Orbital obliquity sampling in the Kepler-20 system using the 3D animation software Blender

TL;DR

This paper introduces a novel photometric method using Blender to analyze orbital obliquities in multi-planet systems, demonstrated on Kepler-20, providing new insights into planetary alignments without relying solely on traditional spectroscopic techniques.

Contribution

The study develops a new approach employing 3D animation software for simulating multi-transit light curves to infer orbital obliquities in systems where conventional methods are challenging.

Findings

Excluded some orbital geometries for Kepler-20 b and c.

Indicated planets tend to eclipse different stellar hemispheres.

Suggested planets have prograde orbital directions.

Abstract

The mutual orbital alignment in multiple planetary systems is an important parameter for understanding their formation. There are a number of elaborate techniques to determine the alignment parameters using photometric or spectroscopic data. Planet--planet occultations (PPOs), which can occur in multiple transiting systems, are one intuitive example. While the presence of PPOs constrains the orbital alignment, the absence at first glance does not. Planetary systems, for which the measurement of orbital obliquities with conventional techniques remains elusive, call for new methods whereby at least some information on the alignments can be obtained. Here we develop a method that uses photometric data to gain this kind of information from multi-transit events. In our approach we synthesize multi-transit light curves of the exoplanets in question via the construction of a grid of projected orbital tilt angles $\alpha$, while keeping all transit parameters constant. These model light curves contain PPOs for some values of $\alpha$. To compute the model light curves, we use the 3D animation software Blender for our transit simulations, which allows the use of arbitrary surface brightness distributions of the star, such as limb darkening from model atmospheres. The resulting model light curves are then compared to actual measurements. We present a detailed study of the multi-transiting planetary system Kepler-20, including parameter fits of the transiting planets and an analysis of the stellar activity. We apply our method to Kepler-20 b and c, where we are able to exclude some orbital geometries, and find a tendency of these planets to eclipse in front of different stellar hemispheres in a prograde direction. [...]