Reducing the Impact of Weak-lensing Errors on Gravitational-wave Standard Sirens

TL;DR

This paper investigates the potential of using convergence maps from shear measurements to reduce weak-lensing errors in gravitational-wave standard sirens, finding limited practical benefits with current methods.

Contribution

It provides a quantitative assessment of delensing effectiveness for SMBHB standard sirens using numerical simulations, highlighting current limitations.

Findings

Weak-lensing errors can be reduced by about a factor of two at high redshift.

Ultra-deep field observations are needed for effective delensing, which is costly.

Current delensing methods are unlikely to significantly improve cosmological parameter estimates.

Abstract

The mergers of supermassive black hole binaries (SMBHBs) can serve as standard sirens: the gravitational wave (GW) analog of standard candles. The upcoming space-borne GW detectors will be able to discover such systems and estimate their luminosity distances precisely. Unfortunately, weak gravitational lensing can induce significant errors in the measured distance of these standard sirens at high redshift, severely limiting their usefulness as precise distance probes. The uncertainty due to weak lensing can be reduced if the lensing magnification of the siren can be estimated independently, a procedure called 'delensing'. With the help of up-to-date numerical simulations, here we investigate how much the weak-lensing errors can be reduced using convergence maps reconstructed from shear measurements. We also evaluate the impact of delensing on cosmological parameter estimation with bright standard sirens. We find that the weak-lensing errors for sirens at $z_s = 2.9$ can be reduced by about a factor of two on average, but to achieve this would require expensive ultra-deep field observations for every siren. Such an approach is likely to be practical in only limited cases, and the reduction in the weak-lensing error is therefore likely to be insufficient to significantly improve the cosmological parameter estimation. We conclude that performing delensing corrections is unlikely to be worthwhile, in contrast to the more positive expectations presented in previous studies. For delensing to become more practicable and useful in the future will require significant improvements in the resolution/depth of weak-lensing surveys and/or the methods to reconstruct convergence maps from these surveys.