Mock Catalogs of Strongly Lensed Gravitational Waves via A Halo Model Approach with Ground-based Detectors

Abstract

As plans for the construction of third-generation gravitational wave (GW) detectors advance, research into strongly lensed GWs has become increasingly critical. It is anticipated that hundreds of multi-image lensed GWs will be detected annually. We present a comprehensive suite of lensed GW mock catalog derived from a composite lens mass model incorporating dark matter halos, galaxies, and subhalos. We analyze three source populations with four detector network configurations considering the earth rotation. Our simulations encompass not only conventional doublets and quadruplets but also subhalo-lensed events, highly magnified systems, and complete three or five image systems with a detectable central image, a feature distinct from optical lensing. For the joint ET+CE network, we forecast an annual detection rate of approximately 400 doublets and 36 quadruplets. Notably, this population includes roughly 107 events lensed by subhalos and 20 complete systems with detectable central images. Furthermore, we analyze high-magnification events ($μ> 3$), predicting approximately 360 such cases. Under a more relaxed selection criterion that requires only at least one lensed signal to exceed the detection threshold, we estimate a total of approximately 617 lensed events. We also investigate the impact of variations in lens mass models and stellar evolution models on event rates, as well as the distributions of SNR pairs and time delays. These results establish a more physically grounded statistical prior for the future identification and authentication of lensed GW signals. The Gravitational Waves-Lensing Mock Catalog (GW-LMC) have been made publicly available.

Figures (12)

• Figure 1: Cross-validation of the redshift distribution from 2013ApJ...779...72D against the power-law evolution model $\mathcal{R}(z) \propto (1+z)^\kappa$ derived from the theligoscientificcollaboration2025gwtc40populationpropertiesmerging population analysis. The horizontal axis represents the GW source redshift, while the vertical axis denotes the number of GW events per unit redshift interval.
• Figure 2: Redshift distributions of GW events for different source types according to Dominik et al. 2013
• Figure 3: The joint probability density distribution of the lens redshift ($z_l$) and source redshift ($z_s$) for 6,172 simulated strongly lensed GW events from the $N_{\mathrm{trig}}$ catalog. The filled curves on the top and right margins illustrate the marginal distributions for $z_l$ and $z_s$, respectively. Within the joint contour plot, the red cross marks the location of the peak probability density, while the orange circle represents the median of the distribution. The diagonal dashed gray line indicates the $z_s = z_l$ reference line.
• Figure 4: Impact of magnification bias on the redshift distribution of observable lensed GW events. The distribution for all detectable events ($N=6172$) peaks at $z_s \approx 4.38$ with a median of $z_s = 5.20$, whereas high-magnification events ($\mu_{\mathrm{max}} > 3$, including both single and multiple images; $N=3593$) exhibit a peak shifted to a higher redshift of $z_s \approx 4.51$ and a median of $z_s = 5.60$. Both distributions feature an extended tail reaching $z_s > 15$, demonstrating that high-magnification lensing events serve as unique probes for binary mergers in the early Universe.
• Figure 5: Differential distribution of the maximum angular separation ($\Delta \theta$) between signal copies for lensed GW multi-image events, plotted as $dN/d\log_{10} \Delta\theta$. The distribution encompasses three distinct lens mass scales: galaxy, group, and cluster scales. Furthermore, contributions from different lens structures are distinguished: host halos are indicated by the red dotted line, subhalos by the orange dashed line, and the total population (host + subhalo) by the red solid line. The overall distribution is predominantly dominated by galaxy-scale lenses, peaking at $\Delta \theta \approx 1.28$ arcseconds, while the cluster scale constitutes the extended tail at large angular separations.