Detectability of strongly lensed gravitational waves using model-independent image parameters

Abstract

Strong gravitational lensing of gravitational waves (GWs) occurs when the GWs from a compact binary system travel near a massive object. The mismatch between a lensed signal and unlensed templates determines whether lensing can be identified in a particular GW event. For axisymmetric lens models, the lensed signal is traditionally calculated in terms of model-dependent lens parameters such as the lens mass $M_L$ and source position $y$. We propose that it is useful to parameterize this signal instead in terms of model-independent image parameters: the flux ratio $I$ and time delay $\Delta t_d$ between images. The functional dependence of the lensed signal on these image parameters is far simpler, facilitating data analysis for events with modest signal-to-noise ratios. In the geometrical-optics approximation, constraints on $I$ and $\Delta t_d$ can be inverted to constrain $M_L$ and $y$ for any lens model including the point mass (PM) and singular isothermal sphere (SIS) that we consider. We use our model-independent image parameters to determine the detectability of gravitational lensing in GW signals and find that for GW events with signal-to-noise ratios $\rho$ and total mass $M$, lensing should in principle be identifiable for flux ratios $I\gtrsim 2{\rho }^{-2}$ and time delays $\Delta t_d\gtrsim M^{-1}$.

11 pages, 8 figures, submitted to PRD

References in corpus (12)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• Probing Dark Low-mass Halos and Primordial Black Holes with Frequency-dependent Gravitational Lensing Dispersions of Gravitational Waves
• Testing the nature of gravitational-wave polarizations using strongly lensed signals
• The finite source size effect and the wave optics in gravitational lensing
• A fast and precise methodology to search for and analyse strongly lensed gravitational-wave events
• Constraining cosmological parameters in FLRW metric with lensed GW+EM signals
• Probing the nature of dark matter via gravitational waves lensed by small dark matter halos
• Strong lensing as a giant telescope to localize the host galaxy of gravitational wave event
• Gravelamps: Gravitational Wave Lensing Mass Profile Model Selection
• Improved statistic to identify strongly lensed gravitational wave events
• Direct measurement of the distribution of dark matter with strongly lensed gravitational waves

Cited by in corpus (6)

• Gravitational wave lensing as a probe of halo properties and dark matter
• Compact Binaries through a Lens: Silent vs. Detectable Microlensing for the LIGO-Virgo-KAGRA Gravitational Wave Observatories
• Parameter estimation of microlensed gravitational waves with Conditional Variational Autoencoders
• An interference-based method for the detection of strongly lensed gravitational waves
• Probing cosmic strings via gravitational-wave lensing
• Parameter inference of millilensed gravitational waves using neural spline flows