Detecting Lensing-Induced Diffraction in Astrophysical Gravitational
  Waves
  Gravitational waves emitted from compact binary coalescence can be subject to
wave diffraction if they are gravitationally lensed by an intervening mass
clump whose Schwarzschild timescale matches the wave period. Waves in the
ground-based frequency band $f\sim 10$--$10^3\,$Hz are sensitive to clumps with
masses $M_E \sim 10^2$--$10^3\,M_\odot$ enclosed within the impact parameter.
These can be the central parts of low mass $M_L \sim 10^3$--$10^6\,M_\odot$
dark matter halos, which are predicted in Cold Dark Matter scenarios but are
challenging to observe. Neglecting finely-tuned impact parameters, we focus on
lenses aligned generally on the Einstein scale for which multiple lensed images
may not form in the case of an extended lens. In this case, diffraction induces
amplitude and phase modulations whose sizes $\sim 10\%$--$20\%$ are small
enough so that standard matched filtering with unlensed waveforms do not
degrade, but are still detectable for events with high signal-to-noise ratio.
We develop and test an agnostic detection method based on dynamic programming,
which does not require a detailed model of the lensed waveforms. For
pseudo-Jaffe lenses aligned up to the Einstein radius, we demonstrate that a
pair of fully upgraded aLIGO/Virgo detectors can extract diffraction imprints
from binary black hole mergers out to $z_s \sim 0.2$--$0.3$. The prospect will
improve dramatically for a third-generation detector for which binary black
hole mergers out to $z_s \sim 2$--$4$ will all become valuable sources.
