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

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 $-\ddot{I}€/12$, 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 $-\ddot{I}€/12$ phase offset when detected by three detectors for H-L optimal SNR $\gtrsim$ 40 and $\mathcal{M}\le 30$. We analyze GW190412 and GW190814 using this parameterization, measuring the offset to be $0.13_{-0.17}^{+0.22}$ for GW190412 and $-0.05_{-0.22}^{+0.20}$ for GW190814. We also measure the Bayes factor in support of zero phase offset, ${\log }_{10}{\mathcal{B}}_{\hat{I}”\ddot{I}†=0}$, 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.

10 pages, 7 figures; v2 - updated for consistency with PRD version, v3 - fixed minor typos