Fourier series for eclipses on exoplanet binaries

Abstract

A double planet system or planet binary undergoes eclipses that modify the reflective light curve. In the time domain, the eclipse events are fast and weak. This would make their signal difficult to find and recognize in the phase light curve, even for small inclinations when eclipses happen frequently. However, due to the quasiperiodic nature of the phenomenon, the Fourier transform of the direct reflection signal consists of a double sum of sharp peaks. These peaks can be resolved for large close binaries and sufficiently long observation times with a star coronagraph. Eclipses modulate the phase curve, having an orbital period $2\pi /\omega$, with a contribution from the relative motion in the binary plane of a period $2\pi /\Omega$. This leads to a spectral structure with basis frequencies $\omega$ and $\Omega$. We aim to characterize these spectra. We studied the regime of short eclipses that occur when the planet radii are small compared to the planet separation. We derived formulas for the peak amplitudes applicable to homogeneous (Lambertian) planet binaries in circular orbit with small inclination. The effects of an eclipse and of double reflection appear as first- and second-order contributions (in planet radius over separation) in the reflection signal respectively. Small peaks appear as observable side bands in the spectrum. Identical structures around $m\Omega$ are characteristic of short-duration eclipses. Deceasing side bands could indicate double reflection between companions. Fourier analysis of the light curve of non-transiting planets can be used to find planets and their moons. Difficulties in interpreting the structures arise for small planet separation and when there are several moons in mean-motion resonance.

arXiv comment12 pages, 10 figures

References in corpus (19)

• Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
• Identifying Exoplanets with Deep Learning: A Five Planet Resonant Chain around Kepler-80 and an Eighth Planet around Kepler-90
• Inverting Phase Functions to Map Exoplanets
• The changing phases of extrasolar planet CoRoT-1b
• The Vector Vortex Coronagraph: Laboratory Results and First Light at Palomar Observatory
• The HARPS search for southern extra-solar planets. XXVII. Up to seven planets orbiting HD 10180: probing the architecture of low-mass planetary systems
• N-body Simulations of Satellite Formation around Giant Planets: Origin of Orbital Configuration of the Galilean Moons
• Mapping Earth Analogs from Photometric Variability: Spin-Orbit Tomography for Planets in Inclined Orbits
• Detecting companions to extrasolar planets using mutual events
• Lightcurves of Stars & Exoplanets: Estimating Inclination, Obliquity, and Albedo
• The fate of moons of close-in giant exoplanets
• Extrasolar Binary Planets I: Formation by tidal capture during planet-planet scattering
• Predictable patterns in planetary transit timing variations and transit duration variations due to exomoons
• An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions
• Extrasolar Binary Planets II: Detectability by Transit Observations
• Formation of Exomoons: A Solar System Perspective
• Decoupling Phase Variations in Multi-Planet Systems
• Fourier spectra from exoplanets with polar caps and ocean glint
• Project Blue: Visible Light Imaging Search for Terrestrial-class Exoplanets in the Habitable Zones of Alpha Centauri A and B