(1)First of all, the definition of γ′ is unclear. Abstract and Introduction say ρtot ∝ r^−γ′ and an isothermal profile corresponds to γ′ = 2. However this is inconsistent with Eq. (4.3) in which γ′ = 1 reduces to an isothermal case. This is important because the interpretation of γout/γin shown e.g., Fig. 7 is different between γ′ = 2 and γ′ = 1 (as ∆γ′ = 0.02 translates into ∆(γout/γin) = 0.01 and 0.02, respectively).
Hi, Adri, is it a slip of the pen about Eq. (4.3)? or we can use the form of the elliptical power-law surface mass density,
\begin{equation}
\label{eq:kappa}
\kappa{epl} (\theta{1},\theta{2}) = \frac{3-\gamma'}{1+q{d}} \left(\frac{\theta{E}}{\sqrt{\theta{1}^2+\theta{2}^2/q{d}^2}}\right)^{\gamma'-1}
\end{equation}
where $q{d}$ is the axis ratio of the elliptical isodensity contours, $\theta{E}$ is the Einstein radius for the spherical-equivalent case.
Of course, in Matt's code, it uses a parameter named ’eta’ to describe the slope of the mass distribution. SIE is defined with eta = 1.
(1)First of all, the definition of γ′ is unclear. Abstract and Introduction say ρtot ∝ r^−γ′ and an isothermal profile corresponds to γ′ = 2. However this is inconsistent with Eq. (4.3) in which γ′ = 1 reduces to an isothermal case. This is important because the interpretation of γout/γin shown e.g., Fig. 7 is different between γ′ = 2 and γ′ = 1 (as ∆γ′ = 0.02 translates into ∆(γout/γin) = 0.01 and 0.02, respectively).
Hi, Adri, is it a slip of the pen about Eq. (4.3)? or we can use the form of the elliptical power-law surface mass density, \begin{equation} \label{eq:kappa} \kappa{epl} (\theta{1},\theta{2}) = \frac{3-\gamma'}{1+q{d}} \left(\frac{\theta{E}}{\sqrt{\theta{1}^2+\theta{2}^2/q{d}^2}}\right)^{\gamma'-1} \end{equation} where $q{d}$ is the axis ratio of the elliptical isodensity contours, $\theta{E}$ is the Einstein radius for the spherical-equivalent case.
Of course, in Matt's code, it uses a parameter named ’eta’ to describe the slope of the mass distribution. SIE is defined with eta = 1.