Fast Computational Convolution Methods for Extended Source Effects in Microlensing Light Curves

• Published in: The Astrophysical journal Vol. 880; no. 2; pp. 152 - 164
• Main Authors: Witt, Hans J., Atrio-Barandela, F.
• Format: Journal Article
• Language: English
• Published: Philadelphia The American Astronomical Society 01-08-2019; IOP Publishing
• Subjects: Algorithms; Astrophysics; Convolution; Darkening; Differential equations; Elliptic functions; Exact solutions; Gravitational lenses; gravitational lensing: micro; gravitational lensing: strong; Light curve; Limb darkening; Microlenses; Model testing; Quadratures; stars: fundamental parameters; Stellar models
• ISSN: 0004-637X; 1538-4357
• DOI: 10.3847/1538-4357/ab2a04

Extended source effects can be seen in gravitational lensing events when sources cross critical lines. Such events probe the stellar intensity profile and could be used to measure limb-darkening coefficients to test stellar model predictions. A database of accurately measured stellar profiles is needed to correctly subtract the stellar flux in planetary transient events. The amount of data that is being produced and that will be produced in current and future microlensing surveys, from both space and ground, requires algorithms that can quickly compute light curves for different source-lens configurations. Based on the convolution method, we describe a general formalism to compute those curves for single lenses. We develop approximations in terms of quadratures of elliptic integrals that we integrate by solving the associated first-order differential equations. We construct analytic solutions for a limb darkening and, for the first time, for a parabolic profile that are accurate at the ∼1%-3% and 0.5% level, respectively. These solutions can be computed orders of magnitude faster than other integration routines. They can be implemented in pipelines processing large data sets to extract stellar parameters in real time.