Analytic Reflected Lightcurves for Exoplanets

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.

8 pages, plus 6 pages of mathematical appendices, 4 figures, to be submitted

References in corpus (9)

• 55 Cancri (Copernicus): A Multi-Planet System with a Hot Super-Earth and a Jupiter Analogue
• Alien Maps of an Ocean-Bearing World
• Inverting Phase Functions to Map Exoplanets
• Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars
• Identifying the rotation rate and the presence of dynamic weather on extrasolar Earth-like planets from photometric observations
• Global Mapping of Earth-like Exoplanets from Scattered Light Curves
• Detection of a Westward Hotspot Offset in the Atmosphere of a Hot Gas Giant CoRoT-2b
• Rotational Spectral Unmixing of Exoplanets: Degeneracies between Surface Colors and Geography
• Odd Harmonics in Exoplanet Photometry: Weather or Artifact?

Cited by in corpus (9)

• STARRY: Analytic Occultation Light Curves
• Using Deep Space Climate Observatory Measurements to Study the Earth as An Exoplanet
• A More Informative Map: Inverting Thermal Orbital Phase and Eclipse Lightcurves of Exoplanets
• exocartographer: A Bayesian Framework for Mapping Exoplanets in Reflected Light
• The Dark World: A Tale of WASP-43b in Reflected Light with HST WFC3/UVIS
• Global Mapping of the Surface Composition on an Exo-Earth using Color Variability
• Analytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons
• Modeling photometric variations due to a global inhomogeneity on an obliquely rotating star: application to lightcurves of white dwarfs
• Analytic model for photometric variation due to starspots on a differentially rotating star