Analytic Reflected Lightcurves for Exoplanets

TL;DR

This paper derives analytic models for the reflected lightcurves of exoplanets with arbitrary orbits, spin, and obliquity, using harmonic maps and Wigner D-matrices, facilitating faster exoplanet mapping.

Contribution

It extends previous models to general orbital and rotational configurations and introduces EARL, an open-source tool for rapid lightcurve computation.

Findings

Analytic solutions for inclined, non-synchronously rotating exoplanets.

Use of Wigner D-matrices to relate different viewing geometries.

Open-source code for fast lightcurve calculations.

Abstract

The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this paper, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points ($\delta$-maps), and spherical harmonics ($Y_l^m$-maps). In particular, we use Wigner $D$-matrices to express an harmonic lightcurve for an arbitrary viewing geometry as a non-linear combination of harmonic lightcurves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected lightcurves, as well as fast calculation of lightcurves for mapping exoplanets based on time-resolved photometry. To these ends we make available Exoplanet Analytic Reflected Lightcurves (EARL), a simple open-source code that allows rapid computation of reflected lightcurves.