Scatter
As we saw before, It's possible to reconstruct kappa_hilbert fairly well.
Stefan has told us that his scheme for combining kappas is simply to add them, (neglecting any knowledge of strong lensing). I use this method for combining kappas in the following plots, but it seems that how we combine kappas produces only a small effect.
Fig 1. Reconstructing kappa for each halo and summing them. This seems to be no better or worse at recovering kappa_hilbert compared to kappa_keeton. It seems we can't beat the ~0.25 error on kappa_reconstruction - kappa_hilbert and it seems that the difference doesn't come from our method of summing kappas.
How much worse do we do if we introduce a scatter to the Halo mass and Halo concentrations?
Adding a scatter to the halo concentration relation is effectively irrelevant - this is understandable, since we aren't reconstructing from concentration_truth, but from the best fit halo Mass-concentration relationship of Neto et al.
Adding a scatter to the halo mass is a much larger effect; it changes the smooth component from a single number to a distribution:
Fig 2. The smooth component correction as a function of error on M_Halo
At 0.3 dex error on log(M_halo), the scatter on the smooth component is ~the reconstruction error on kappa_reconstruct-kappa_hilbert. (These errors should add in quadrature).
Of course, adding a scatter to halo masses also introduces an error on the kappa_reconstruct too. More on that to follow.
Reconstructing M_Halo from M_stellar:
Fig 3. The star formation efficiency derived from Stefan's catalogue. The M✳-Mhalo relation looks wrong (at least for low mass halos).
So how can we infer what the true M✳-Mhalo errors will be? Behroozi et al. Gives an M✳-M_halo relation inferred from abundance matching. I've inverted Behroozi et al.'s relation to generate M✳ from M_Halo (with a scatter of 0.15 dex on the final M✳ - as given by Behroozi et al.), and then I use Behroozi et al.'s relation to go back to the M_halo.
Fig 4. The reconstructed kappa distribution, derived from reconstructing M✳ using the true M_Halo and Behroozi relation and then reconstructing M_Halo.
Fig 5. As Fig 4, but adding a 0.15 dex scatter to observed stellar mass. (The observed stellar mass will also have some scatter from the true stellar mass, hence the additional 0.15dex scatter.) This gives a total M✳ scatter of 0.15 dex from the Behroozi relation, and 0.15 dex from observations (add in quadrature).