# The degeneracy between microlensing wave effect and precession in strongly lensed gravitational wave

## TL;DR

This paper investigates the degeneracy between microlensing effects caused by stellar fields in strong gravitational lensing and intrinsic spin precession in gravitational waves, assessing how microlensing can mimic precession signals and affect parameter estimation.

## Contribution

It provides a quantitative analysis of the degeneracy between stellar-field microlensing and spin precession in strongly lensed gravitational waves, highlighting conditions under which microlensing can produce false precession evidence.

## Key findings

- Microlensing-induced false precession evidence is generally weak at current sensitivities.
- Highly magnified events show a high likelihood (72%) of significant precession evidence due to microlensing.
- A positive correlation exists between microlensing strength and precession evidence, especially in Type II SLGWs.

## Abstract

Microlensing induced by the stellar field within a strong lensing galaxy can introduce fluctuations in the waveforms of strongly-lensed gravitational waves. When fitting these signals with templates that do not account for microlensing,possible degeneracies can lead to false evidence of certain intrinsic parameters,resulting in a misinterpretation of the properties of the underlying system. For example,the wave effect of microlensing may mimic spin precessions,as both effects generically induce periodic waveform modulations. Although previous studies suggest that lensing-induced modulations can be distinguished from precession using parameter estimation under a geometric-optic approximation,it does not directly apply for lensed image through stellar fields due to large number of stars involved an wave-optic effects. This study aims to evaluate the degree of degeneracy between the stellar-field microlensing and spin precession,investigating whether microlensing leads false evidence of precession. In other words,to what extent observed SLGWs are identified with false evidence of precession. The main findings are as follows. First,assuming O5 sensitivity and parallel spins for the underlying binary black holes,microlensing-induced false evidence of precession is generally weak(15% of the events show significant evidence,30% if the signal-to-noise ratio doubles). Second,for highly magnified events,about 72% of the population show significant evidence of precession,which could serve as an identification criterion for microlensing. This implies the possibility of strong lensing for the recent event GW231123,which is in the mass gap and also shows evidence of precession. Finally,a moderate to strong positive correlation exists between microlensing strength and precession evidence,more pronounced in Type II SLGWs.