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

TL;DR

This paper establishes the conditions under which the linear approximation of the central caustic in planetary microlensing is valid, explaining the close/wide binary degeneracy and its implications for lensing feature degeneracies.

Contribution

It derives a precise condition for the validity of the linear caustic approximation and links it to the observed degeneracy in planetary microlensing.

Findings

Linear approximation valid if |1-s| >> q^{1/3}

Close/wide degeneracy explained via caustic invariance

Local degeneracies can persist near the approximation boundary

Abstract

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.