VBMicroLensing: Three algorithms for multiple lensing with contour integration

¹ Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, Via Giovanni Paolo 132, Fisciano 84084, Italy
² Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Via Cintia, Napoli 80126, Italy
³ Dipartimento di Fisica “Ettore Pancini”, Università di Napoli Federico II, Napoli, Italy
⁴ INAF – Osservatorio Astronomico di Capodimonte, Salita Moiariello 16 80131, Napoli, Italy
⁵ Department of Astronomy, Tsinghua University, Beijing 100084, China

^★ Corresponding author; valboz@sa.infn.it

Received: 17 October 2024
Accepted: 29 December 2024

Abstract

Context. Modeling of microlensing events poses computational challenges for the resolution of the lens equation and the high dimensionality of the parameter space. In particular, numerical noise represents a severe limitation to fast and efficient calculations of microlensing by multiple systems, which are of particular interest in exoplanetary searches.

Aims. We present a new public code built on our previous experience on binary lenses that introduces three new algorithms for the computation of magnification and astrometry in multiple microlensing.

Methods. In addition to the classical polynomial resolution, we introduce a multi-polynomial approach in which each root is calculated in a frame centered on the closest lens. In addition, we propose a new algorithm based on a modified Newton-Raphson method applied to the original lens equation without any numerical manipulation.

Results. These new algorithms are more accurate and robust compared to traditional single-polynomial approaches at a modest computational cost, opening the way to massive studies of multiple lenses. The new algorithms can be used in a complementary way to optimize efficiency and robustness.