Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems from CORBITS

TL;DR

The paper introduces CORBITS, an efficient semi-analytical algorithm that accurately computes the geometric probabilities of multiple transiting exoplanets, improving speed and precision over previous methods, and applies it to Kepler data.

Contribution

It presents CORBITS, a novel semi-analytical algorithm for calculating multi-transiting exoplanet probabilities, surpassing previous numerical approaches in accuracy and efficiency.

Findings

CORBITS is faster and more accurate than previous algorithms.

The solar system could show up to 3 transiting planets at once.

Kepler's multi-planet candidate distributions shift to larger values after correction.

Abstract

NASA's Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called CORBITS which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere (see Ragozzine & Holman 2010). The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of 3 transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions towards slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (Planet-Planet Occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available at https://github.com/jbrakensiek/CORBITS