Dark Matter Subhalos and Higher Order Catastrophes in Gravitational Wave Lensing

TL;DR

This work investigates how dark matter subhalos within galaxy-scale lenses imprint distinctive signatures on strongly lensed gravitational waves. By combining wave-optics and geometric-optics formalisms with a composite lens model (eSIS main halo plus NFW subhalos via pyHalo) and solving the full diffraction integral with GLoW, the authors show two robust channels to detect substructure: (i) higher order catastrophes near caustics yielding $\mu_r>2$ at short $\Delta T$, and (ii) the emergence of more than three highly magnified images, with rates highly sensitive to subhalo concentrations and densities. They demonstrate that subhalos break universal $\mu_r-\Delta T$ relations and enhance wave-optics phenomena, with large sensitivity to the subhalo $c$–$M$ relation, while several model variants reveal how increased concentration or number density alters the observable distributions. Their higher-order catastrophe analysis (swallowtail and butterfly) and toy-model results illustrate concrete pathways by which single lensed GW events could reveal subhalo populations, offering a powerful route to constrain dark matter properties with upcoming LVK, ET, and LISA observations. Overall, the paper underscores the potential of lensed gravitational waves as precision probes of small-scale dark matter structure and the importance of incorporating subhalo-induced catastrophes into GW lens modeling for cosmology and particle physics implications.

Abstract

Gravitational lensing is an invaluable probe of the nature of dark matter, and the structures it forms. Lensed gravitational waves in particular allow for unparalleled sensitivity to small scale structures within the lenses, due to the precise time resolution in combination with the continuous monitoring of the entire sky. In this work, we show two distinct ways of using strongly lensed gravitational waves to identify the presence of dark matter subhalos: \emph{i)} through higher order caustics generating high relative magnification ($μ_r > 2$), short time delay image pairs that break the caustic universality relations of single dark matter halos, which occur for $\sim 1-10$ percent of strongly lensed events in our cold dark matter models, and \emph{ii)} through the presence of more than three highly magnified images, which occur for $\sim 0.01-1$ percent of the same simulated events. We find that these results are highly sensitive to the concentrations of subhalos in our simulations, and more mildly to their number densities. The presence of low-mass subhalos increases the probability of observing wave-optics lensing in lensed gravitational waves, which is studied by solving the diffraction integral with the stationary phase approximation, as well as numerically. We also report distinct quantitative and qualitative differences in the distributions of relative magnifications and time delays for subhalo populations with increased number densities or concentrations. With the upcoming detection of strongly lensed events by ground- and space- based detectors, comparisons against these simulated distributions will provide insight into the nature of dark matter.

Figures (13)

• Figure 1: Magnification ($\mu$) map of an example galaxy populated with cold dark matter subhalos in the image (left) and source (right) plane. Note that this example corresponds to the increased concentration case explored later in the work.
• Figure 2: Relative magnification ($\mu_r$) vs time delay ($\Delta T$) for the two brightest images of sources placed near the caustics of a single elliptical single isothermal sphere halo without (left), and with subhalos (right). The grey lines in both plots represent the asymptotic values for the relative magnifications for sources very close to the caustics, where $\mu_r = 2$ is the limit for the cusp. Note that in the case of subhalo perturbers, the relative magnifications at low time delays can greatly exceed the theoretical limit set by the cusp caustic. The vertical blue line corresponds to the shortest time delay measured in the EM,a quadruply lensed quasar found to have a time delay of $\Delta T = 0.8 ^{+0.8}_{-0.7}$ days Millon:2020xab.
• Figure 3: Concentrations (top) and number counts (bottom) of subhalos as a function of mass ($M_{200}$) for the fiducial Diemer-Joyce parameters Diemer:2018vmz, shown for an opening angle of 30 arcseconds.
• Figure 4: Relative magnifications and time delays for the highest concentration $c$ and subhalo number density (parametrized by $\Sigma_{sub}$) considered in this work.The fiducial models are shown in gray.
• Figure 5: Relative magnifications of the brightest and second brightest images compared against the time delays of the third and fourth brightest images for the fiducial, high number density, and high concentration models. Note that the existence of the population of short time delay pairs for this image pair is due to these sources falling within higher order or nested caustics. All other source locations fall in the high $\Delta T \ $ branch of the distributions.