On the perturbative picture and the Chang–Refsdal lens approximation for planetary microlensing

Under the perturbative picture of planetary microlensing, planet is considered to act as a uniform-shear Chang-Refsdal lens on one two images produced by host star that comes close angular Einstein radius planet, leaving other image unaffected. However, this approximation only valid for isolated caustics and breaks down in resonant regime. Recently, planetary-caustic degeneracy arising from above formalism found generalize regime central caustics, indicating may have been under-explored past. Here, I introduce new variable-shear approximation, which not supports but also enables full magnification maps be calculated analytically. Moreover, generalized picture, relaxes required proximity between being perturbed previous work. Specifically, always perturbs same half plane itself, largely It demonstrated how framework results offset consequence physical symmetry. The points an approach solve two-body equation semi-analytically. analytic semi-analytic microlensing solutions associated with work allow substantially faster light-curve calculations modeling observed events. A python implementation provided.