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Fix use of approximation in shear profile #705

@m-aguena

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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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