Mock Catalogs of Strongly Lensed Gravitational Waves via a Halo Model Approach with Space-borne Detectors

The gist: This work develops a comprehensive framework to simulate strongly lensed gravitational waves in the context of space-borne detectors, constructing mock catalogs for LISA and DECIGO based on realistic astrophysical models.

Lensing Framework

The lensing framework is based on the new-generation code Strong Lensing Halo Model–based Mock Catalogs (SL-Hammocks) (Abe et al. 2025). This formalism provides a self-consistent description of lens systems across a broad mass range, from sub-galaxy-scale to cluster-scale halos, unlike the traditional OM10 model which is restricted to galaxy-scale lenses The population of host dark matter halos is generated using the halo mass function defined in terms of the virial mass from Tinker et al. (2008) The mass distribution of host halos is modeled by the Navarro–Frenk–White (NFW; Navarro et al. 1996) density profile Ellipticity is incorporated by replacing the spherical radius r in the NFW profile with the elliptical radius v defined in equation (5) Each host halo is assumed to contain a central galaxy modeled by an elliptical Hernquist profile A key advantage of this halo-based framework is that no scale-dependent assumptions are imposed on the lens population.

LISA Mock Catalog Construction

For LISA, the primary science targets are massive black hole binaries (MBHBs), and six specific realizations of seed formation scenarios are adopted, including HSnodnoSN, PopIIId, Q3d, Q3nod The SNR is computed using the IMRPhenomHM waveform model in combination with the LISA noise power spectral density A key feature of this work is the explicit treatment of GW signal duration, which can be comparable to or even exceed typical lensing time delays, leading to potential overlap between lensed signals. The strategy adopted is that if the lensing time delay is shorter than the GW signal duration, the lensed signals overlap in time and are treated as a single combined signal If the lensing time delay exceeds the GW signal duration, the images are treated as independent signals.

DECIGO Mock Catalog Construction

For DECIGO, the focus is on stellar-mass binary black holes (BBHs), binary neutron stars (BNSs), and neutron star–black hole binaries (NSBHs) The signal duration for these sources in the DECIGO band is generally much shorter than those of MBHBs in the LISA band, implying that signal overlap induced by lensing time delays is less likely to occur compared to LISA. The number of lensed events without imposing an SNR threshold for each source type is presented in Table 8 The resulting lensing probability for the DECIGO case is approximately 0.15%, which is smaller than that in the LISA case.

Key Findings on Signal Overlap and Magnification

The analysis demonstrates that signal overlap induced by lensing time delays can significantly affect the observed properties of lensed GWs, particularly for events with long durations and short time delays For the LISA case, about 60% of the baseline multiple-image events are reduced to single-image events when the effect of signal overlap is taken into account. For DECIGO, nearly 45% of the baseline multiple-image events are reduced to single-image events when overlap is considered for BNSs and NSBHs, whereas for BBHs, only about 4% of such events are reduced. Furthermore, a significant fraction of lensed events have maximum magnification factors greater than 3 (rmax > 3), while no events exhibit extreme magnifications (rmax > 10) in the DECIGO case, in contrast to the LISA results.

Conclusion and Implications

By building mock catalogs of strongly lensed GWs for both LISA and DECIGO, this work provides valuable insights into the expected rates and properties of lensed GW events in these future detectors The main characteristics of our mock catalogs include realistic lensing analysis, incorporation of signal overlap, and a comprehensive parameter space that enables exploration of the full parameter space. Accounting for signal overlap can therefore improve the accuracy and reliability of parameter estimation for lensed GW events. The mock catalogs can be directly used, for example, to train machine learning algorithms or to perform population studies aimed at constraining the properties of GW sources and distribution of lenses.

The paper is organized as follows: In Section 2, we summarize the main components of the lens model based on the SL-Hammocks framework In Section 3, we describe the MBHB source model and present the mock catalog of strongly lensed GWs detectable by LISA In Section 4, we perform a similar analysis for DECIGO, focusing on stellar-mass BBHs, BNSs, and NSBHs Finally, we present our conclusions in Section 5. The results highlight the importance of accounting for signal overlap in the analysis of strongly lensed GW events in future space-borne GW observations. This work was supported by National Key R&D Program of China (No. 2024YFC2207400). T.Y. is supported by the National Natural Science Foundation of China Grants No. 12575063. M.B. was supported by the Polish National Science Centre grant 2023/50/A/ST9/00579. We thank Mengfei Sun for useful discussion about response function of DECIGO. Mock catalogs of strongly lensed gravitational wave events generated in this work are publicly available at https://github.com/LensedGW/GW-LMC-Space. The paper is organized as follows: In Section 2, we summarize the main components of the lens model based on the SL-Hammocks framework In Section 3, we describe the MBHB source model and present the mock catalog of strongly lensed GWs detectable by LISA In Section 4, we perform a similar analysis for DECIGO, focusing on stellar-mass BBHs, BNSs, and NSBHs Finally, we present our conclusions in Section 5. The results highlight the importance of accounting for signal overlap in the analysis of strongly lensed GW events in future space-borne GW observations. This work was supported by National Key R&D Program of China (No. 2024YFC2207400). T.Y. is supported by the National Natural Science Foundation of China Grants No. 12575063. M.B. was supported by the Polish National Science Centre grant 2023/50/A/ST9/00579. We thank Mengfei Sun for useful discussion about response function of DECIGO. Mock catalogs of strongly lensed gravitational wave events generated in this work are publicly available at https://github.com/LensedGW/GW-LMC-Space. The paper is organized as follows: In Section 2, we summarize the main components of the lens model based on the SL-Hammocks framework In Section 3, we describe the MBHB source model and present the mock catalog of strongly lensed GWs detectable by LISA In Section 4, we perform a similar analysis for DECIGO, focusing on stellar-mass BBHs, BNSs, and NSBHs Finally, we present our conclusions in Section 5<ref:

1. Improved simulation fidelity for strongly lensed GWs by explicitly treating signal overlap whether multiple images appear as independent signals or as a single overlapping signal depends on the comparison between the GW signal duration and the lensing time delay. This allows AI systems to accurately estimate event identification and SNR, moving beyond assumptions made in ground-based studies.

2. Enhanced source population modeling for LISA by incorporating two main classes of seed formation scenarios, including the light-seed model (PopIII) and the heavyseed model (HS/Q3), allowing AI to explore a broader range of MBHB evolutionary pathways.

3. Advanced detection capability for future space-borne detectors by providing mock catalogs for LISA and DECIGO, enabling AI to perform comparative studies on the expected number of lensed events (e.g., for a four-year LISA observation, the expected number of lensed events ranges from 0 to 131).

4. Refined analysis methodology by replacing simple optical-depth approximations with a realistic framework, as noted by finding that "our work employs a realistic lensing simulation to generate individual lens systems, whereas the previous study estimated the lensing probability using an optical-depth approximation with simple Singular Isothermal Sphere (SIS) model." This leads to more accurate lensing probability estimates.

5. Improved parameter estimation for lensed events by moving from simple magnification factors to an effective magnification as the ratio of the SNR of the overlapped signal to that of the unlensed signal, denoted as r. This is crucial because the conventional magnification factor µ is no longer directly applicable in overlapping scenarios.