Source Distributions of Cosmic Shear Surveys in Efficiency Space

We show that the lensing efficiency of cosmic shear generically has a simple shape, even in the case of a tomographic survey with badly behaved photometric redshifts. We argue that source distributions for cosmic shear can therefore be more effectively parametrised in ``efficiency space''. Using realistic simulations, we find that the true lensing efficiency of a current cosmic shear survey without disconnected outliers in the redshift distributions can be described to per cent accuracy with only two parameters, and the approach straightforwardly generalises to other parametric forms and surveys. The cosmic shear signal is thus largely insensitive to the details of the source distributions, and the features that matter can be summarised by a small number of suitable efficiency parameters. For the simulated survey, we show that prior knowledge at the 10% level, which is attainable e.g. from photometric redshifts, is enough to marginalise over the efficiency parameters without severely affecting the constraints on the cosmology parameters $\Omega_m$ and $\sigma_8$....