Scatter

As we saw before, It's possible to reconstruct kappa_hilbert fairly well.

But what happens if I introduce a scatter to the Halo mass and Halo concentrations?

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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.

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Adding a scatter to the halo mass is a much larger effect; it changes the smooth component from a single number to a distribution:

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. Below are kappa_reconstruct histograms as a function of error on log(M_halo) (in dex)