Statistical Distributions of Orbital Resonances in Multi Exoplanet Systems

Statistical distributions of mean motion resonances and near-resonances in multiplanetary systems

Authors:

Ghilea et al

Abstract:

The orbits of the confirmed exoplanets from all multiple systems known to date are investigated. Observational data from 1822 objects, of which 1144 are part of multiplanetary systems, are compiled and analyzed. Mean motion resonances and near-resonances up to the forth order and up to the denominator 4 are tested for all adjacent exoplanet orbits. Each host star's "snow line" is calculated using a simple algorithm. The planets are reclassified into categories as a function of the semimajor axis size relative to the snow line location and the semimajor axis vs mass distribution. The fraction of planets in/near resonance is then plotted as a function of both resonance number and resonance order for all the exoplanet population and, separately, for each planet type. In the resonance number plot it appears that the 2/1 and 3/2 resonances and near-resonances are dominant overall, but the observed distribution changes significantly with each planet category, with terrestrial, neptune-type and mini-neptune planets showing the largest variation. In the order-based resonance/near-resonance plot, the observed distribution appears to follow an exponential decay for the general population, but varies widely again with the planet type, with terrestrial and neptune-type planets displaying the largest differences. Approximate methods to estimate resonance/near resonance distributions are also attempted for the systems with unknown planet mass or with unknown star and/or planet mass and compared with the distribution of the planets with all the parameters known. A separate study of the resonance/near resonance fraction distribution as a function of mass is also attempted, but the low statistical data at very high planetary masses prevent the finding of an accurate equation to describe such a dependency.