Probing wave-optics effects and dark-matter subhalos with lensing of gravitational waves from massive black holes

The Laser Interferometer Space Antenna (LISA) will detect gravitational waves (GWs) emitted by massive black hole binaries (MBHBs) in the low-frequency ($\sim$mHz) band. Low-mass lenses, such as dark-matter (DM) subhalos, have sizes comparable to the wavelength of these GWs. Encounters with these lenses produce wave-optics (WO) effects that alter waveform phase and amplitude. Thus, a single event with observable WO effects can be used to probe the lens properties. In this paper, we first compute the probability of observing WO effects in a model-agnostic way. We perform parameter estimation over approximately 1000 MBHBs with total mass, mass ratio, and redshift spanning the ranges relevant to LISA. We then calculate lensing rates using three semi-analytical models of MBHB populations. In both cases, we use a waveform model that includes merger, ringdown, and higher-order modes. We use two lens population models: the theory-based Press-Schechter halo mass function and an observation-based model derived from Sloan Digital Sky Survey, called the measured velocity function. We find that the probability of detecting WO effects can be as large as $\sim 3\%$, $\sim1.5\%$, and $\sim 1 \%$ at $1\sigma$, $3\sigma$, and $5\sigma$ confidence levels, respectively. The most optimistic MBHB population model yields $\sim 8$, $\sim 4$, and $\sim 3$ events at the same confidence levels, while the rates drop to $\sim 0.01$ in the more pessimistic scenarios. The most likely lens masses probed by LISA are in the range $(10^3, 10^8)\, M_{\odot}$, and the most probable redshifts are in the range $(0.3, 1.7)$. Therefore, LISA observations of WO effects can probe DM subhalos, complementing strong lensing and other observations.
Comment: 24 pages, 15 figures. Comments are welcome