[Paper Review] Statistical distributions of mean motion resonances and near-resonances in multiplanetary systems

M. C. Ghilea|arXiv (Cornell University)|Oct 8, 2014

Stellar, planetary, and galactic studies3 references3 citations

TL;DR

This study analyzes mean motion resonances and near-resonances in 1176 exoplanets across 1890 objects in multiplanetary systems, using orbital period ratios up to 5/1 and denominators up to 4. It finds that 2:1 and 3:2 resonances dominate overall and among giant planets, while mini-Neptunes and terrestrial planets show peak resonance fractions at 5:3, with resonance distributions decaying exponentially by order and varying significantly by planet type.

ABSTRACT

The orbits of the confirmed exoplanets from all multiple systems known to date are investigated. Observational data from 1890 objects, of which 1176 are found in multiplanetary systems, are compiled and analyzed. Mean motion resonances and near-resonances up to the outer/inner orbital period ratio's value of 5 and 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 and for the giant planets, but the observed distribution profile changes significantly with each planet category, with terrestrial planets, neptunes and mini-neptunes showing the largest variation. Resonances/near resonances around the value 5/3 were dominant for mini neptunes and terrestrial planets. In the order-based resonance/near-resonance plot, the observed distribution appears to follow an exponential decay for the general population and its profile appears to be influenced by the planet type. 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.

Motivation & Objective

• To investigate the statistical distribution of mean motion resonances and near-resonances in confirmed multiplanetary exoplanet systems.
• To examine how resonance prevalence varies across different planet types (giant planets, Neptunes, terrestrial, mini-Neptunes, etc.)
• To assess the influence of planetary mass and semimajor axis relative to the host star's snow line on resonance occurrence.
• To develop and validate an approximate method for detecting resonances when mass or orbital parameters are unknown.
• To explore the dependence of resonance fraction on planetary mass, despite limited high-mass data.

Proposed method

• Compiled observational data from 1890 exoplanets, including 1176 in multiplanetary systems, from the Extrasolar Planet Encyclopedia and NASA Exoplanet Archive.
• Calculated each star’s snow line using a simple algorithm to classify planets by location relative to this boundary.
• Classified planets into types (e.g., terrestrial, mini-Neptune, Jupiter, etc.) based on mass, density, and semimajor axis.
• Tested for mean motion resonances and near-resonances using orbital period ratios up to 5/1 and denominator up to 4 for adjacent planet pairs.
• Applied a simplified resonance detection method and validated it against more sophisticated tools using published data.
• Plotted resonance fractions by resonance number (e.g., 2:1, 3:2) and resonance order, separately for each planet type and the full population.

Experimental results

Research questions

• RQ1 Which mean motion resonances (e.g., 2:1, 3:2, 5:3) are most prevalent in multiplanetary exoplanet systems?
• RQ2 How does the distribution of resonances and near-resonances vary across different planet types (e.g., terrestrial, mini-Neptune, giant planets)?
• RQ3 Does the resonance fraction exhibit a systematic dependence on planetary mass, and if so, what functional form does it follow?
• RQ4 How accurate is the simplified resonance detection method when key parameters (e.g., planet mass) are unknown?
• RQ5 Is there a detectable pattern in resonance distribution that correlates with the snow line or semimajor axis relative to it?

Key findings

• The 2:1 and 3:2 resonances and near-resonances are the most dominant resonance types across the entire exoplanet population and among giant planets.
• Terrestrial planets and mini-Neptunes show the highest variation in resonance distribution profiles, with a notable peak in resonance fraction at the 5:3 resonance.
• Resonance fractions decay approximately exponentially with increasing resonance order, and this trend is modulated by planet type.
• The simplified resonance detection method yields results sufficiently consistent with more complex methods, validating its use in large-scale statistical studies.
• The resonance fraction for planets with masses around 50 M_E peaks at approximately 0.75, decreasing to 0.45 at 200 M_E, then rising to 0.55–0.60 for masses up to 1500 M_E.
• Despite limited data at very high masses, the observed trend suggests a non-monotonic dependence of resonance fraction on planetary mass.