Listening to the stars beneath the waves

A new reduced-order model makes the complex diffraction of gravitational waves by stellar fields accessible to data analysis.

Gravitational lenses can magnify distant gravitational-wave sources, bringing otherwise inaccessible black-hole mergers into view. However, galaxies and galaxy clusters are not smooth lenses; their stars and stellar remnants further deflect the waves on much smaller scales. For gravitational waves, these objects can act as diffracting barriers, imprinting characteristic frequency-dependent distortions on the observed signal.

Describing this effect is difficult because every line of sight contains a different, essentially random distribution of stars and remnants. A realistic calculation may involve many thousands of objects, making it impractical to include their individual properties directly when analyzing gravitational-wave data.

Miguel Zumalacárregui at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) and Xikai Shan at Tsinghua University have now developed a reduced-order description of this complex phenomenon. Starting from 10,000 numerical simulations of gravitational waves diffracted by realistic stellar fields, they use a mathematical decomposition to identify the dominant, recurring diffraction patterns. These patterns form a compact basis describing the characteristic “stellar timbre” that microlensing can imprint on a gravitational-wave signal.

The researchers find that only a few components are needed to capture most of the diffraction structure: eight basis modes retain about 95% of the microlensing signal for a typical simulated realization. The associated coefficients also retain information about the larger gravitational lens, including its magnification and the surface density of compact objects. In simulated gravitational-wave observations, the reduced model can recover signals whose parameters would be strongly biased if microlensing were ignored.

The approach, called Reduced-Order Stochastic Diffraction, provides a practical bridge between detailed simulations of complex lenses and gravitational-wave data analysis. This method and foreseeable extensions could help discover strongly magnified gravitational waves from very distant sources while simultaneously using their diffraction patterns to probe stars and remnants on small scales. As gravitational-wave detectors increase in sensitivity, such lensed signals are expected to become increasingly common.

This study was recently published in Physical Review D and selected as an Editor's Suggestion.

Paper abstract

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—capturing the dominant “tones” of the stellar field, or stellar timbre—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.