Arguably the simplest lens model is a point mass (Schwarzschild) lens, which is described by two parameters, namely, mass ($M$) and source position ($y$). The $(\psi, \hat{\alpha}, \kappa)$ for a point mass lens are given as,
\[\begin{align*} \psi(\theta) &= \theta_E^2 \ln(\theta), \\ \hat{\alpha}(\theta) &= \frac{\theta_E^2}{\theta}, \\ \kappa(\theta) &= \frac{M}{\Sigma_{\rm cr}} \delta(\theta), \end{align*}\]
where $\theta_E$ is the Einstein angle, which is given as,
\[\begin{equation*} \theta_E = \sqrt{\frac{4{\rm G}M}{\rm c^2} \frac{D_{ds}}{D_d D_s}}. \end{equation*}\]
LensFactory.Lenses.init_PointLens — Type
init_PointLens(D_d::RV=NaN, x_c::RV=0.0, y_c::RV=0.0, mass::RV=NaN)Initialize a point lens with the given parameters.
LensFactory.Lenses.PointLens.potential! — Function
potential!(ψ::T, θx::T, θy::T, D_d::RV, θxc::RV, θyc::RV, mass::RV) where T <: RVpotential!(ψ::T, θx::T, θy::T, D_d::RV, θxc::RV, θyc::RV, mass::RV) where T <: ROALensFactory.Lenses.PointLens.deflection! — Function
deflection!(ψx::T, ψy::T, θx::T, θy::T, D_d::RV, θxc::RV, θyc::RV, mass::RV) where T <: RVdeflection!(ψx::T, ψy::T, θx::T, θy::T, D_d::RV, θxc::RV, θyc::RV, mass::RV) where T <: ROALensFactory.Lenses.PointLens.jacobian! — Function
jacobian!(ψxx::T, ψyy::T, ψxy::T, θx::T, θy::T, D_d::RV, θxc::RV, θyc::RV, mass::RV) where T <: RVjacobian!(ψxx::T, ψyy::T, ψxy::T, θx::T, θy::T, D_d::RV, θxc::RV, θyc::RV, mass::RV) where T <: ROALensFactory.Lenses.PointLens.einstein_angle — Function
einstein_angle(;D_d::Float64=NaN, D_ds::Float64=NaN, D_s::Float64=NaN, mass::Float64=NaN)