Discovering gravitationally lensed gravitational waves: predicted rates, candidate selection, and localization with the Vera Rubin Observatory

Abstract

The first secure detection of a gravitationally lensed gravitational (GW) will be a watershed moment, as it will bring together these two pillars of General Relativity for the first time. Accurate selection and interpretation of candidate lensed GWs is challenging for numerous reasons, including large sky localization uncertainties for most GW detections, the broad range of gravitational lenses spanning galaxy/group/cluster-scales in the dark matter halo mass function, and uncertainty in the intrinsic mass function of compact object remnants of stellar evolution. We introduce a new magnification-based approach to predicting the rates of lensed GWs that is agnostic to the mass and structure of the lenses and combine it with expressions for arrival time difference for representative lenses and their catastrophes to delineate the range of expected arrival time differences. We also predict the lightcurves of lensed kilonova counterparts to lensed binary neutron star (NS-NS) mergers and assess the feasibility of detection with the Vera Rubin Observatory. Our main conclusions are: (1) selection of candidate lensed NS-NS mergers from the mass gap between NS and black holes in low latency is an efficient approach with a rate approaching one per year in the mid-2020s, (2) the arrival time differences of lensed NS-NS/kilonovae are typically 1 year, and thus well-matched to the operations of GW detectors and optical telescopes, and (3) detection of lensed kilonovae is feasible with the Vera Rubin Observatory. Whilst our predictions are motivated by lensing, they provide a physically well-understood approach to exploring the mass gap electromagnetically as the number of detections in this exciting region of parameter space grows.

On the gravitational lensing interpretation of three gravitational wave detections in the mass gap by LIGO and Virgo

“…The cluster RX J2129.6+0005 was the only cluster left from our search at p=0.876 corresponding to an area = 226.05 deg 2 . Furthermore, at 𝐷 300 Mpc, this detection is close to the peak of the predicted population of lensed BNS mergers in LVK's third run (Smith et al 2022). Following the GW trigger announcement, two GCN circulars confirmed the detection of a contextual neutrino by IceCube and a sub-threshold gamma-ray source by HAWC from a sky position offset from RX J2129.6+0005 (IceCube Collaboration 2019; HAWC Collaboration 2019).…”

“…theoretical surfaces corresponding to infinite magnification. Smith et al (2022) showed that the pseudo catastrophe of the singular isothermal lens and the fold catastrophe bracket the range of time delays measured to date for lensed quasars, and thus form a solid basis for predicting time delays for other lensed transients. We therefore adopt the following convenient scaling relations for lenses with an isothermal slope:…”

“…This section summarises the principal details behind the model for the population of compact objects used to study the impact of lensing on the detection of GWs; we refer the reader to Smith et al (2022) for the complete description of the models.…”

“…If the EM counterpart to a gravitationally lensed BNS merger located at 𝑧 1 has a similar luminosity, then its apparent magnitude is given by: 𝑚 −14 + 5 log(𝐷/10pc) − 2.5 log(𝜇) where 𝐷 is the intrinsic luminosity distance to the lensed GW, 𝜇 = (𝐷/ 𝐷) 2 is the gravitational magnification suffered by the source, and 𝐷 is the luminosity distance initially assigned to the source by LVK assuming 𝜇 = 1. Interestingly, 𝑚 −14 + 5 log( 𝐷/10 pc), because the inverse square law cancels the gravitational magnification and 𝑘-corrections appear to be modest (Smith et al 2022). Assuming that the GW is initially placed at 𝐷 = 600 Mpc, this implies an apparent magnitude of 𝑚 25.…”

“…Assuming that the GW is initially placed at 𝐷 = 600 Mpc, this implies an apparent magnitude of 𝑚 25. Once a typical strong lensing magnification for lensed BNS mergers of 𝜇 = 100 (Smith et al 2022) is taken into consideration, the effective magnitude that can be accessed reaches 𝑚 + 2.5 log(𝜇), equalling 𝑚 ≈ 30. Therefore, lensing is crucial not only to boost the EM counterpart signal, but also necessary to access BNS mergers at redshift 𝑧 1.…”