Paper detail

On the condition for the central caustic degeneracy of the planetary microlensing

It is shown that the linear approximation of the central caustic for the planetary ($q\ll1$) microlensing is valid if $|1-s|\gg q^{1/3}$ (where $q$ is the mass ratio and $s$ is the projected separation in the unit of the Einstein ring radius of the primary). The condition is also consistent with the requirement that the binary separation is far from those in the resonant binary regime resulting in a single six-cusp caustic. Given that the linear approximation of the caustic is invariant under $s\leftrightarrow s^{-1}$, the close/wide binary degeneracy observed under the same condition may be understood via the linear approximation of the central caustic. Finally it is argued that the local degeneracies of lensing features associated with caustic crossings can still persist in the planetary events even when $|1-s|\sim q^{1/3}$ although the overall caustic shape may not be degenerate at all.