Fourier spectra from exoplanets with polar caps and ocean glint

TL;DR

This paper explores how Fourier analysis of reflected light curves from exoplanets with polar caps and ocean glint can reveal surface features, providing a new approach to studying exoplanet surfaces.

Contribution

It derives a general expression for Fourier coefficients of quasiperiodic light curves based on planetary surface albedo maps, offering analytical tools for surface feature detection.

Findings

Fourier spectra depend on planetary inclination, obliquity, and cap size.

Sharp edges of ice caps and ocean glint produce recognizable spectral peaks.

Analytic expressions enable interpretation of light curve features in the Fourier domain.

Abstract

The weak orbital-phase dependent reflection signal of an exoplanet contains information on the planet surface, such as the distribution of continents and oceans on terrestrial planets. This light curve is usually studied in the time domain, but because the signal from a stationary surface is (quasi)periodic, analysis of the Fourier series may provide an alternative, complementary approach. We study Fourier spectra from reflected light curves for geometrically simple configurations. Depending on its atmospheric properties, a rotating planet in the habitable zone could have circular polar ice caps. Tidally locked planets, on the other hand, may have symmetric circular oceans facing the star. These cases are interesting because the high-albedo contrast at the sharp edges of the ice-sheets and the glint from the host star in the ocean may produce recognizable light curves with orbital periodicity, which could also be interpreted in the Fourier domain. We derive a simple general expression for the Fourier coefficients of a quasiperiodic light curve in terms of the albedo map of a Lambertian planet surface. Analytic expressions for light curves and their spectra are calculated for idealized situations, and dependence of spectral peaks on the key parameters inclination, obliquity, and cap size is studied.