Eclipses by exomoons

Abstract

The aim of this research is to study a method to find exomoons and to find specific characteristics that point to the existence of exomoons. Exomoons are natural satellites orbiting an extrasolar (exo)planet in an extrasolar system. By looking at eclipses on exoplanets, we can find these characteristics.
We consider the reflected light signals of exoplanets with an exomoon. The reflected light signal is the intensity of light the planet reflects from the host star towards the observer.
We derive the reflected light signal in a planetary system with one exoplanet and in a system with an exoplanet and an exomoon. We made the assumptions that the exoplanets and exomoons have
a homogeneous surface (albedo is 1) and move in circular orbits around a star with an inclination angle between the orbital planes. Along the orbit the planet and the moon have changing phases. The moon is always close to its planet, so the phases of the exomoon and the exoplanet are the
same. For exoplanets, it is not possible to spatially separate a moon from its planet. One only sees the total signal of both bodies, the light originating from the star, reflected by the two bodies towards the observer.
Maybe we can find an exomoon by examining eclipses. Eclipses occur when the exoplanet and exomoon are aligned with the star, so that the body closest to the star blocks the light towards the
body farthest from the star. Finding eclipses is one of the few methods to discover exomoons. The systems are modeled with the assumption that any total eclipse happens every time r = R or −r = R, we see short dips in the reflected light signal. These dips are periodic and make the complete signal quasi-periodic. That is why we also calculate the Fourier transform of the reflected light signal. This quasi-periodicity causes the Fourier spectrum to have side bands that are repeated and are copies of themselves.
In this research, the orbit of the exomoon is tilted to see the effect of inclination in the reflected light signal. The result is fewer eclipses. At most twice a year for a short amount of time an eclipse
can occur. In the Fourier domain, this results in more peaks, but the pattern is still repeated.
From this research, we cannot conclude whether or not an exomoon is present from measured data.
What we learned, is that if an exomoon is present, short dips in the received light signal occur and this results in periodic side bands in the Fourier domain with respect to the system of one planet.
The duration of an eclipse is very short, so the detection of the eclipse can easily be missed. The Fourier transform signal becomes stronger when a longer time has been measured.