# Analytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons

@article{Luger2022AnalyticLC, title={Analytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons}, author={Rodrigo Luger and Eric Agol and Fran Bartoli'c and Daniel Foreman-Mackey}, journal={The Astronomical Journal}, year={2022}, volume={164} }

We derive efficient, closed-form, differentiable, and numerically stable solutions for the flux measured from a spherical planet or moon seen in reflected light, either in or out of occultation. Our expressions apply to the computation of scattered light phase curves of exoplanets, secondary eclipse light) curves in the optical, or future measurements of planet–moon and planet–planet occultations, as well as to photometry of solar system bodies. We derive our solutions for Lambertian bodies…

## References

SHOWING 1-10 OF 69 REFERENCES

starry: Analytic Occultation Light Curves

- Physics, Geology
- 2019

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…

Analytic reflected light curves for exoplanets

- Geology, Physics
- 2018

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 Planetary Transit Light Curves and Derivatives for Stars with Polynomial Limb Darkening

- PhysicsThe Astronomical Journal
- 2020

We derive analytic, closed-form solutions for the light curve of a planet transiting a star with a limb-darkening profile that is a polynomial function of the stellar elevation, up to an arbitrary…

Resolving the Surfaces of Extrasolar Planets with Secondary Eclipse Light Curves

- Physics, Geology
- 2006

We present a method that employs the secondary eclipse light curves of transiting extrasolar planets to probe the spatial variation of their thermal emission. This technique permits an observer to…

Closed-form ab initio solutions of geometric albedos and reflected light phase curves of exoplanets

- Geology, PhysicsNature Astronomy
- 2021

Studying the albedos of the planets and moons of the Solar System dates back at least a century [1, 2, 3, 4]. Of particular interest is the relationship between the albedo measured at superior…

Mapping Stellar Surfaces. I. Degeneracies in the Rotational Light-curve Problem

- Physics, GeologyThe Astronomical Journal
- 2021

Thanks to missions like Kepler and TESS, we now have access to tens of thousands of high-precision, fast-cadence, and long-baseline stellar photometric observations. In principle, these light curves…

Analytic Light Curves for Planetary Transit Searches

- Physics, Geology
- 2002

We present exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening. In the limit that the planet radius is less than a tenth of the stellar radius, we…

Inferring planetary obliquity using rotational and orbital photometry

- Physics, Geology
- 2016

The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over…

exocartographer: A Bayesian Framework for Mapping Exoplanets in Reflected Light

- Geology, PhysicsThe Astronomical Journal
- 2018

Future space telescopes will directly image extrasolar planets at visible wavelengths. Time-resolved reflected light from an exoplanet encodes information about atmospheric and surface…

A More Informative Map: Inverting Thermal Orbital Phase and Eclipse Light Curves of Exoplanets

- Physics, GeologyThe Astronomical Journal
- 2018

Only one exoplanet has so far been mapped in both longitude and latitude, but the James Webb Space Telescope should provide mapping-quality data for dozens of exoplanets. The thermal phase mapping…