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Fix use of approximation in shear profile #705

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@m-aguena

Currently, we have implemented in reduced shear:

  • order1:
    $\Large g_t=\frac{\langle\beta_s\rangle\gamma_\infty}{1-\langle\beta_s\rangle\kappa_\infty}$,
    from Hoekstra et al 1998 (Eq. 5)
  • order2:
    $\Large g_t=\frac{\langle\beta_s\rangle\gamma_\infty}{1-\langle\beta_s\rangle\kappa\infty}\left[1+\left(\frac{\langle\beta_s^2\rangle}{\langle\beta_s\rangle^2}-1\right)\langle\beta_s\rangle\kappa_\infty\right]$,
    from Hoekstra et al 1998 (Eq. 7) and Schrabback1 et al 2017 (Eq. 12)

I suggest renaming this order1 with order0, and making a new order1:

$\Large g_t=\frac{\langle\beta_s\rangle\gamma_\infty}{1-\frac{\langle\beta_s^2\rangle}{\langle\beta_s\rangle}\kappa_\infty}$,
from Seitz & Schneider et al 1997 (Eq. A2.4) and Applegate et al 2014 (Eq. 6)

That is the equation that was implemented in v1.0 but I think it accidentally got overwritte.

Note

In the future, we can also implement a new approach:
$\Large g_t=\frac{1-\frac{\langle\beta_s^3\rangle}{\langle\beta_s^2\rangle}\kappa_\infty+\frac{\langle\beta_s^2\rangle}{\langle\beta_s\rangle}\kappa_\infty}{1-\frac{\langle\beta_s^3\rangle}{\langle\beta_s^2\rangle}\kappa_\infty}\langle\beta_s\rangle\gamma_\infty$,
from Seitz & Schneider et al 1997 (Eq. A2.5)

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  1. hsinfan1996 commented on Apr 10, 2026

    @hsinfan1996
    Collaborator

    It was dropped because 'order2' took the result directly from 'order1'. And yes, the calculation is actually Applegate et al 2014 Eq. 1, so we still need to add the Eq. 6 in the paper.

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