Effects of Galaxy Cluster Structure on Lensed Gravitational Waves

TL;DR

This paper investigates how realistic galaxy cluster structure affects lensed gravitational waves, contrasting multi-halo cluster models with single-halo SIS benchmarks using three clusters (Abell 2390, Abell 370, El Gordo) and LENSTOOL-based mass components. By populating BBH/BNS mergers with LVK-based rates and computing detector-specific SNRs under O4 and future sensitivities, the authors quantify observables such as time delays $\Delta t$, magnifications $\mu$, and image multiplicities, and assess detection rates. They find that realistic clusters exhibit substantially smaller strong-lensing cross sections than SIS, but have broadened high-magnification tails and higher image multiplicities; time delays shift to smaller values, and a larger share of images have positive parity. These results imply that GW-only lens reconstruction for clusters is challenging due to degeneracies, yet lensed GW signals can still provide lower limits on lens masses and benefit from cross-correlation with cluster catalogs; there is also potential to use substructure signatures to probe dark matter models with future wave-optics effects. Overall, the work highlights the importance of realistic cluster modeling for interpreting lensed transients and informs strategies for identifying lensed GW events in upcoming surveys.

Abstract

Strong gravitational lenses come in many forms, but are typically divided into two populations: galaxies, and groups and clusters of galaxies. The largest objects in the Universe (i.e. galaxy clusters) are highly irregular and composed of many components due to a history of (or active) hierarchical mergers. In this work, we analyze the discrepancies in the observables of strongly lensed gravitational wave transients in both scenarios, namely relative magnifications, time delays, and image multiplicities. We compare the detection rates between the single spherical dark matter halo models found in the literature, and publicly available state-of-the-art cluster lens models. We find there to be approximately an order of magnitude fewer detection of strongly lensed transients in the realistic model case, likely caused by their loss of overall strong lensing optical depth. We also report detection rates in the weak lensing or single-image regime. Additionally, we find a systemic shift towards lower time delays between the brightest image pairs in the cases of the realistic models, as well as higher fractions of positive versus negative parity images, which was previously reported in the literature. This deviation in the joint relative magnification factor-time delay distribution will hinder the feasibility of the reconstruction of cluster-scale lenses through gravitational wave transients alone, but can still provide a lower limit on the lens mass.

Figures (10)

• Figure 1: Source plane (top) and image plane (bottom) absolute magnification ($\mu$) maps of Abell 2390 (left, green), Abell 370 (middle, pink) and El Gordo (right, blue) for a source at $z=3$. These three clusters exhibit a rich morphology. They have similar total mass, $\sim10^{15}M_\odot$, but different number of member galaxies. They are also located at different redshifts, increasing from left to right (see Table \ref{['tab:clusters']} for details). This changes the angular size, which can be compared to the reference scale in the solid black line.
• Figure 2: Normalized distribution of image plane magnification factors for a source at $z=3$ for the three clusters in this study, compared against the singular isothermal sphere (SIS) model. The high magnification tail is enhanced in the realistic models.
• Figure 3: Time delay $t_d$ vs relative magnification factor $\mu_r$ of detectable lensed binary black hole image pairs at O4 sensitivity for Abell 2390 (left), Abell 370 (middle), and El Gordo (right) up to $z=3$. Results are plotted against those from their respective SIS models. Due to the substructure, the maximum time delay of the realistic clusters decreases considerably compared to the isothermal model. The relative magnifications also spread significantly compared to the SIS band, which traces the relation $\mu_r(\Delta t)$ (cf. Eq. \ref{['eq:sismur']}) over the possible source redshifts.
• Figure 4: Optical depth ($\tau_{SL}$) of the three cluster models (solid lines) compared against the SIS predictions (dashed lines).
• Figure 5: Normalized distribution of image multiplicity regions in the source plane for Abell 2390 (green), Abell 370 (pink), and El Gordo (blue). Note that the SIS model can only produce one or two images.