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Gravitational lensing induces significant errors in the measured distances to high‐redshift standard candles and standard sirens such as Type Ia supernovae, gamma‐ray bursts and merging supermassive black hole binaries. There will therefore be a significant benefit from correcting for the lensing error by using independent and accurate estimates of the lensing magnification. Here, we investigate how accurately the magnification can be inferred from convergence maps reconstructed from galaxy shear and flexion data. We employ ray‐tracing through the Millennium Simulation (MS) to simulate lensing observations in large fields, and perform a weak‐lensing reconstruction on the simulated fields. We identify optimal ways to filter the reconstructed convergence maps and to convert them to magnification maps, and analyse the resulting relation between the estimated and true magnification for sources at redshifts   z  S = 1  to 5. We find that a deep shear survey with 100 galaxies arcmin  −2   can help to reduce the lensing‐induced distance errors for standard candles/sirens at redshifts   z  S ≈ 1.5  (  z  S ≈ 5 ) on average by  20  per cent ( 10  per cent), whereas a futuristic survey with shear and flexion estimates from 500 galaxies arcmin  −2   yields much larger reductions of 50 per cent (35 per cent). For redshifts   z  S ≥ 3 , a further improvement by  ∼ 5 per cent can be achieved, if the individual redshifts of the galaxies are used in the reconstruction. Moreover, the reconstruction allows one to identify regions for which the convergence is low, and in which an error reduction by up to  75  per cent can be achieved. Such strongly reduced magnification uncertainties will greatly improve the value of high‐redshift standard candles/sirens as cosmological probes.

Reducing distance errors for standard candles and standard sirens with weak‐lensing shear and flexion maps