Redshift and shear calibration: Impact on cosmic shear studies and survey design

The cosmological interpretation of weak lensing by large-scale structures requires knowledge of the redshift distribution of the source galaxies. Current lensing surveys are often calibrated using external redshift samples which span a significantly smaller sky area in comparison to the lensing survey, and are thus subject to sample variance. Some future lensing surveys are expected to be calibrated in the same way, in particular the fainter galaxy populations where the entire color coverage, and hence photometric redshift estimate, could be challenging to obtain. With N-body simulations, we study the impact of this sample variance on cosmic shear analysis and show that, to first approximation, it behaves like a shear calibration error 1 ± ϵ. Using the Hubble Deep Field as a redshift calibration survey could therefore be a problem for current lensing surveys. We discuss the impact of the redshift distribution sampling error and a shear calibration error on the design of future lensing surveys, and find that a lensing survey of area Θ square degrees and limiting magnitude mlim, has a minimum shear and redshift calibration accuracy requirements given by ϵ=ϵ010β(mlim-24.5)(Θ/200)-1/2. Above that limit, lensing surveys would not reach their full potential. Using the galaxy number counts from the Hubble Ultra-Deep Field, we find (ϵ0, β) = (0.015, −0.18) and (ϵ0, β) = (0.011, −0.23) for ground and space based surveys respectively. Lensing surveys with no or limited redshift information and/or poor shear calibration accuracy will loose their potential to analyse the cosmic shear signal in the sub-degree angular scales, and therefore complete photometric redshift coverage should be a top priority for future lensing surveys.