Gravitational Wave Diffractive Images Reveal the Structure of Astrophysical Objects

Abstract

Scattering patterns encode the structure of extended objects, as demonstrated by charged particle scattering on atomic nuclei. Gravitational wave (GW) diffraction offers an analogous probe of otherwise invisible mass distributions. At linear order in the lens potential we derive expressions relating the central diffractive image contribution to a gravitationally lensed GW waveform to the Fourier transform of the projected lens density. For finite mass lenses this contribution takes the form of a point mass Born amplitude multiplied by a normalized mass form factor, analogous to that in nuclear scattering. As the frequency of GWs from a merging compact binary source evolves the signal samples this form factor across spatial scales, imprinting lens structure through interference with the primary image. Using full numerical wave optics calculations we quantify the observational reach for extended dark matter objects, primordial black holes halo-dressed by dark matter halos and superradiance clouds of ultralight bosons around black holes. For the considered source populations, five year observations with next generation detectors can distinguish extended lenses from point masses, probing dark matter fractions down to $\mathcal{O}(10^{-5})$, and halo-dressed primordial black holes from matched bare black holes, probing primordial black hole dark matter fractions down to $\mathcal{O}(10^{-6})$. For sufficiently close source-lens configurations, scalar superradiance clouds can produce distinguishable diffraction signatures for boson masses of approximately $10^{-17}-10^{-12}~\mathrm{eV}$. These results provide a framework for characterizing extended dark matter and compact object astrophysical environments.