Phase consistency test to identify type II strongly lensed gravitational wave signals using a single event

TL;DR

This paper introduces a phase consistency test to identify type II strongly lensed gravitational wave signals by analyzing phase offsets between modes, using simulations and real GW data, but finds no definitive evidence for lensing in the analyzed events.

Contribution

The paper develops a new waveform parameter to detect phase offsets indicative of type II lensing in gravitational wave signals, validated through simulations and applied to real events.

Findings

Test reproduces expected phase offset in simulations at high SNR.

Measured phase offsets in GW190412 and GW190814 are consistent with no lensing.

Results do not provide strong evidence for type II lensing in the analyzed events.

Abstract

For gravitationally lensed type II signals, the phase of the dominant (2, 2) mode and the higher order (3, 3) mode is offset by $-\pi/12$, or roughly -0.26 radians. Using this, we develop a test for type II imagery by allowing the phases of the (2,2) and (3,3) modes to vary separately and introducing a new waveform parameter to represent the phase offset between the two. We use simulated, asymmetric mass ratio, precessing signals to show that the test can reproduce the $-\pi/12$ phase offset when detected by three detectors for H-L optimal SNR $\gtrsim$ 40 and $\mathcal{M} \leq 30$. We analyze GW190412 and GW190814 using this parameterization, measuring the offset to be $0.13^{+0.22}_{-0.17}$ for GW190412 and $-0.05^{+0.20}_{-0.22}$ for GW190814. We also measure the Bayes factor in support of zero phase offset, $\log_{10} \mathcal{B}_{\Delta \varphi = 0}$, to be $-0.14$ for GW190412 and $0.21$ for GW190814. This implies our results are not strong enough to confidently argue if either event is a type II image, and is consistent with our statistical analysis.