Effective description of lensed gravitational waves diffracted by stellar fields

As natural telescopes, Gravitational lenses enable the observation of sources that would otherwise be too distant and faint. Stellar-mass objects, or microlenses, act as impurities in the lens, producing subtle distortions of the source. These effects are necessary to correctly interpret observations, and may in some cases be themselves evidence of gravitational magnification. Gravitational waves (GWs) observed by ground detectors and magnified by galaxies and clusters will undergo microlensing by fields of stars and remnants: describing these systems requires not only considering a large number of small-scale lenses (microlenses), but also including wave-optics effects, leading to frequency dependent modulations of the signal. Here we present novel models for Reduced-Order Stochastic Diffraction (ROSD), which overcome these challenges in the search for GW lensing signatures: an effective description is synthesized from numerical simulations of wave-optics lensing by stellar fields via a singular value decomposition. The procedure yields an optimized orthonormal basis to describe microlensing distortions and a probability density function for the coefficients, which can be used as priors or to verify the consistency with stellar-field lensing. We present SVD-stellar-I5-aLIGO as an example of this model category, discuss the role of truncation order and demonstrate how it can be applied to GW data via injection and recovery in Bayesian parameter estimation. ROSD can be tailored to account for detector sensitivity and the type of source under analysis, and extended to different microlens populations and external potentials. ROSD models open a new window to probe small-scale objects (stars, remnants and potentially dark matter) and facilitate the discovery of the most distant compact binary mergers.