Fractal algorithm for multiple lens analyses

TL;DR

This paper introduces a fractal-based algorithm for analyzing complex multiple lens systems in microlensing, significantly improving computational efficiency and accuracy over previous methods, and applicable to exoplanet and quasar studies.

Contribution

A novel fractal algorithm that handles unlimited lenses without root finding, reducing errors and computation time in microlensing analysis.

Findings

Dramatic reduction in computation time compared to inverse-ray shooting.

No limit on the number of lenses in the analysis.

Flexible accuracy and speed adjustment in calculations.

Abstract

A microlensing exoplanet search is a unique method for finding planets orbiting distant stars. However, in the past, the method used to analyze microlensing data could not deal with complex lens systems. The number of lenses was limited three or less. Positions calculations of images and integration of them suffered from severe round-off errors because of singularities. We developed a new algorithm to calculate the light curves of multiple lens systems. In this algorithm, fractal-like consecutive self-similar division (SSD) is used to find sparse images. SSD is also useful for integrating images to efficiently obtain magnifications. The new algorithm does not use root finding for the lens equation and is free from caustic singularities. There is no limit on the number of lenses. Compared to inverse-ray shooting, this method dramatically improves the computing time. The calculation can be adjusted to obtain either a high-precision final result or high-speed quick result. Although this new algorithm was developed for a microlensing planet search, its application to quasar microlensing is also expected. This paper discusses problems in the modeling of a multiple lens system and then presents the new algorithm in detail.