STARRY: Analytic Occultation Light Curves

TL;DR

STARRY provides fast, accurate analytic solutions for modeling occultation light curves of celestial bodies using spherical harmonics, enabling efficient inference of surface maps and properties.

Contribution

This work introduces a novel analytic formalism and an open-source software package for computing and differentiating occultation light curves with high speed and precision.

Findings

Algorithm is six orders of magnitude faster than numerical methods

Provides analytic derivatives for efficient parameter inference

Applicable to various astronomical transit and occultation scenarios

Abstract

We derive analytic, closed form, numerically stable solutions for the total flux received from a spherical planet, moon or star during an occultation if the specific intensity map of the body is expressed as a sum of spherical harmonics. Our expressions are valid to arbitrary degree and may be computed recursively for speed. The formalism we develop here applies to the computation of stellar transit light curves, planetary secondary eclipse light curves, and planet-planet/planet-moon occultation light curves, as well as thermal (rotational) phase curves. In this paper we also introduce STARRY, an open-source package written in C++ and wrapped in Python that computes these light curves. The algorithm in STARRY is six orders of magnitude faster than direct numerical integration and several orders of magnitude more precise. STARRY also computes analytic derivatives of the light curves with respect to all input parameters for use in gradient-based optimization and inference, such as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit observed light curves to infer properties of a celestial body's surface map.