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#### Detection and parameter estimation challenges of Type-II lensed binary black hole signals

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##### Citation

Vijaykumar, A., Mehta, A. K., & Ganguly, A. (2023). Detection and parameter estimation
challenges of Type-II lensed binary black hole signals.* Physical Review D,* *108*(4):
043036. doi:10.1103/PhysRevD.108.043036.

Cite as: https://hdl.handle.net/21.11116/0000-000D-D6D5-1

##### Abstract

Strong lensing of {gravitational-wave signals} can produce three types of

images, denoted as Type-I, Type-II and Type-III, corresponding to the minima,

saddle and maxima of the lensing potential of the lensed images. Type-II

images, in particular, receive a non-trivial phase shift of $\pi/2$. This phase

shift can introduce additional distortions in the strains produced by the

Type-II image of the binary black hole signals depending on the morphology of

the signals, e.g., when they have contributions from higher harmonics,

precession, eccentricity, etc. {The probability of observing Type-II images is

nearly the same as that of strong lensing itself, and thus these signals are

likely to be observed in the near future.} In this work, we investigate the

potential applicability of these distortions in helping identify Type-II

signals from a single detection and the systematic biases that could arise in

the inference of parameters if they are recovered with gravitational-wave

templates that do not take the distortion into account. We show that the

lensing distortions will allow us to confidently identify the Type-II images

for highly inclined binaries: at network signal-to-noise ratio (SNR)

$\rho=20(50)$, individual Type-II images should be identifiable with ln Bayes

factor $\ln \mathcal{B} > 2$ for inclinations $ \iota > 5 \pi/12 (\pi/3) $.

Furthermore, based on the trends we observe in these results, we predict that,

at high SNRs ($\gtrsim 100$), individual Type-II images would be identifiable

even when the inclination angle is much lower ($\sim \pi/6$). We then show that

neglecting physical effects arising from these identifiable Type-II images can

significantly bias the estimates of source parameters. Thus, in the future,

using templates that take into account the lensing deformation would be

necessary to extract source parameters from Type-II lensed signals.

images, denoted as Type-I, Type-II and Type-III, corresponding to the minima,

saddle and maxima of the lensing potential of the lensed images. Type-II

images, in particular, receive a non-trivial phase shift of $\pi/2$. This phase

shift can introduce additional distortions in the strains produced by the

Type-II image of the binary black hole signals depending on the morphology of

the signals, e.g., when they have contributions from higher harmonics,

precession, eccentricity, etc. {The probability of observing Type-II images is

nearly the same as that of strong lensing itself, and thus these signals are

likely to be observed in the near future.} In this work, we investigate the

potential applicability of these distortions in helping identify Type-II

signals from a single detection and the systematic biases that could arise in

the inference of parameters if they are recovered with gravitational-wave

templates that do not take the distortion into account. We show that the

lensing distortions will allow us to confidently identify the Type-II images

for highly inclined binaries: at network signal-to-noise ratio (SNR)

$\rho=20(50)$, individual Type-II images should be identifiable with ln Bayes

factor $\ln \mathcal{B} > 2$ for inclinations $ \iota > 5 \pi/12 (\pi/3) $.

Furthermore, based on the trends we observe in these results, we predict that,

at high SNRs ($\gtrsim 100$), individual Type-II images would be identifiable

even when the inclination angle is much lower ($\sim \pi/6$). We then show that

neglecting physical effects arising from these identifiable Type-II images can

significantly bias the estimates of source parameters. Thus, in the future,

using templates that take into account the lensing deformation would be

necessary to extract source parameters from Type-II lensed signals.