Probing Dark Matter Substructure with Wave-Optics Distortions of Strongly Lensed LISA Gravitational Waves
Abstract
Strong lensing changes the phase of a gravitational-wave signal as well as its amplitude and arrival time. We study whether this phase information can distinguish between three dark-matter structures in the lens: a Navarro--Frenk--White halo (NFW), a self-interacting dark matter (SIDM) halo, and a fuzzy-dark-matter field (FDM). We generate waveforms for the detectable lensed massive-black-hole-binary population of a four-year LISA mission and fit every signal with the same smooth singular-isothermal-ellipsoid lens with external shear. In 132 lens systems, 311 images are resolved as separate signals in time. NFW and SIDM produce real waveform changes, but their slowly varying part is largely degenerate with the constant, gradient, and Hessian of the smooth Fermat potential at the image. The coherent density fluctuations of FDM leave a larger frequency-dependent residual after this fit. The NFW--FDM and SIDM--FDM populations become distinguishable with about 60 and 110 resolved image waveforms, respectively. These results show that repeated lensed LISA signals can probe the spatial form of dark matter in lens galaxies, rather than only the total lensing mass.
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BibTeX
@misc{liu2026probing,
title = {{Probing Dark Matter Substructure with Wave-Optics Distortions of Strongly Lensed LISA Gravitational Waves}},
author = {Tonghua Liu and Kai Liao and Marek Biesiada and Jieci Wang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.22787},
eprint = {2607.22787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.22787},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Probing Dark Matter Substructure with Wave-Optics Distortions of Strongly Lensed LISA Gravitational Waves
AU - Tonghua Liu
AU - Kai Liao
AU - Marek Biesiada
AU - Jieci Wang
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2607.22787
UR - https://arxiv.org/abs/2607.22787
AB - Strong lensing changes the phase of a gravitational-wave signal as well as its amplitude and arrival time. We study whether this phase information can distinguish between three dark-matter structures in the lens: a Navarro--Frenk--White halo (NFW), a self-interacting dark matter (SIDM) halo, and a fuzzy-dark-matter field (FDM). We generate waveforms for the detectable lensed massive-black-hole-binary population of a four-year LISA mission and fit every signal with the same smooth singular-isothermal-ellipsoid lens with external shear. In 132 lens systems, 311 images are resolved as separate signals in time. NFW and SIDM produce real waveform changes, but their slowly varying part is largely degenerate with the constant, gradient, and Hessian of the smooth Fermat potential at the image. The coherent density fluctuations of FDM leave a larger frequency-dependent residual after this fit. The NFW--FDM and SIDM--FDM populations become distinguishable with about 60 and 110 resolved image waveforms, respectively. These results show that repeated lensed LISA signals can probe the spatial form of dark matter in lens galaxies, rather than only the total lensing mass.
ER -