Differences in kappa scheme

It's important to use the correct scheme for combining kappas from different redshifts. When you choose a biased sample of lines of sight the result from the Keeton scheme varies significantly from the additive scheme. It's important that we use an approximation that is good enough for our purpose: 1% accuracy on time delay distances.

Fig 1. Reconstructions of (top) kappa_add and (middle) kappa_keeton compared with (bottom) Stefan's ray-traced kappa. This is shown for 1000 lines of sight that have between 80 and 87 (inclusive) galaxies within 45 arcseconds that have [i+z]/2 magnitudes between 18.5 and 24.5. This roughly corresponds to <N_45>*[2.0+/-0.1].

Fig 2. As figure one but shown for 1000 lines of sight that have between 38 and 45 (inclusive) galaxies within 45 arcseconds that have [i+z]/2 magnitudes between 18.5 and 24.5. This roughly corresponds to <N_45>*[1.0+/-0.1].