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Abstract
Supermassive black hole binary systems (SMBHB) are standard sirens -- the gravitational
wave analogue of standard candles -- and if discovered by gravitational wave detectors,
they could be used as precise distance indicators. Unfortunately, gravitational lensing
will randomly magnify SMBHB signals, seriously degrading any distance measurements.
Using a weak lensing map of the SMBHB line of sight, we can estimate its magnification
and thereby remove some uncertainty in its distance, a procedure we call "delensing."
We find that delensing is significantly improved when galaxy shears are combined with
flexion measurements, which reduce small-scale noise in reconstructed magnification
maps. Under a Gaussian approximation, we estimate that delensing with a 2D mosaic
image from an Extremely Large Telescope (ELT) could reduce distance errors by about
30-40% for a SMBHB at z=2. Including an additional wide shear map from a space survey
telescope could reduce distance errors by 50%. Such improvement would make SMBHBs
considerably more valuable as cosmological distance probes or as a fully independent
check on existing probes.