Reduced shear correction for DeltaSigma model

[combet]

When we measure DeltaSigma from the data, we basically compute g*Sigma_c, where g is the reduced shear and not the shear gamma (g = gamma/(1-kappa)). However, the model definition of DeltaSigma is DeltaSigma = gamma*Sigma_c.

Far from the halo center, where kappa<<1, g = gamma and the DeltaSigma model (that we have currently in CLMM) that corresponds to gamma*Sigma_c is sufficient. However, when kappa starts to be "large" (R<~1 Mpc), kappa becomes sufficiently large that we need to account for it. In practice, this means multiplying DeltaSigma as defined in CLMM's theory modules by

(See McClintock (2019))

Below the the difference between the two for a 1e15 Msun cluster at z=0.5 and a source at z=2.

We should provide a function that implements the correction.

[hsinfan1996]

Does that mean users need to provide z_src to compute Sigma_c in the correction factor?

[combet]

Yes, this becomes dependent on the source redshift (either individual or distribution).