On the waveforms of gravitationally lensed gravitational waves

TL;DR

This paper studies how strong gravitational lensing affects the waveforms of gravitational waves, revealing unique distortions for different image types that can help identify lensing effects and improve understanding of the lensing objects.

Contribution

It demonstrates that lensing-induced waveform distortions can be characterized as specific rotations of the line of sight and are distinguishable among multiple images, providing new tools for lensing analysis.

Findings

Type-II images exhibit waveform distortions equivalent to a 45° rotation of the line of sight.

Type-III images preserve waveform shape but with a sign flip.

Distortions in eccentric binaries are distinct from changes in orbital parameters.

Abstract

Strong lensing by intervening galaxies can produce multiple images of gravitational waves from sources at cosmological distances. These images acquire additional phase-shifts as the over-focused wavefront passes through itself along the line of sight. Time domain waveforms of Type-II images (associated with saddle points of the time delay) exhibit a non-trivial distortion from the unlensed waveforms. This phenomenon is in addition to the usual frequency-independent magnification, and happens even in the geometric limit where the wavelength is much shorter than the deflector's gravitational length scale. Similarly, Type-III images preserve the original waveform's shape but exhibit a sign flip. We show that for non-precessing binaries undergoing circular inspiral and merger, these distortions are equivalent to rotating the line of sight about the normal to the orbital plane by $45^\circ$ (Type II) and $90^\circ$ (Type III). This effect will enable us to distinguish between the different topological types among a set of multiple images, and give us valuable insight into the lens model. Furthermore, we show that for eccentric binaries, the waveform of a Type-II image is distorted in a manner that is inequivalent to a change of the source's orbital parameters.