Speeding up low-mass planetary microlensing simulations and modeling: The caustic region of influence

Extensive simulations of planetary microlensing are necessary both before and after a survey is conducted: before to design and optimize the survey and after to understand its detection efficiency. The major bottleneck in such computations is the computation of light curves. However, for low-mass planets, most of these computations are wasteful, as most light curves do not contain detectable planetary signatures. In this paper, I develop a parameterization of the binary microlens that is conducive to avoiding light curve computations. I empirically find analytic expressions describing the limits of the parameter space that contain the vast majority of low-mass planet detections. Through a large-scale simulation, I measure the (in)completeness of the parameterization and the speed-up it is possible to achieve. For Earth-mass planets in a wide range of orbits, it is possible to speed up simulations by a factor of ∼30-125 (depending on the survey's annual duty-cycle) at the cost of missing ∼1% of detections (which is actually a smaller loss than for the arbitrary parameter limits typically applied in microlensing simulations). The benefits of the parameterization probably outweigh the costs for planets below 100 M_⊕. For planets at the sensitivity limit of AFTA-WFIRST, simulation speed-ups of a factor ∼1000 or more are possible.