Efficient Geometric Probabilities of MultiTransiting Exoplanetary Systems from CORBITS
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, semianalytical algorithm called the Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems (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. 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 three 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 multitransiting planet candidates, which results in shifting these distributions toward slightly larger values. In an Appendix, we present additional semianalytical methods for determining the frequency of exoplanet mutual events, I.e., the geometric probability that two planets will transit each other (planetplanet 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 2016
 DOI:
 10.3847/0004637X/821/1/47
 arXiv:
 arXiv:1602.07014
 Bibcode:
 2016ApJ...821...47B
 Keywords:

 celestial mechanics;
 methods: analytical;
 methods: numerical;
 occultations;
 planetary systems;
 planets and satellites: detection;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 15 pages, 7 figures, accepted by the Astrophysical Journal