Speeding up low-mass planetary microlensing simulations and modelling: 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 lightcurves. However, for low-mass planets most of these computations are wasteful, as most lightcurves do not contain detectable planetary signatures. In this paper I develop a parameterization of the binary microlens that is conducive to avoiding lightcurve 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 ${\sim} 30$-$125$ (depending on the survey's annual duty-cycle) at the cost of missing ${\sim} 1$ percent 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 $100M_{\oplus}$. For planets at the sensitivity limit of AFTA-WFIRST, simulation speed-ups of a factor ${\sim} 1000$ or more are possible.