing the important role of star bursting, which we test by adding a stochastic lognormal term to the intensity distributions. The novel aspects of our filtering and lensing pipeline should prove useful for any radiant background, including line intensity maps.

    more » « less

    When travelling from their source to the observer, gravitational waves can get deflected by massive objects along their travel path. For a massive lens and a good source-lens alignment, the wave undergoes strong lensing, leading to several images with the same frequency evolution. These images are separated in time, magnified, and can undergo an overall phase shift. Searches for strongly lensed gravitational waves look for events with similar masses, spins, and sky location and linked through so-called lensing parameters. However, the agreement between these quantities can also happen by chance. To reduce the overlap between background and foreground, one can include lensing models. When doing realistic searches, one does not know which model is the correct one to be used. Using an incorrect model could lead to the non-detection of genuinely lensed events. In this work, we investigate how one can reduce the false alarm probability when searching for strongly lensed events. We focus on the impact of the addition of a model for the lens density profile and investigate the effect of potential errors in the modelling. We show that the risks of false alarm are high without the addition of a lens model. We also show that slight variations in the profile of the lens model are tolerable, but a model with an incorrect assumption about the underlying lens population causes significant errors in the identification process. We also suggest some strategies to improve confidence in the detection of strongly lensed gravitational waves.

    more » « less