Delensing gravitational wave standard sirens with shear and flexion maps

Supermassive black hole binary (SMBHB) systems 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 could reduce distance errors by about 25–30 per cent for an SMBHB at z= 2. Including an additional wide shear map from a space survey telescope could reduce distance errors by nearly a factor of 2. Such improvement would make SMBHBs considerably more valuable as cosmological distance probes or as a fully independent check on existing probes.