Gravitational lensing of gravitational waves by galaxy clusters

RESUMO

Strongly lensed gravitational waves (GWs) are commonly searched for using population priors, including time-delay and magnification-ratio distributions, to suppress false alarms. Current LIGO, Virgo, and KAGRA (LVK) searches mainly adopt priors calibrated with galaxy-scale lenses; however, these may penalize the longer time delays produced by galaxy clusters, which could contribute 10%--20% of lensed events. Cluster member galaxies may also perturb the macro-lens potential and alter image magnifications. We investigate the time-delay and magnification-ratio distributions of binary black hole GWs lensed by galaxy clusters, together with microlensing systematics. In the full lensed sample, the median time delay is about 76 days for cluster lenses, compared with 6.9 days for galaxy lenses. After imposing an SNR threshold of $\rho>8$ at LVK O4 sensitivity, the medians are 15.4 and 0.24 days. The detected cluster sample retains a long-delay tail, with 9.1% of image pairs delayed by more than 365 days and 3.3% by more than 1000 days, so galaxy-based time-delay priors can suppress cluster-lensed pairs. By contrast, although cluster member galaxies broaden the magnification-ratio distribution of the full cluster sample, the detected cluster- and galaxy-lensing samples are very similar at O4 sensitivity, suggesting little bias in candidate selection. Cluster lenses also generally produce weak microlensing distortions: only about 0.8% of single-image mismatches exceed ${\cal M}=0.03$, while 4.8% exceed the parameter-estimation threshold $1.35/\rho^2$. Thus, microlensing is subdominant for most cluster-lensed events, mainly because images often form far from the brightest cluster galaxy, where the stellar density is low and dominated by intracluster light, although nearby satellites can locally enhance it. These results motivate a dedicated cluster-lensing pipeline for GW lensing searches.