Period Ratio Sculpting near Secondorder Meanmotion Resonances
Abstract
Secondorder meanmotion resonances lead to an interesting phenomenon in the sculpting of the periodratio distribution, due to their shape and width in periodratio/eccentricity space. As the osculating periods librate in resonance, the timeaveraged period ratio approaches the exact commensurability. The width of secondorder resonances increases with increasing eccentricity, and thus more eccentric systems have a stronger peak at commensurability when averaged over sufficient time. The libration period is short enough that this timeaveraging behavior is expected to appear on the timescale of the Kepler mission. Using Nbody integrations of simulated planet pairs near the 5:3 and 3:1 meanmotion resonances, we investigate the eccentricity distribution consistent with the planet pairs observed by Kepler. This analysis, an approach independent from previous studies, shows no statistically significant peak at the 3:1 resonance and a small peak at the 5:3 resonance, placing an upper limit on the Rayleigh scale parameter, σ, of the eccentricity of the observed Kepler planets at σ = 0.245 (3:1) and σ = 0.095 (5:3) at 95% confidence, consistent with previous results from other methods.
 Publication:

The Astronomical Journal
 Pub Date:
 January 2022
 DOI:
 10.3847/15383881/ac2f46
 arXiv:
 arXiv:2110.06317
 Bibcode:
 2022AJ....163...13B
 Keywords:

 211;
 1695;
 1083;
 484;
 490;
 1181;
 1177;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 Accepted for publication in AJ