2011/06/27 by Scott Tremaine, Subo Dong · 177 citations
Physics and Astronomy · #Astronomy and Astrophysical Research #Exoplanet #Kepler #Multiplicity (mathematics) #Observable #Planet #Planetary system #Scientific Research and Discoveries #Stars #Stellar, planetary, and galactic studies #Transit (satellite) #astro-ph.EP
paper · pdf · doi:10.1088/0004-6256/143/4/94
published in The Astronomical Journal 143(4), 94 (Institute of Physics) · 34 pages, 10 figures
arxiv created 2011/06/27 · openalex publication_date 2012/03/15 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We describe statistical methods for measuring the exoplanet multiplicity function (the fraction of host stars containing a given number of planets) and inclination distribution from transit and radial-velocity (RV) surveys. The analysis is based on the approximation of separability—that the distribution of planetary parameters in an n -planet system is the product of identical 1-planet distributions. We review the evidence that separability is a valid approximation for exoplanets and conclude that it captures many, but not all, of the known characteristics of multi-planet systems. We show how to relate the observable multiplicity function in surveys with similar host-star populations but different sensitivities. We also show how to correct for geometrical selection effects to derive the multiplicity function from transit surveys if the distribution of relative inclinations is known. Applying these tools to the Kepler transit survey and to RV surveys, we find that (1) the Kepler data alone do not constrain the mean inclination of multi-planet systems; even spherical distributions are allowed by the data but only if a small fraction of host stars contain large planet populations (≳ 30); (2) comparing the Kepler and RV surveys shows that the mean inclination of multi-planet systems is less than 5°; and (3) the multiplicity function of the Kepler planets is not well determined by the present data.