Wave-Optics Imprints of Dark Matter Subhalos on Strongly Lensed Gravitational Waves

Abstract

Wave-optics effects in strongly lensed gravitational waves (GWs) provide a new interferometric probe of dark matter substructure. We compute the full diffraction integral for GWs propagating through statistically generated cold dark matter subhalo populations and quantify the resulting frequency-dependent amplification in the Laser Interferometer Space Antenna (LISA) band. We show that realistic galaxy-scale lenses generically produce percent-level amplitude and phase distortions in strongly magnified images, primarily induced by subhalos in the mass range $10^4$-$10^7\,M_{\odot}$. These signatures arise naturally within the standard cold dark matter paradigm and should be detectable in high signal-to-noise LISA events. Strongly lensed GWs thus offer a direct and complementary window on dark matter structure at subgalactic mass scales inaccessible to electromagnetic measurements.

Figures (7)

• Figure 1: Spatial distribution of dark-matter subhalos in a representative realization of the strongly lensed system. The red cross (triangle) marks the macro minimum (saddle) image. Colored points in the main panel denote 26 low-mass subhalos ($10^4$--$10^9\,M_\odot$) included explicitly in the WO calculation, while the inset shows 13 massive subhalos ($m_{\rm sub}>10^9\,M_\odot$) treated in the GO limit. For visual clarity, subhalos in the mass range $10^2$--$10^4\,M_\odot$ (1218 objects in this realization) are not displayed, although they are included in the WO calculation. The color scale indicates $\log_{10}(m_{\rm sub}/M_\odot)$.
• Figure 2: Frequency-dependent gravitational-wave amplification factor in the fiducial strongly lensed configuration. Top: absolute amplification $|F(f)|$. Middle: relative amplitude modulation $|F(f)/F(0.1\,\mathrm{Hz})|-1$. Bottom: phase shift $\arg F(f)$. Shaded bands indicate the 68% and 95% ranges over 200 independent subhalo realizations, and the black curve shows the median. Thin red curves illustrate three representative realizations.
• Figure 3: Dependence of the GW amplification factor $|F(f)|$ on the minimum subhalo mass included in the WO calculation. From top to bottom panels, three realizations (the same as in Fig. \ref{['fig:Fw_percentiles']}) are shown. Different line styles correspond to different minimum subhalo masses $m_{\rm sub,min}=10^{2}$--$10^{7}\,M_\odot$.
• Figure 4: Distribution of the dimensionless Fermat potential $I(\tau)$ for three representative realizations, shown for different minimum subhalo masses $m_{\rm sub,min}=10^{4}$--$10^{7}\,M_\odot$ (see legend). In the pure geometric-optics limit, $I(\tau)$ would be constant (for a quadratic minimum) with normalization proportional to the macro magnification. Including progressively lower-mass subhalos introduces localized distortions in the shape of $I(\tau)$, while leaving its overall normalization largely unchanged. These distortions are responsible for the frequency-dependent structure of the amplification factor $F(w)$.
• Figure 5: Frequency-domain amplification factor $|F(f)|$ computed without the external macro field. The same three realizations and mass thresholds as in Fig. \ref{['fig:Fw_msubmin']} are shown. Across the LISA band, the amplification factor is nearly frequency-independent, with only weak broadband curvature and no prominent oscillatory structure.