Hexadecapole Approximation in Planetary Microlensing

TL;DR

This paper introduces a hexadecapole approximation method that significantly speeds up the modeling of planetary microlensing events, especially in high-magnification cases, enabling more efficient analysis of complex events.

Contribution

The paper presents a simple, fast hexadecapole approximation that reduces computational time for microlensing modeling and allows the application of magnification-map techniques to dynamic planetary events.

Findings

Hexadecapole approximation speeds up modeling by up to several orders of magnitude.

The method accurately models regions away from caustics and cusps.

Enables application of magnification-map approach to events with planetary orbital motion.

Abstract

The frequency of microlensing planet detections, particularly in difficult-to-model high-magnification events, is increasing. Their analysis can require tens of thousands of processor hours or more, primarily because of the high density and high precision of measurements whose modeling requires time-consuming finite-source calculations. I show that a large fraction of these measurements, those that lie at least one source diameter from a caustic or the extension from a cusp, can be modeled using a very simple hexadecapole approximation, which is one to several orders of magnitude faster than full-fledged finite-source calculations. Moreover, by restricting the regions that actually require finite-source calculations to a few isolated `caustic features', the hexadecapole approximation will, for the first time, permit the powerful `magnification-map' approach to be applied to events for which the planet's orbital motion is important.