Breaking the mass-sheet degeneracy with gravitational wave interference in lensed events

Abstract

The mass-sheet degeneracy is a well-known problem in gravitational lensing which limits our capability to infer astrophysical lens properties or cosmological parameters from observations. As the number of gravitational wave observations grows, detecting lensed events will become more likely, and to assess how the mass-sheet degeneracy may affect them is crucial. Here we study both analytically and numerically how the lensed waveforms are affected by the mass-sheet degeneracy computing the amplification factor from the diffraction integral. In particular, we differentiate between the geometrical optics, wave optics and interference regimes, focusing on ground-based gravitational waves detectors. In agreement with expectations of gravitational lensing of electromagnetic radiation, we confirm how, in the geometrical optics scenario, the mass-sheet degeneracy cannot be broken with only one lensed image. However, we find that in the interference regime, and in part in the wave-optics regime, the mass-sheet degeneracy can be broken with only one lensed waveform thanks to the characteristic interference patterns of the signal. Finally, we quantify, through template matching, how well the mass-sheet degeneracy can be broken. We find that, within present GW detector sensitivities and considering signals as strong as those which have been detected so far, the mass-sheet degeneracy can lead to a 1σ uncertainty on the lens mass of ∼ 12%. With these values the MSD might still be a problematic issue. But in case of signals with higher signal-to-noise ratio, the uncertainty can drop to ∼ 2%, which is less than the current indeterminacy achieved by dynamical mass measurements.

Lensing of Gravitational Waves as a Novel Probe of Graviton Mass

“…Lensing is a crucial astrophysical probe. For example, lensing of gravitational waves might provide us with the information of the existence of intermediate-mass black holes (of mass ∼ 10 2 M − 10 3 M ) [38], cosmological expansion [27,33] and testing general relativity [26,30,45,46]. Since the direct detection of gravitational waves, searches for lensed gravitational waves has been popular [22,32,44].…”

On the identification of individual gravitational wave image types of a lensed system using higher-order modes

“…As a consequence, search techniques for strong lensing have been developed over * j.janquart@uu.nl the last years [11,[21][22][23][24] and several searches for lensing signatures in the LIGO-Virgo data have been conducted [21,22,25,26]. The science cases also now include studies spanning the domains of fundamental physics, astrophysics, and cosmology [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”